| 1 | (function(window,factory){if(typeof exports==="object"){module.exports=factory()}else if(typeof define==="function"&&define.amd){define(factory)}else{window.jStat=factory()}})(this,function(){var jStat=function(Math,undefined){console.warn("The npm package jStat is no longer maintained. Instead use jstat (lowercase).");console.warn("Visit https://www.npmjs.com/package/jstat for more information.");var concat=Array.prototype.concat;var slice=Array.prototype.slice;var toString=Object.prototype.toString;function calcRdx(n,m){var val=n>m?n:m;return Math.pow(10,17-~~(Math.log(val>0?val:-val)*Math.LOG10E))}var isArray=Array.isArray||function isArray(arg){return toString.call(arg)==="[object Array]"};function isFunction(arg){return toString.call(arg)==="[object Function]"}function isNumber(arg){return typeof arg==="number"&&arg===arg}function toVector(arr){return concat.apply([],arr)}function jStat(){return new jStat._init(arguments)}jStat.fn=jStat.prototype;jStat._init=function _init(args){if(isArray(args[0])){if(isArray(args[0][0])){if(isFunction(args[1]))args[0]=jStat.map(args[0],args[1]);for(var i=0;i<args[0].length;i++)this[i]=args[0][i];this.length=args[0].length}else{this[0]=isFunction(args[1])?jStat.map(args[0],args[1]):args[0];this.length=1}}else if(isNumber(args[0])){this[0]=jStat.seq.apply(null,args);this.length=1}else if(args[0]instanceof jStat){return jStat(args[0].toArray())}else{this[0]=[];this.length=1}return this};jStat._init.prototype=jStat.prototype;jStat._init.constructor=jStat;jStat.utils={calcRdx:calcRdx,isArray:isArray,isFunction:isFunction,isNumber:isNumber,toVector:toVector};jStat._random_fn=Math.random;jStat.setRandom=function setRandom(fn){if(typeof fn!=="function")throw new TypeError("fn is not a function");jStat._random_fn=fn};jStat.extend=function extend(obj){var i,j;if(arguments.length===1){for(j in obj)jStat[j]=obj[j];return this}for(i=1;i<arguments.length;i++){for(j in arguments[i])obj[j]=arguments[i][j]}return obj};jStat.rows=function rows(arr){return arr.length||1};jStat.cols=function cols(arr){return arr[0].length||1};jStat.dimensions=function dimensions(arr){return{rows:jStat.rows(arr),cols:jStat.cols(arr)}};jStat.row=function row(arr,index){if(isArray(index)){return index.map(function(i){return jStat.row(arr,i)})}return arr[index]};jStat.rowa=function rowa(arr,i){return jStat.row(arr,i)};jStat.col=function col(arr,index){if(isArray(index)){var submat=jStat.arange(arr.length).map(function(){return new Array(index.length)});index.forEach(function(ind,i){jStat.arange(arr.length).forEach(function(j){submat[j][i]=arr[j][ind]})});return submat}var column=new Array(arr.length);for(var i=0;i<arr.length;i++)column[i]=[arr[i][index]];return column};jStat.cola=function cola(arr,i){return jStat.col(arr,i).map(function(a){return a[0]})};jStat.diag=function diag(arr){var nrow=jStat.rows(arr);var res=new Array(nrow);for(var row=0;row<nrow;row++)res[row]=[arr[row][row]];return res};jStat.antidiag=function antidiag(arr){var nrow=jStat.rows(arr)-1;var res=new Array(nrow);for(var i=0;nrow>=0;nrow--,i++)res[i]=[arr[i][nrow]];return res};jStat.transpose=function transpose(arr){var obj=[];var objArr,rows,cols,j,i;if(!isArray(arr[0]))arr=[arr];rows=arr.length;cols=arr[0].length;for(i=0;i<cols;i++){objArr=new Array(rows);for(j=0;j<rows;j++)objArr[j]=arr[j][i];obj.push(objArr)}return obj.length===1?obj[0]:obj};jStat.map=function map(arr,func,toAlter){var row,nrow,ncol,res,col;if(!isArray(arr[0]))arr=[arr];nrow=arr.length;ncol=arr[0].length;res=toAlter?arr:new Array(nrow);for(row=0;row<nrow;row++){if(!res[row])res[row]=new Array(ncol);for(col=0;col<ncol;col++)res[row][col]=func(arr[row][col],row,col)}return res.length===1?res[0]:res};jStat.cumreduce=function cumreduce(arr,func,toAlter){var row,nrow,ncol,res,col;if(!isArray(arr[0]))arr=[arr];nrow=arr.length;ncol=arr[0].length;res=toAlter?arr:new Array(nrow);for(row=0;row<nrow;row++){if(!res[row])res[row]=new Array(ncol);if(ncol>0)res[row][0]=arr[row][0];for(col=1;col<ncol;col++)res[row][col]=func(res[row][col-1],arr[row][col])}return res.length===1?res[0]:res};jStat.alter=function alter(arr,func){return jStat.map(arr,func,true)};jStat.create=function create(rows,cols,func){var res=new Array(rows);var i,j;if(isFunction(cols)){func=cols;cols=rows}for(i=0;i<rows;i++){res[i]=new Array(cols);for(j=0;j<cols;j++)res[i][j]=func(i,j)}return res};function retZero(){return 0}jStat.zeros=function zeros(rows,cols){if(!isNumber(cols))cols=rows;return jStat.create(rows,cols,retZero)};function retOne(){return 1}jStat.ones=function ones(rows,cols){if(!isNumber(cols))cols=rows;return jStat.create(rows,cols,retOne)};jStat.rand=function rand(rows,cols){if(!isNumber(cols))cols=rows;return jStat.create(rows,cols,jStat._random_fn)};function retIdent(i,j){return i===j?1:0}jStat.identity=function identity(rows,cols){if(!isNumber(cols))cols=rows;return jStat.create(rows,cols,retIdent)};jStat.symmetric=function symmetric(arr){var size=arr.length;var row,col;if(arr.length!==arr[0].length)return false;for(row=0;row<size;row++){for(col=0;col<size;col++)if(arr[col][row]!==arr[row][col])return false}return true};jStat.clear=function clear(arr){return jStat.alter(arr,retZero)};jStat.seq=function seq(min,max,length,func){if(!isFunction(func))func=false;var arr=[];var hival=calcRdx(min,max);var step=(max*hival-min*hival)/((length-1)*hival);var current=min;var cnt;for(cnt=0;current<=max&&cnt<length;cnt++,current=(min*hival+step*hival*cnt)/hival){arr.push(func?func(current,cnt):current)}return arr};jStat.arange=function arange(start,end,step){var rl=[];var i;step=step||1;if(end===undefined){end=start;start=0}if(start===end||step===0){return[]}if(start<end&&step<0){return[]}if(start>end&&step>0){return[]}if(step>0){for(i=start;i<end;i+=step){rl.push(i)}}else{for(i=start;i>end;i+=step){rl.push(i)}}return rl};jStat.slice=function(){function _slice(list,start,end,step){var i;var rl=[];var length=list.length;if(start===undefined&&end===undefined&&step===undefined){return jStat.copy(list)}start=start||0;end=end||list.length;start=start>=0?start:length+start;end=end>=0?end:length+end;step=step||1;if(start===end||step===0){return[]}if(start<end&&step<0){return[]}if(start>end&&step>0){return[]}if(step>0){for(i=start;i<end;i+=step){rl.push(list[i])}}else{for(i=start;i>end;i+=step){rl.push(list[i])}}return rl}function slice(list,rcSlice){var colSlice,rowSlice;rcSlice=rcSlice||{};if(isNumber(rcSlice.row)){if(isNumber(rcSlice.col))return list[rcSlice.row][rcSlice.col];var row=jStat.rowa(list,rcSlice.row);colSlice=rcSlice.col||{};return _slice(row,colSlice.start,colSlice.end,colSlice.step)}if(isNumber(rcSlice.col)){var col=jStat.cola(list,rcSlice.col);rowSlice=rcSlice.row||{};return _slice(col,rowSlice.start,rowSlice.end,rowSlice.step)}rowSlice=rcSlice.row||{};colSlice=rcSlice.col||{};var rows=_slice(list,rowSlice.start,rowSlice.end,rowSlice.step);return rows.map(function(row){return _slice(row,colSlice.start,colSlice.end,colSlice.step)})}return slice}();jStat.sliceAssign=function sliceAssign(A,rcSlice,B){var nl,ml;if(isNumber(rcSlice.row)){if(isNumber(rcSlice.col))return A[rcSlice.row][rcSlice.col]=B;rcSlice.col=rcSlice.col||{};rcSlice.col.start=rcSlice.col.start||0;rcSlice.col.end=rcSlice.col.end||A[0].length;rcSlice.col.step=rcSlice.col.step||1;nl=jStat.arange(rcSlice.col.start,Math.min(A.length,rcSlice.col.end),rcSlice.col.step);var m=rcSlice.row;nl.forEach(function(n,i){A[m][n]=B[i]});return A}if(isNumber(rcSlice.col)){rcSlice.row=rcSlice.row||{};rcSlice.row.start=rcSlice.row.start||0;rcSlice.row.end=rcSlice.row.end||A.length;rcSlice.row.step=rcSlice.row.step||1;ml=jStat.arange(rcSlice.row.start,Math.min(A[0].length,rcSlice.row.end),rcSlice.row.step);var n=rcSlice.col;ml.forEach(function(m,j){A[m][n]=B[j]});return A}if(B[0].length===undefined){B=[B]}rcSlice.row.start=rcSlice.row.start||0;rcSlice.row.end=rcSlice.row.end||A.length;rcSlice.row.step=rcSlice.row.step||1;rcSlice.col.start=rcSlice.col.start||0;rcSlice.col.end=rcSlice.col.end||A[0].length;rcSlice.col.step=rcSlice.col.step||1;ml=jStat.arange(rcSlice.row.start,Math.min(A.length,rcSlice.row.end),rcSlice.row.step);nl=jStat.arange(rcSlice.col.start,Math.min(A[0].length,rcSlice.col.end),rcSlice.col.step);ml.forEach(function(m,i){nl.forEach(function(n,j){A[m][n]=B[i][j]})});return A};jStat.diagonal=function diagonal(diagArray){var mat=jStat.zeros(diagArray.length,diagArray.length);diagArray.forEach(function(t,i){mat[i][i]=t});return mat};jStat.copy=function copy(A){return A.map(function(row){if(isNumber(row))return row;return row.map(function(t){return t})})};var jProto=jStat.prototype;jProto.length=0;jProto.push=Array.prototype.push;jProto.sort=Array.prototype.sort;jProto.splice=Array.prototype.splice;jProto.slice=Array.prototype.slice;jProto.toArray=function toArray(){return this.length>1?slice.call(this):slice.call(this)[0]};jProto.map=function map(func,toAlter){return jStat(jStat.map(this,func,toAlter))};jProto.cumreduce=function cumreduce(func,toAlter){return jStat(jStat.cumreduce(this,func,toAlter))};jProto.alter=function alter(func){jStat.alter(this,func);return this};(function(funcs){for(var i=0;i<funcs.length;i++)(function(passfunc){jProto[passfunc]=function(func){var self=this,results;if(func){setTimeout(function(){func.call(self,jProto[passfunc].call(self))});return this}results=jStat[passfunc](this);return isArray(results)?jStat(results):results}})(funcs[i])})("transpose clear symmetric rows cols dimensions diag antidiag".split(" "));(function(funcs){for(var i=0;i<funcs.length;i++)(function(passfunc){jProto[passfunc]=function(index,func){var self=this;if(func){setTimeout(function(){func.call(self,jProto[passfunc].call(self,index))});return this}return jStat(jStat[passfunc](this,index))}})(funcs[i])})("row col".split(" "));(function(funcs){for(var i=0;i<funcs.length;i++)(function(passfunc){jProto[passfunc]=function(){return jStat(jStat[passfunc].apply(null,arguments))}})(funcs[i])})("create zeros ones rand identity".split(" "));return jStat}(Math);(function(jStat,Math){var isFunction=jStat.utils.isFunction;function ascNum(a,b){return a-b}function clip(arg,min,max){return Math.max(min,Math.min(arg,max))}jStat.sum=function sum(arr){var sum=0;var i=arr.length;while(--i>=0)sum+=arr[i];return sum};jStat.sumsqrd=function sumsqrd(arr){var sum=0;var i=arr.length;while(--i>=0)sum+=arr[i]*arr[i];return sum};jStat.sumsqerr=function sumsqerr(arr){var mean=jStat.mean(arr);var sum=0;var i=arr.length;var tmp;while(--i>=0){tmp=arr[i]-mean;sum+=tmp*tmp}return sum};jStat.sumrow=function sumrow(arr){var sum=0;var i=arr.length;while(--i>=0)sum+=arr[i];return sum};jStat.product=function product(arr){var prod=1;var i=arr.length;while(--i>=0)prod*=arr[i];return prod};jStat.min=function min(arr){var low=arr[0];var i=0;while(++i<arr.length)if(arr[i]<low)low=arr[i];return low};jStat.max=function max(arr){var high=arr[0];var i=0;while(++i<arr.length)if(arr[i]>high)high=arr[i];return high};jStat.unique=function unique(arr){var hash={},_arr=[];for(var i=0;i<arr.length;i++){if(!hash[arr[i]]){hash[arr[i]]=true;_arr.push(arr[i])}}return _arr};jStat.mean=function mean(arr){return jStat.sum(arr)/arr.length};jStat.meansqerr=function meansqerr(arr){return jStat.sumsqerr(arr)/arr.length};jStat.geomean=function geomean(arr){return Math.pow(jStat.product(arr),1/arr.length)};jStat.median=function median(arr){var arrlen=arr.length;var _arr=arr.slice().sort(ascNum);return!(arrlen&1)?(_arr[arrlen/2-1]+_arr[arrlen/2])/2:_arr[arrlen/2|0]};jStat.cumsum=function cumsum(arr){return jStat.cumreduce(arr,function(a,b){return a+b})};jStat.cumprod=function cumprod(arr){return jStat.cumreduce(arr,function(a,b){return a*b})};jStat.diff=function diff(arr){var diffs=[];var arrLen=arr.length;var i;for(i=1;i<arrLen;i++)diffs.push(arr[i]-arr[i-1]);return diffs};jStat.rank=function(arr){var arrlen=arr.length;var sorted=arr.slice().sort(ascNum);var ranks=new Array(arrlen);var val;for(var i=0;i<arrlen;i++){var first=sorted.indexOf(arr[i]);var last=sorted.lastIndexOf(arr[i]);if(first===last){val=first}else{val=(first+last)/2}ranks[i]=val+1}return ranks};jStat.mode=function mode(arr){var arrLen=arr.length;var _arr=arr.slice().sort(ascNum);var count=1;var maxCount=0;var numMaxCount=0;var mode_arr=[];var i;for(i=0;i<arrLen;i++){if(_arr[i]===_arr[i+1]){count++}else{if(count>maxCount){mode_arr=[_arr[i]];maxCount=count;numMaxCount=0}else if(count===maxCount){mode_arr.push(_arr[i]);numMaxCount++}count=1}}return numMaxCount===0?mode_arr[0]:mode_arr};jStat.range=function range(arr){return jStat.max(arr)-jStat.min(arr)};jStat.variance=function variance(arr,flag){return jStat.sumsqerr(arr)/(arr.length-(flag?1:0))};jStat.pooledvariance=function pooledvariance(arr){var sumsqerr=arr.reduce(function(a,samples){return a+jStat.sumsqerr(samples)},0);var count=arr.reduce(function(a,samples){return a+samples.length},0);return sumsqerr/(count-arr.length)};jStat.deviation=function(arr){var mean=jStat.mean(arr);var arrlen=arr.length;var dev=new Array(arrlen);for(var i=0;i<arrlen;i++){dev[i]=arr[i]-mean}return dev};jStat.stdev=function stdev(arr,flag){return Math.sqrt(jStat.variance(arr,flag))};jStat.pooledstdev=function pooledstdev(arr){return Math.sqrt(jStat.pooledvariance(arr))};jStat.meandev=function meandev(arr){var mean=jStat.mean(arr);var a=[];for(var i=arr.length-1;i>=0;i--){a.push(Math.abs(arr[i]-mean))}return jStat.mean(a)};jStat.meddev=function meddev(arr){var median=jStat.median(arr);var a=[];for(var i=arr.length-1;i>=0;i--){a.push(Math.abs(arr[i]-median))}return jStat.median(a)};jStat.coeffvar=function coeffvar(arr){return jStat.stdev(arr)/jStat.mean(arr)};jStat.quartiles=function quartiles(arr){var arrlen=arr.length;var _arr=arr.slice().sort(ascNum);return[_arr[Math.round(arrlen/4)-1],_arr[Math.round(arrlen/2)-1],_arr[Math.round(arrlen*3/4)-1]]};jStat.quantiles=function quantiles(arr,quantilesArray,alphap,betap){var sortedArray=arr.slice().sort(ascNum);var quantileVals=[quantilesArray.length];var n=arr.length;var i,p,m,aleph,k,gamma;if(typeof alphap==="undefined")alphap=3/8;if(typeof betap==="undefined")betap=3/8;for(i=0;i<quantilesArray.length;i++){p=quantilesArray[i];m=alphap+p*(1-alphap-betap);aleph=n*p+m;k=Math.floor(clip(aleph,1,n-1));gamma=clip(aleph-k,0,1);quantileVals[i]=(1-gamma)*sortedArray[k-1]+gamma*sortedArray[k]}return quantileVals};jStat.percentile=function percentile(arr,k,exclusive){var _arr=arr.slice().sort(ascNum);var realIndex=k*(_arr.length+(exclusive?1:-1))+(exclusive?0:1);var index=parseInt(realIndex);var frac=realIndex-index;if(index+1<_arr.length){return _arr[index-1]+frac*(_arr[index]-_arr[index-1])}else{return _arr[index-1]}};jStat.percentileOfScore=function percentileOfScore(arr,score,kind){var counter=0;var len=arr.length;var strict=false;var value,i;if(kind==="strict")strict=true;for(i=0;i<len;i++){value=arr[i];if(strict&&value<score||!strict&&value<=score){counter++}}return counter/len};jStat.histogram=function histogram(arr,binCnt){binCnt=binCnt||4;var first=jStat.min(arr);var binWidth=(jStat.max(arr)-first)/binCnt;var len=arr.length;var bins=[];var i;for(i=0;i<binCnt;i++)bins[i]=0;for(i=0;i<len;i++)bins[Math.min(Math.floor((arr[i]-first)/binWidth),binCnt-1)]+=1;return bins};jStat.covariance=function covariance(arr1,arr2){var u=jStat.mean(arr1);var v=jStat.mean(arr2);var arr1Len=arr1.length;var sq_dev=new Array(arr1Len);var i;for(i=0;i<arr1Len;i++)sq_dev[i]=(arr1[i]-u)*(arr2[i]-v);return jStat.sum(sq_dev)/(arr1Len-1)};jStat.corrcoeff=function corrcoeff(arr1,arr2){return jStat.covariance(arr1,arr2)/jStat.stdev(arr1,1)/jStat.stdev(arr2,1)};jStat.spearmancoeff=function(arr1,arr2){arr1=jStat.rank(arr1);arr2=jStat.rank(arr2);return jStat.corrcoeff(arr1,arr2)};jStat.stanMoment=function stanMoment(arr,n){var mu=jStat.mean(arr);var sigma=jStat.stdev(arr);var len=arr.length;var skewSum=0;for(var i=0;i<len;i++)skewSum+=Math.pow((arr[i]-mu)/sigma,n);return skewSum/arr.length};jStat.skewness=function skewness(arr){return jStat.stanMoment(arr,3)};jStat.kurtosis=function kurtosis(arr){return jStat.stanMoment(arr,4)-3};var jProto=jStat.prototype;(function(funcs){for(var i=0;i<funcs.length;i++)(function(passfunc){jProto[passfunc]=function(fullbool,func){var arr=[];var i=0;var tmpthis=this;if(isFunction(fullbool)){func=fullbool;fullbool=false}if(func){setTimeout(function(){func.call(tmpthis,jProto[passfunc].call(tmpthis,fullbool))});return this}if(this.length>1){tmpthis=fullbool===true?this:this.transpose();for(;i<tmpthis.length;i++)arr[i]=jStat[passfunc](tmpthis[i]);return arr}return jStat[passfunc](this[0],fullbool)}})(funcs[i])})("cumsum cumprod".split(" "));(function(funcs){for(var i=0;i<funcs.length;i++)(function(passfunc){jProto[passfunc]=function(fullbool,func){var arr=[];var i=0;var tmpthis=this;if(isFunction(fullbool)){func=fullbool;fullbool=false}if(func){setTimeout(function(){func.call(tmpthis,jProto[passfunc].call(tmpthis,fullbool))});return this}if(this.length>1){if(passfunc!=="sumrow")tmpthis=fullbool===true?this:this.transpose();for(;i<tmpthis.length;i++)arr[i]=jStat[passfunc](tmpthis[i]);return fullbool===true?jStat[passfunc](jStat.utils.toVector(arr)):arr}return jStat[passfunc](this[0],fullbool)}})(funcs[i])})(("sum sumsqrd sumsqerr sumrow product min max unique mean meansqerr "+"geomean median diff rank mode range variance deviation stdev meandev "+"meddev coeffvar quartiles histogram skewness kurtosis").split(" "));(function(funcs){for(var i=0;i<funcs.length;i++)(function(passfunc){jProto[passfunc]=function(){var arr=[];var i=0;var tmpthis=this;var args=Array.prototype.slice.call(arguments);var callbackFunction;if(isFunction(args[args.length-1])){callbackFunction=args[args.length-1];var argsToPass=args.slice(0,args.length-1);setTimeout(function(){callbackFunction.call(tmpthis,jProto[passfunc].apply(tmpthis,argsToPass))});return this}else{callbackFunction=undefined;var curriedFunction=function curriedFunction(vector){return jStat[passfunc].apply(tmpthis,[vector].concat(args))}}if(this.length>1){tmpthis=tmpthis.transpose();for(;i<tmpthis.length;i++)arr[i]=curriedFunction(tmpthis[i]);return arr}return curriedFunction(this[0])}})(funcs[i])})("quantiles percentileOfScore".split(" "))})(jStat,Math);(function(jStat,Math){jStat.gammaln=function gammaln(x){var j=0;var cof=[76.18009172947146,-86.50532032941678,24.01409824083091,-1.231739572450155,.001208650973866179,-5395239384953e-18];var ser=1.000000000190015;var xx,y,tmp;tmp=(y=xx=x)+5.5;tmp-=(xx+.5)*Math.log(tmp);for(;j<6;j++)ser+=cof[j]/++y;return Math.log(2.5066282746310007*ser/xx)-tmp};jStat.gammafn=function gammafn(x){var p=[-1.716185138865495,24.76565080557592,-379.80425647094563,629.3311553128184,866.9662027904133,-31451.272968848367,-36144.413418691176,66456.14382024054];var q=[-30.8402300119739,315.35062697960416,-1015.1563674902192,-3107.771671572311,22538.11842098015,4755.846277527881,-134659.9598649693,-115132.2596755535];var fact=false;var n=0;var xden=0;var xnum=0;var y=x;var i,z,yi,res;if(y<=0){res=y%1+36e-17;if(res){fact=(!(y&1)?1:-1)*Math.PI/Math.sin(Math.PI*res);y=1-y}else{return Infinity}}yi=y;if(y<1){z=y++}else{z=(y-=n=(y|0)-1)-1}for(i=0;i<8;++i){xnum=(xnum+p[i])*z;xden=xden*z+q[i]}res=xnum/xden+1;if(yi<y){res/=yi}else if(yi>y){for(i=0;i<n;++i){res*=y;y++}}if(fact){res=fact/res}return res};jStat.gammap=function gammap(a,x){return jStat.lowRegGamma(a,x)*jStat.gammafn(a)};jStat.lowRegGamma=function lowRegGamma(a,x){var aln=jStat.gammaln(a);var ap=a;var sum=1/a;var del=sum;var b=x+1-a;var c=1/1e-30;var d=1/b;var h=d;var i=1;var ITMAX=-~(Math.log(a>=1?a:1/a)*8.5+a*.4+17);var an;if(x<0||a<=0){return NaN}else if(x<a+1){for(;i<=ITMAX;i++){sum+=del*=x/++ap}return sum*Math.exp(-x+a*Math.log(x)-aln)}for(;i<=ITMAX;i++){an=-i*(i-a);b+=2;d=an*d+b;c=b+an/c;d=1/d;h*=d*c}return 1-h*Math.exp(-x+a*Math.log(x)-aln)};jStat.factorialln=function factorialln(n){return n<0?NaN:jStat.gammaln(n+1)};jStat.factorial=function factorial(n){return n<0?NaN:jStat.gammafn(n+1)};jStat.combination=function combination(n,m){return n>170||m>170?Math.exp(jStat.combinationln(n,m)):jStat.factorial(n)/jStat.factorial(m)/jStat.factorial(n-m)};jStat.combinationln=function combinationln(n,m){return jStat.factorialln(n)-jStat.factorialln(m)-jStat.factorialln(n-m)};jStat.permutation=function permutation(n,m){return jStat.factorial(n)/jStat.factorial(n-m)};jStat.betafn=function betafn(x,y){if(x<=0||y<=0)return undefined;return x+y>170?Math.exp(jStat.betaln(x,y)):jStat.gammafn(x)*jStat.gammafn(y)/jStat.gammafn(x+y)};jStat.betaln=function betaln(x,y){return jStat.gammaln(x)+jStat.gammaln(y)-jStat.gammaln(x+y)};jStat.betacf=function betacf(x,a,b){var fpmin=1e-30;var m=1;var qab=a+b;var qap=a+1;var qam=a-1;var c=1;var d=1-qab*x/qap;var m2,aa,del,h;if(Math.abs(d)<fpmin)d=fpmin;d=1/d;h=d;for(;m<=100;m++){m2=2*m;aa=m*(b-m)*x/((qam+m2)*(a+m2));d=1+aa*d;if(Math.abs(d)<fpmin)d=fpmin;c=1+aa/c;if(Math.abs(c)<fpmin)c=fpmin;d=1/d;h*=d*c;aa=-(a+m)*(qab+m)*x/((a+m2)*(qap+m2));d=1+aa*d;if(Math.abs(d)<fpmin)d=fpmin;c=1+aa/c;if(Math.abs(c)<fpmin)c=fpmin;d=1/d;del=d*c;h*=del;if(Math.abs(del-1)<3e-7)break}return h};jStat.gammapinv=function gammapinv(p,a){var j=0;var a1=a-1;var EPS=1e-8;var gln=jStat.gammaln(a);var x,err,t,u,pp,lna1,afac;if(p>=1)return Math.max(100,a+100*Math.sqrt(a));if(p<=0)return 0;if(a>1){lna1=Math.log(a1);afac=Math.exp(a1*(lna1-1)-gln);pp=p<.5?p:1-p;t=Math.sqrt(-2*Math.log(pp));x=(2.30753+t*.27061)/(1+t*(.99229+t*.04481))-t;if(p<.5)x=-x;x=Math.max(.001,a*Math.pow(1-1/(9*a)-x/(3*Math.sqrt(a)),3))}else{t=1-a*(.253+a*.12);if(p<t)x=Math.pow(p/t,1/a);else x=1-Math.log(1-(p-t)/(1-t))}for(;j<12;j++){if(x<=0)return 0;err=jStat.lowRegGamma(a,x)-p;if(a>1)t=afac*Math.exp(-(x-a1)+a1*(Math.log(x)-lna1));else t=Math.exp(-x+a1*Math.log(x)-gln);u=err/t;x-=t=u/(1-.5*Math.min(1,u*((a-1)/x-1)));if(x<=0)x=.5*(x+t);if(Math.abs(t)<EPS*x)break}return x};jStat.erf=function erf(x){var cof=[-1.3026537197817094,.6419697923564902,.019476473204185836,-.00956151478680863,-.000946595344482036,.000366839497852761,42523324806907e-18,-20278578112534e-18,-1624290004647e-18,130365583558e-17,1.5626441722e-8,-8.5238095915e-8,6.529054439e-9,5.059343495e-9,-9.91364156e-10,-2.27365122e-10,96467911e-18,2394038e-18,-6886027e-18,894487e-18,313092e-18,-112708e-18,381e-18,7106e-18,-1523e-18,-94e-18,121e-18,-28e-18];var j=cof.length-1;var isneg=false;var d=0;var dd=0;var t,ty,tmp,res;if(x<0){x=-x;isneg=true}t=2/(2+x);ty=4*t-2;for(;j>0;j--){tmp=d;d=ty*d-dd+cof[j];dd=tmp}res=t*Math.exp(-x*x+.5*(cof[0]+ty*d)-dd);return isneg?res-1:1-res};jStat.erfc=function erfc(x){return 1-jStat.erf(x)};jStat.erfcinv=function erfcinv(p){var j=0;var x,err,t,pp;if(p>=2)return-100;if(p<=0)return 100;pp=p<1?p:2-p;t=Math.sqrt(-2*Math.log(pp/2));x=-.70711*((2.30753+t*.27061)/(1+t*(.99229+t*.04481))-t);for(;j<2;j++){err=jStat.erfc(x)-pp;x+=err/(1.1283791670955126*Math.exp(-x*x)-x*err)}return p<1?x:-x};jStat.ibetainv=function ibetainv(p,a,b){var EPS=1e-8;var a1=a-1;var b1=b-1;var j=0;var lna,lnb,pp,t,u,err,x,al,h,w,afac;if(p<=0)return 0;if(p>=1)return 1;if(a>=1&&b>=1){pp=p<.5?p:1-p;t=Math.sqrt(-2*Math.log(pp));x=(2.30753+t*.27061)/(1+t*(.99229+t*.04481))-t;if(p<.5)x=-x;al=(x*x-3)/6;h=2/(1/(2*a-1)+1/(2*b-1));w=x*Math.sqrt(al+h)/h-(1/(2*b-1)-1/(2*a-1))*(al+5/6-2/(3*h));x=a/(a+b*Math.exp(2*w))}else{lna=Math.log(a/(a+b));lnb=Math.log(b/(a+b));t=Math.exp(a*lna)/a;u=Math.exp(b*lnb)/b;w=t+u;if(p<t/w)x=Math.pow(a*w*p,1/a);else x=1-Math.pow(b*w*(1-p),1/b)}afac=-jStat.gammaln(a)-jStat.gammaln(b)+jStat.gammaln(a+b);for(;j<10;j++){if(x===0||x===1)return x;err=jStat.ibeta(x,a,b)-p;t=Math.exp(a1*Math.log(x)+b1*Math.log(1-x)+afac);u=err/t;x-=t=u/(1-.5*Math.min(1,u*(a1/x-b1/(1-x))));if(x<=0)x=.5*(x+t);if(x>=1)x=.5*(x+t+1);if(Math.abs(t)<EPS*x&&j>0)break}return x};jStat.ibeta=function ibeta(x,a,b){var bt=x===0||x===1?0:Math.exp(jStat.gammaln(a+b)-jStat.gammaln(a)-jStat.gammaln(b)+a*Math.log(x)+b*Math.log(1-x));if(x<0||x>1)return false;if(x<(a+1)/(a+b+2))return bt*jStat.betacf(x,a,b)/a;return 1-bt*jStat.betacf(1-x,b,a)/b};jStat.randn=function randn(n,m){var u,v,x,y,q;if(!m)m=n;if(n)return jStat.create(n,m,function(){return jStat.randn()});do{u=jStat._random_fn();v=1.7156*(jStat._random_fn()-.5);x=u-.449871;y=Math.abs(v)+.386595;q=x*x+y*(.196*y-.25472*x)}while(q>.27597&&(q>.27846||v*v>-4*Math.log(u)*u*u));return v/u};jStat.randg=function randg(shape,n,m){var oalph=shape;var a1,a2,u,v,x,mat;if(!m)m=n;if(!shape)shape=1;if(n){mat=jStat.zeros(n,m);mat.alter(function(){return jStat.randg(shape)});return mat}if(shape<1)shape+=1;a1=shape-1/3;a2=1/Math.sqrt(9*a1);do{do{x=jStat.randn();v=1+a2*x}while(v<=0);v=v*v*v;u=jStat._random_fn()}while(u>1-.331*Math.pow(x,4)&&Math.log(u)>.5*x*x+a1*(1-v+Math.log(v)));if(shape==oalph)return a1*v;do{u=jStat._random_fn()}while(u===0);return Math.pow(u,1/oalph)*a1*v};(function(funcs){for(var i=0;i<funcs.length;i++)(function(passfunc){jStat.fn[passfunc]=function(){return jStat(jStat.map(this,function(value){return jStat[passfunc](value)}))}})(funcs[i])})("gammaln gammafn factorial factorialln".split(" "));(function(funcs){for(var i=0;i<funcs.length;i++)(function(passfunc){jStat.fn[passfunc]=function(){return jStat(jStat[passfunc].apply(null,arguments))}})(funcs[i])})("randn".split(" "))})(jStat,Math);(function(jStat,Math){(function(list){for(var i=0;i<list.length;i++)(function(func){jStat[func]=function(a,b,c){if(!(this instanceof arguments.callee))return new arguments.callee(a,b,c);this._a=a;this._b=b;this._c=c;return this};jStat.fn[func]=function(a,b,c){var newthis=jStat[func](a,b,c);newthis.data=this;return newthis};jStat[func].prototype.sample=function(arr){var a=this._a;var b=this._b;var c=this._c;if(arr)return jStat.alter(arr,function(){return jStat[func].sample(a,b,c)});else return jStat[func].sample(a,b,c)};(function(vals){for(var i=0;i<vals.length;i++)(function(fnfunc){jStat[func].prototype[fnfunc]=function(x){var a=this._a;var b=this._b;var c=this._c;if(!x&&x!==0)x=this.data;if(typeof x!=="number"){return jStat.fn.map.call(x,function(x){return jStat[func][fnfunc](x,a,b,c)})}return jStat[func][fnfunc](x,a,b,c)}})(vals[i])})("pdf cdf inv".split(" "));(function(vals){for(var i=0;i<vals.length;i++)(function(fnfunc){jStat[func].prototype[fnfunc]=function(){return jStat[func][fnfunc](this._a,this._b,this._c)}})(vals[i])})("mean median mode variance".split(" "))})(list[i])})(("beta centralF cauchy chisquare exponential gamma invgamma kumaraswamy "+"laplace lognormal noncentralt normal pareto studentt weibull uniform "+"binomial negbin hypgeom poisson triangular tukey arcsine").split(" "));jStat.extend(jStat.beta,{pdf:function pdf(x,alpha,beta){if(x>1||x<0)return 0;if(alpha==1&&beta==1)return 1;if(alpha<512&&beta<512){return Math.pow(x,alpha-1)*Math.pow(1-x,beta-1)/jStat.betafn(alpha,beta)}else{return Math.exp((alpha-1)*Math.log(x)+(beta-1)*Math.log(1-x)-jStat.betaln(alpha,beta))}},cdf:function cdf(x,alpha,beta){return x>1||x<0?(x>1)*1:jStat.ibeta(x,alpha,beta)},inv:function inv(x,alpha,beta){return jStat.ibetainv(x,alpha,beta)},mean:function mean(alpha,beta){return alpha/(alpha+beta)},median:function median(alpha,beta){return jStat.ibetainv(.5,alpha,beta)},mode:function mode(alpha,beta){return(alpha-1)/(alpha+beta-2)},sample:function sample(alpha,beta){var u=jStat.randg(alpha);return u/(u+jStat.randg(beta))},variance:function variance(alpha,beta){return alpha*beta/(Math.pow(alpha+beta,2)*(alpha+beta+1))}});jStat.extend(jStat.centralF,{pdf:function pdf(x,df1,df2){var p,q,f;if(x<0)return 0;if(df1<=2){if(x===0&&df1<2){return Infinity}if(x===0&&df1===2){return 1}return 1/jStat.betafn(df1/2,df2/2)*Math.pow(df1/df2,df1/2)*Math.pow(x,df1/2-1)*Math.pow(1+df1/df2*x,-(df1+df2)/2)}p=df1*x/(df2+x*df1);q=df2/(df2+x*df1);f=df1*q/2;return f*jStat.binomial.pdf((df1-2)/2,(df1+df2-2)/2,p)},cdf:function cdf(x,df1,df2){if(x<0)return 0;return jStat.ibeta(df1*x/(df1*x+df2),df1/2,df2/2)},inv:function inv(x,df1,df2){return df2/(df1*(1/jStat.ibetainv(x,df1/2,df2/2)-1))},mean:function mean(df1,df2){return df2>2?df2/(df2-2):undefined},mode:function mode(df1,df2){return df1>2?df2*(df1-2)/(df1*(df2+2)):undefined},sample:function sample(df1,df2){var x1=jStat.randg(df1/2)*2;var x2=jStat.randg(df2/2)*2;return x1/df1/(x2/df2)},variance:function variance(df1,df2){if(df2<=4)return undefined;return 2*df2*df2*(df1+df2-2)/(df1*(df2-2)*(df2-2)*(df2-4))}});jStat.extend(jStat.cauchy,{pdf:function pdf(x,local,scale){if(scale<0){return 0}return scale/(Math.pow(x-local,2)+Math.pow(scale,2))/Math.PI},cdf:function cdf(x,local,scale){return Math.atan((x-local)/scale)/Math.PI+.5},inv:function(p,local,scale){return local+scale*Math.tan(Math.PI*(p-.5))},median:function median(local){return local},mode:function mode(local){return local},sample:function sample(local,scale){return jStat.randn()*Math.sqrt(1/(2*jStat.randg(.5)))*scale+local}});jStat.extend(jStat.chisquare,{pdf:function pdf(x,dof){if(x<0)return 0;return x===0&&dof===2?.5:Math.exp((dof/2-1)*Math.log(x)-x/2-dof/2*Math.log(2)-jStat.gammaln(dof/2))},cdf:function cdf(x,dof){if(x<0)return 0;return jStat.lowRegGamma(dof/2,x/2)},inv:function(p,dof){return 2*jStat.gammapinv(p,.5*dof)},mean:function(dof){return dof},median:function median(dof){return dof*Math.pow(1-2/(9*dof),3)},mode:function mode(dof){return dof-2>0?dof-2:0},sample:function sample(dof){return jStat.randg(dof/2)*2},variance:function variance(dof){return 2*dof}});jStat.extend(jStat.exponential,{pdf:function pdf(x,rate){return x<0?0:rate*Math.exp(-rate*x)},cdf:function cdf(x,rate){return x<0?0:1-Math.exp(-rate*x)},inv:function(p,rate){return-Math.log(1-p)/rate},mean:function(rate){return 1/rate},median:function(rate){return 1/rate*Math.log(2)},mode:function mode(){return 0},sample:function sample(rate){return-1/rate*Math.log(jStat._random_fn())},variance:function(rate){return Math.pow(rate,-2)}});jStat.extend(jStat.gamma,{pdf:function pdf(x,shape,scale){if(x<0)return 0;return x===0&&shape===1?1/scale:Math.exp((shape-1)*Math.log(x)-x/scale-jStat.gammaln(shape)-shape*Math.log(scale))},cdf:function cdf(x,shape,scale){if(x<0)return 0;return jStat.lowRegGamma(shape,x/scale)},inv:function(p,shape,scale){return jStat.gammapinv(p,shape)*scale},mean:function(shape,scale){return shape*scale},mode:function mode(shape,scale){if(shape>1)return(shape-1)*scale;return undefined},sample:function sample(shape,scale){return jStat.randg(shape)*scale},variance:function variance(shape,scale){return shape*scale*scale}});jStat.extend(jStat.invgamma,{pdf:function pdf(x,shape,scale){if(x<=0)return 0;return Math.exp(-(shape+1)*Math.log(x)-scale/x-jStat.gammaln(shape)+shape*Math.log(scale))},cdf:function cdf(x,shape,scale){if(x<=0)return 0;return 1-jStat.lowRegGamma(shape,scale/x)},inv:function(p,shape,scale){return scale/jStat.gammapinv(1-p,shape)},mean:function(shape,scale){return shape>1?scale/(shape-1):undefined},mode:function mode(shape,scale){return scale/(shape+1)},sample:function sample(shape,scale){return scale/jStat.randg(shape)},variance:function variance(shape,scale){if(shape<=2)return undefined;return scale*scale/((shape-1)*(shape-1)*(shape-2))}});jStat.extend(jStat.kumaraswamy,{pdf:function pdf(x,alpha,beta){if(x===0&&alpha===1)return beta;else if(x===1&&beta===1)return alpha;return Math.exp(Math.log(alpha)+Math.log(beta)+(alpha-1)*Math.log(x)+(beta-1)*Math.log(1-Math.pow(x,alpha)))},cdf:function cdf(x,alpha,beta){if(x<0)return 0;else if(x>1)return 1;return 1-Math.pow(1-Math.pow(x,alpha),beta)},inv:function inv(p,alpha,beta){return Math.pow(1-Math.pow(1-p,1/beta),1/alpha)},mean:function(alpha,beta){return beta*jStat.gammafn(1+1/alpha)*jStat.gammafn(beta)/jStat.gammafn(1+1/alpha+beta)},median:function median(alpha,beta){return Math.pow(1-Math.pow(2,-1/beta),1/alpha)},mode:function mode(alpha,beta){if(!(alpha>=1&&beta>=1&&(alpha!==1&&beta!==1)))return undefined;return Math.pow((alpha-1)/(alpha*beta-1),1/alpha)},variance:function variance(){throw new Error("variance not yet implemented")}});jStat.extend(jStat.lognormal,{pdf:function pdf(x,mu,sigma){if(x<=0)return 0;return Math.exp(-Math.log(x)-.5*Math.log(2*Math.PI)-Math.log(sigma)-Math.pow(Math.log(x)-mu,2)/(2*sigma*sigma))},cdf:function cdf(x,mu,sigma){if(x<0)return 0;return.5+.5*jStat.erf((Math.log(x)-mu)/Math.sqrt(2*sigma*sigma))},inv:function(p,mu,sigma){return Math.exp(-1.4142135623730951*sigma*jStat.erfcinv(2*p)+mu)},mean:function mean(mu,sigma){return Math.exp(mu+sigma*sigma/2)},median:function median(mu){return Math.exp(mu)},mode:function mode(mu,sigma){return Math.exp(mu-sigma*sigma)},sample:function sample(mu,sigma){return Math.exp(jStat.randn()*sigma+mu)},variance:function variance(mu,sigma){return(Math.exp(sigma*sigma)-1)*Math.exp(2*mu+sigma*sigma)}});jStat.extend(jStat.noncentralt,{pdf:function pdf(x,dof,ncp){var tol=1e-14;if(Math.abs(ncp)<tol)return jStat.studentt.pdf(x,dof);if(Math.abs(x)<tol){return Math.exp(jStat.gammaln((dof+1)/2)-ncp*ncp/2-.5*Math.log(Math.PI*dof)-jStat.gammaln(dof/2))}return dof/x*(jStat.noncentralt.cdf(x*Math.sqrt(1+2/dof),dof+2,ncp)-jStat.noncentralt.cdf(x,dof,ncp))},cdf:function cdf(x,dof,ncp){var tol=1e-14;var min_iterations=200;if(Math.abs(ncp)<tol)return jStat.studentt.cdf(x,dof);var flip=false;if(x<0){flip=true;ncp=-ncp}var prob=jStat.normal.cdf(-ncp,0,1);var value=tol+1;var lastvalue=value;var y=x*x/(x*x+dof);var j=0;var p=Math.exp(-ncp*ncp/2);var q=Math.exp(-ncp*ncp/2-.5*Math.log(2)-jStat.gammaln(3/2))*ncp;while(j<min_iterations||lastvalue>tol||value>tol){lastvalue=value;if(j>0){p*=ncp*ncp/(2*j);q*=ncp*ncp/(2*(j+1/2))}value=p*jStat.beta.cdf(y,j+.5,dof/2)+q*jStat.beta.cdf(y,j+1,dof/2);prob+=.5*value;j++}return flip?1-prob:prob}});jStat.extend(jStat.normal,{pdf:function pdf(x,mean,std){return Math.exp(-.5*Math.log(2*Math.PI)-Math.log(std)-Math.pow(x-mean,2)/(2*std*std))},cdf:function cdf(x,mean,std){return.5*(1+jStat.erf((x-mean)/Math.sqrt(2*std*std)))},inv:function(p,mean,std){return-1.4142135623730951*std*jStat.erfcinv(2*p)+mean},mean:function(mean){return mean},median:function median(mean){return mean},mode:function(mean){return mean},sample:function sample(mean,std){return jStat.randn()*std+mean},variance:function(mean,std){return std*std}});jStat.extend(jStat.pareto,{pdf:function pdf(x,scale,shape){if(x<scale)return 0;return shape*Math.pow(scale,shape)/Math.pow(x,shape+1)},cdf:function cdf(x,scale,shape){if(x<scale)return 0;return 1-Math.pow(scale/x,shape)},inv:function inv(p,scale,shape){return scale/Math.pow(1-p,1/shape)},mean:function mean(scale,shape){if(shape<=1)return undefined;return shape*Math.pow(scale,shape)/(shape-1)},median:function median(scale,shape){return scale*(shape*Math.SQRT2)},mode:function mode(scale){return scale},variance:function(scale,shape){if(shape<=2)return undefined;return scale*scale*shape/(Math.pow(shape-1,2)*(shape-2))}});jStat.extend(jStat.studentt,{pdf:function pdf(x,dof){dof=dof>1e100?1e100:dof;return 1/(Math.sqrt(dof)*jStat.betafn(.5,dof/2))*Math.pow(1+x*x/dof,-((dof+1)/2))},cdf:function cdf(x,dof){var dof2=dof/2;return jStat.ibeta((x+Math.sqrt(x*x+dof))/(2*Math.sqrt(x*x+dof)),dof2,dof2)},inv:function(p,dof){var x=jStat.ibetainv(2*Math.min(p,1-p),.5*dof,.5);x=Math.sqrt(dof*(1-x)/x);return p>.5?x:-x},mean:function mean(dof){return dof>1?0:undefined},median:function median(){return 0},mode:function mode(){return 0},sample:function sample(dof){return jStat.randn()*Math.sqrt(dof/(2*jStat.randg(dof/2)))},variance:function variance(dof){return dof>2?dof/(dof-2):dof>1?Infinity:undefined}});jStat.extend(jStat.weibull,{pdf:function pdf(x,scale,shape){if(x<0||scale<0||shape<0)return 0;return shape/scale*Math.pow(x/scale,shape-1)*Math.exp(-Math.pow(x/scale,shape))},cdf:function cdf(x,scale,shape){return x<0?0:1-Math.exp(-Math.pow(x/scale,shape))},inv:function(p,scale,shape){return scale*Math.pow(-Math.log(1-p),1/shape)},mean:function(scale,shape){return scale*jStat.gammafn(1+1/shape)},median:function median(scale,shape){return scale*Math.pow(Math.log(2),1/shape)},mode:function mode(scale,shape){if(shape<=1)return 0;return scale*Math.pow((shape-1)/shape,1/shape)},sample:function sample(scale,shape){return scale*Math.pow(-Math.log(jStat._random_fn()),1/shape)},variance:function variance(scale,shape){return scale*scale*jStat.gammafn(1+2/shape)-Math.pow(jStat.weibull.mean(scale,shape),2)}});jStat.extend(jStat.uniform,{pdf:function pdf(x,a,b){return x<a||x>b?0:1/(b-a)},cdf:function cdf(x,a,b){if(x<a)return 0;else if(x<b)return(x-a)/(b-a);return 1},inv:function(p,a,b){return a+p*(b-a)},mean:function mean(a,b){return.5*(a+b)},median:function median(a,b){return jStat.mean(a,b)},mode:function mode(){throw new Error("mode is not yet implemented")},sample:function sample(a,b){return a/2+b/2+(b/2-a/2)*(2*jStat._random_fn()-1)},variance:function variance(a,b){return Math.pow(b-a,2)/12}});function betinc(x,a,b,eps){var a0=0;var b0=1;var a1=1;var b1=1;var m9=0;var a2=0;var c9;while(Math.abs((a1-a2)/a1)>eps){a2=a1;c9=-(a+m9)*(a+b+m9)*x/(a+2*m9)/(a+2*m9+1);a0=a1+c9*a0;b0=b1+c9*b0;m9=m9+1;c9=m9*(b-m9)*x/(a+2*m9-1)/(a+2*m9);a1=a0+c9*a1;b1=b0+c9*b1;a0=a0/b1;b0=b0/b1;a1=a1/b1;b1=1}return a1/a}jStat.extend(jStat.binomial,{pdf:function pdf(k,n,p){return p===0||p===1?n*p===k?1:0:jStat.combination(n,k)*Math.pow(p,k)*Math.pow(1-p,n-k)},cdf:function cdf(x,n,p){var betacdf;var eps=1e-10;if(x<0)return 0;if(x>=n)return 1;if(p<0||p>1||n<=0)return NaN;x=Math.floor(x);var z=p;var a=x+1;var b=n-x;var s=a+b;var bt=Math.exp(jStat.gammaln(s)-jStat.gammaln(b)-jStat.gammaln(a)+a*Math.log(z)+b*Math.log(1-z));if(z<(a+1)/(s+2))betacdf=bt*betinc(z,a,b,eps);else betacdf=1-bt*betinc(1-z,b,a,eps);return Math.round((1-betacdf)*(1/eps))/(1/eps)}});jStat.extend(jStat.negbin,{pdf:function pdf(k,r,p){if(k!==k>>>0)return false;if(k<0)return 0;return jStat.combination(k+r-1,r-1)*Math.pow(1-p,k)*Math.pow(p,r)},cdf:function cdf(x,r,p){var sum=0,k=0;if(x<0)return 0;for(;k<=x;k++){sum+=jStat.negbin.pdf(k,r,p)}return sum}});jStat.extend(jStat.hypgeom,{pdf:function pdf(k,N,m,n){if(k!==k|0){return false}else if(k<0||k<m-(N-n)){return 0}else if(k>n||k>m){return 0}else if(m*2>N){if(n*2>N){return jStat.hypgeom.pdf(N-m-n+k,N,N-m,N-n)}else{return jStat.hypgeom.pdf(n-k,N,N-m,n)}}else if(n*2>N){return jStat.hypgeom.pdf(m-k,N,m,N-n)}else if(m<n){return jStat.hypgeom.pdf(k,N,n,m)}else{var scaledPDF=1;var samplesDone=0;for(var i=0;i<k;i++){while(scaledPDF>1&&samplesDone<n){scaledPDF*=1-m/(N-samplesDone);samplesDone++}scaledPDF*=(n-i)*(m-i)/((i+1)*(N-m-n+i+1))}for(;samplesDone<n;samplesDone++){scaledPDF*=1-m/(N-samplesDone)}return Math.min(1,Math.max(0,scaledPDF))}},cdf:function cdf(x,N,m,n){if(x<0||x<m-(N-n)){return 0}else if(x>=n||x>=m){return 1}else if(m*2>N){if(n*2>N){return jStat.hypgeom.cdf(N-m-n+x,N,N-m,N-n)}else{return 1-jStat.hypgeom.cdf(n-x-1,N,N-m,n)}}else if(n*2>N){return 1-jStat.hypgeom.cdf(m-x-1,N,m,N-n)}else if(m<n){return jStat.hypgeom.cdf(x,N,n,m)}else{var scaledCDF=1;var scaledPDF=1;var samplesDone=0;for(var i=0;i<x;i++){while(scaledCDF>1&&samplesDone<n){var factor=1-m/(N-samplesDone);scaledPDF*=factor;scaledCDF*=factor;samplesDone++}scaledPDF*=(n-i)*(m-i)/((i+1)*(N-m-n+i+1));scaledCDF+=scaledPDF}for(;samplesDone<n;samplesDone++){scaledCDF*=1-m/(N-samplesDone)}return Math.min(1,Math.max(0,scaledCDF))}}});jStat.extend(jStat.poisson,{pdf:function pdf(k,l){if(l<0||k%1!==0||k<0){return 0}return Math.pow(l,k)*Math.exp(-l)/jStat.factorial(k)},cdf:function cdf(x,l){var sumarr=[],k=0;if(x<0)return 0;for(;k<=x;k++){sumarr.push(jStat.poisson.pdf(k,l))}return jStat.sum(sumarr)},mean:function(l){return l},variance:function(l){return l},sample:function sample(l){var p=1,k=0,L=Math.exp(-l);do{k++;p*=jStat._random_fn()}while(p>L);return k-1}});jStat.extend(jStat.triangular,{pdf:function pdf(x,a,b,c){if(b<=a||c<a||c>b){return NaN}else{if(x<a||x>b){return 0}else if(x<c){return 2*(x-a)/((b-a)*(c-a))}else if(x===c){return 2/(b-a)}else{return 2*(b-x)/((b-a)*(b-c))}}},cdf:function cdf(x,a,b,c){if(b<=a||c<a||c>b)return NaN;if(x<=a)return 0;else if(x>=b)return 1;if(x<=c)return Math.pow(x-a,2)/((b-a)*(c-a));else return 1-Math.pow(b-x,2)/((b-a)*(b-c))},inv:function inv(p,a,b,c){if(b<=a||c<a||c>b){return NaN}else{if(p<=(c-a)/(b-a)){return a+(b-a)*Math.sqrt(p*((c-a)/(b-a)))}else{return a+(b-a)*(1-Math.sqrt((1-p)*(1-(c-a)/(b-a))))}}},mean:function mean(a,b,c){return(a+b+c)/3},median:function median(a,b,c){if(c<=(a+b)/2){return b-Math.sqrt((b-a)*(b-c))/Math.sqrt(2)}else if(c>(a+b)/2){return a+Math.sqrt((b-a)*(c-a))/Math.sqrt(2)}},mode:function mode(a,b,c){return c},sample:function sample(a,b,c){var u=jStat._random_fn();if(u<(c-a)/(b-a))return a+Math.sqrt(u*(b-a)*(c-a));return b-Math.sqrt((1-u)*(b-a)*(b-c))},variance:function variance(a,b,c){return(a*a+b*b+c*c-a*b-a*c-b*c)/18}});jStat.extend(jStat.arcsine,{pdf:function pdf(x,a,b){if(b<=a)return NaN;return x<=a||x>=b?0:2/Math.PI*Math.pow(Math.pow(b-a,2)-Math.pow(2*x-a-b,2),-.5)},cdf:function cdf(x,a,b){if(x<a)return 0;else if(x<b)return 2/Math.PI*Math.asin(Math.sqrt((x-a)/(b-a)));return 1},inv:function(p,a,b){return a+(.5-.5*Math.cos(Math.PI*p))*(b-a)},mean:function mean(a,b){if(b<=a)return NaN;return(a+b)/2},median:function median(a,b){if(b<=a)return NaN;return(a+b)/2},mode:function mode(){throw new Error("mode is not yet implemented")},sample:function sample(a,b){return(a+b)/2+(b-a)/2*Math.sin(2*Math.PI*jStat.uniform.sample(0,1))},variance:function variance(a,b){if(b<=a)return NaN;return Math.pow(b-a,2)/8}});function laplaceSign(x){return x/Math.abs(x)}jStat.extend(jStat.laplace,{pdf:function pdf(x,mu,b){return b<=0?0:Math.exp(-Math.abs(x-mu)/b)/(2*b)},cdf:function cdf(x,mu,b){if(b<=0){return 0}if(x<mu){return.5*Math.exp((x-mu)/b)}else{return 1-.5*Math.exp(-(x-mu)/b)}},mean:function(mu){return mu},median:function(mu){return mu},mode:function(mu){return mu},variance:function(mu,b){return 2*b*b},sample:function sample(mu,b){var u=jStat._random_fn()-.5;return mu-b*laplaceSign(u)*Math.log(1-2*Math.abs(u))}});function tukeyWprob(w,rr,cc){var nleg=12;var ihalf=6;var C1=-30;var C2=-50;var C3=60;var bb=8;var wlar=3;var wincr1=2;var wincr2=3;var xleg=[.9815606342467192,.9041172563704749,.7699026741943047,.5873179542866175,.3678314989981802,.1252334085114689];var aleg=[.04717533638651183,.10693932599531843,.16007832854334622,.20316742672306592,.2334925365383548,.24914704581340277];var qsqz=w*.5;if(qsqz>=bb)return 1;var pr_w=2*jStat.normal.cdf(qsqz,0,1,1,0)-1;if(pr_w>=Math.exp(C2/cc))pr_w=Math.pow(pr_w,cc);else pr_w=0;var wincr;if(w>wlar)wincr=wincr1;else wincr=wincr2;var blb=qsqz;var binc=(bb-qsqz)/wincr;var bub=blb+binc;var einsum=0;var cc1=cc-1;for(var wi=1;wi<=wincr;wi++){var elsum=0;var a=.5*(bub+blb);var b=.5*(bub-blb);for(var jj=1;jj<=nleg;jj++){var j,xx;if(ihalf<jj){j=nleg-jj+1;xx=xleg[j-1]}else{j=jj;xx=-xleg[j-1]}var c=b*xx;var ac=a+c;var qexpo=ac*ac;if(qexpo>C3)break;var pplus=2*jStat.normal.cdf(ac,0,1,1,0);var pminus=2*jStat.normal.cdf(ac,w,1,1,0);var rinsum=pplus*.5-pminus*.5;if(rinsum>=Math.exp(C1/cc1)){rinsum=aleg[j-1]*Math.exp(-(.5*qexpo))*Math.pow(rinsum,cc1);elsum+=rinsum}}elsum*=2*b*cc/Math.sqrt(2*Math.PI);einsum+=elsum;blb=bub;bub+=binc}pr_w+=einsum;if(pr_w<=Math.exp(C1/rr))return 0;pr_w=Math.pow(pr_w,rr);if(pr_w>=1)return 1;return pr_w}function tukeyQinv(p,c,v){var p0=.322232421088;var q0=.099348462606;var p1=-1;var q1=.588581570495;var p2=-.342242088547;var q2=.531103462366;var p3=-.204231210125;var q3=.10353775285;var p4=-453642210148e-16;var q4=.0038560700634;var c1=.8832;var c2=.2368;var c3=1.214;var c4=1.208;var c5=1.4142;var vmax=120;var ps=.5-.5*p;var yi=Math.sqrt(Math.log(1/(ps*ps)));var t=yi+((((yi*p4+p3)*yi+p2)*yi+p1)*yi+p0)/((((yi*q4+q3)*yi+q2)*yi+q1)*yi+q0);if(v<vmax)t+=(t*t*t+t)/v/4;var q=c1-c2*t;if(v<vmax)q+=-c3/v+c4*t/v;return t*(q*Math.log(c-1)+c5)}jStat.extend(jStat.tukey,{cdf:function cdf(q,nmeans,df){var rr=1;var cc=nmeans;var nlegq=16;var ihalfq=8;var eps1=-30;var eps2=1e-14;var dhaf=100;var dquar=800;var deigh=5e3;var dlarg=25e3;var ulen1=1;var ulen2=.5;var ulen3=.25;var ulen4=.125;var xlegq=[.9894009349916499,.9445750230732326,.8656312023878318,.755404408355003,.6178762444026438,.45801677765722737,.2816035507792589,.09501250983763744];var alegq=[.027152459411754096,.062253523938647894,.09515851168249279,.12462897125553388,.14959598881657674,.16915651939500254,.18260341504492358,.1894506104550685];if(q<=0)return 0;if(df<2||rr<1||cc<2)return NaN;if(!Number.isFinite(q))return 1;if(df>dlarg)return tukeyWprob(q,rr,cc);var f2=df*.5;var f2lf=f2*Math.log(df)-df*Math.log(2)-jStat.gammaln(f2);var f21=f2-1;var ff4=df*.25;var ulen;if(df<=dhaf)ulen=ulen1;else if(df<=dquar)ulen=ulen2;else if(df<=deigh)ulen=ulen3;else ulen=ulen4;f2lf+=Math.log(ulen);var ans=0;for(var i=1;i<=50;i++){var otsum=0;var twa1=(2*i-1)*ulen;for(var jj=1;jj<=nlegq;jj++){var j,t1;if(ihalfq<jj){j=jj-ihalfq-1;t1=f2lf+f21*Math.log(twa1+xlegq[j]*ulen)-(xlegq[j]*ulen+twa1)*ff4}else{j=jj-1;t1=f2lf+f21*Math.log(twa1-xlegq[j]*ulen)+(xlegq[j]*ulen-twa1)*ff4}var qsqz;if(t1>=eps1){if(ihalfq<jj){qsqz=q*Math.sqrt((xlegq[j]*ulen+twa1)*.5)}else{qsqz=q*Math.sqrt((-(xlegq[j]*ulen)+twa1)*.5)}var wprb=tukeyWprob(qsqz,rr,cc);var rotsum=wprb*alegq[j]*Math.exp(t1);otsum+=rotsum}}if(i*ulen>=1&&otsum<=eps2)break;ans+=otsum}if(otsum>eps2){throw new Error("tukey.cdf failed to converge")}if(ans>1)ans=1;return ans},inv:function(p,nmeans,df){var rr=1;var cc=nmeans;var eps=1e-4;var maxiter=50;if(df<2||rr<1||cc<2)return NaN;if(p<0||p>1)return NaN;if(p===0)return 0;if(p===1)return Infinity;var x0=tukeyQinv(p,cc,df);var valx0=jStat.tukey.cdf(x0,nmeans,df)-p;var x1;if(valx0>0)x1=Math.max(0,x0-1);else x1=x0+1;var valx1=jStat.tukey.cdf(x1,nmeans,df)-p;var ans;for(var iter=1;iter<maxiter;iter++){ans=x1-valx1*(x1-x0)/(valx1-valx0);valx0=valx1;x0=x1;if(ans<0){ans=0;valx1=-p}valx1=jStat.tukey.cdf(ans,nmeans,df)-p;x1=ans;var xabs=Math.abs(x1-x0);if(xabs<eps)return ans}throw new Error("tukey.inv failed to converge")}})})(jStat,Math);(function(jStat,Math){var push=Array.prototype.push;var isArray=jStat.utils.isArray;function isUsable(arg){return isArray(arg)||arg instanceof jStat}jStat.extend({add:function add(arr,arg){if(isUsable(arg)){if(!isUsable(arg[0]))arg=[arg];return jStat.map(arr,function(value,row,col){return value+arg[row][col]})}return jStat.map(arr,function(value){return value+arg})},subtract:function subtract(arr,arg){if(isUsable(arg)){if(!isUsable(arg[0]))arg=[arg];return jStat.map(arr,function(value,row,col){return value-arg[row][col]||0})}return jStat.map(arr,function(value){return value-arg})},divide:function divide(arr,arg){if(isUsable(arg)){if(!isUsable(arg[0]))arg=[arg];return jStat.multiply(arr,jStat.inv(arg))}return jStat.map(arr,function(value){return value/arg})},multiply:function multiply(arr,arg){var row,col,nrescols,sum,nrow,ncol,res,rescols;if(arr.length===undefined&&arg.length===undefined){return arr*arg}nrow=arr.length,ncol=arr[0].length,res=jStat.zeros(nrow,nrescols=isUsable(arg)?arg[0].length:ncol),rescols=0;if(isUsable(arg)){for(;rescols<nrescols;rescols++){for(row=0;row<nrow;row++){sum=0;for(col=0;col<ncol;col++)sum+=arr[row][col]*arg[col][rescols];res[row][rescols]=sum}}return nrow===1&&rescols===1?res[0][0]:res}return jStat.map(arr,function(value){return value*arg})},outer:function outer(A,B){return jStat.multiply(A.map(function(t){return[t]}),[B])},dot:function dot(arr,arg){if(!isUsable(arr[0]))arr=[arr];if(!isUsable(arg[0]))arg=[arg];var left=arr[0].length===1&&arr.length!==1?jStat.transpose(arr):arr,right=arg[0].length===1&&arg.length!==1?jStat.transpose(arg):arg,res=[],row=0,nrow=left.length,ncol=left[0].length,sum,col;for(;row<nrow;row++){res[row]=[];sum=0;for(col=0;col<ncol;col++)sum+=left[row][col]*right[row][col];res[row]=sum}return res.length===1?res[0]:res},pow:function pow(arr,arg){return jStat.map(arr,function(value){return Math.pow(value,arg)})},exp:function exp(arr){return jStat.map(arr,function(value){return Math.exp(value)})},log:function exp(arr){return jStat.map(arr,function(value){return Math.log(value)})},abs:function abs(arr){return jStat.map(arr,function(value){return Math.abs(value)})},norm:function norm(arr,p){var nnorm=0,i=0;if(isNaN(p))p=2;if(isUsable(arr[0]))arr=arr[0];for(;i<arr.length;i++){nnorm+=Math.pow(Math.abs(arr[i]),p)}return Math.pow(nnorm,1/p)},angle:function angle(arr,arg){return Math.acos(jStat.dot(arr,arg)/(jStat.norm(arr)*jStat.norm(arg)))},aug:function aug(a,b){var newarr=[];var i;for(i=0;i<a.length;i++){newarr.push(a[i].slice())}for(i=0;i<newarr.length;i++){push.apply(newarr[i],b[i])}return newarr},inv:function inv(a){var rows=a.length;var cols=a[0].length;var b=jStat.identity(rows,cols);var c=jStat.gauss_jordan(a,b);var result=[];var i=0;var j;for(;i<rows;i++){result[i]=[];for(j=cols;j<c[0].length;j++)result[i][j-cols]=c[i][j]}return result},det:function det(a){var alen=a.length,alend=alen*2,vals=new Array(alend),rowshift=alen-1,colshift=alend-1,mrow=rowshift-alen+1,mcol=colshift,i=0,result=0,j;if(alen===2){return a[0][0]*a[1][1]-a[0][1]*a[1][0]}for(;i<alend;i++){vals[i]=1}for(i=0;i<alen;i++){for(j=0;j<alen;j++){vals[mrow<0?mrow+alen:mrow]*=a[i][j];vals[mcol<alen?mcol+alen:mcol]*=a[i][j];mrow++;mcol--}mrow=--rowshift-alen+1;mcol=--colshift}for(i=0;i<alen;i++){result+=vals[i]}for(;i<alend;i++){result-=vals[i]}return result},gauss_elimination:function gauss_elimination(a,b){var i=0,j=0,n=a.length,m=a[0].length,factor=1,sum=0,x=[],maug,pivot,temp,k;a=jStat.aug(a,b);maug=a[0].length;for(i=0;i<n;i++){pivot=a[i][i];j=i;for(k=i+1;k<m;k++){if(pivot<Math.abs(a[k][i])){pivot=a[k][i];j=k}}if(j!=i){for(k=0;k<maug;k++){temp=a[i][k];a[i][k]=a[j][k];a[j][k]=temp}}for(j=i+1;j<n;j++){factor=a[j][i]/a[i][i];for(k=i;k<maug;k++){a[j][k]=a[j][k]-factor*a[i][k]}}}for(i=n-1;i>=0;i--){sum=0;for(j=i+1;j<=n-1;j++){sum=sum+x[j]*a[i][j]}x[i]=(a[i][maug-1]-sum)/a[i][i]}return x},gauss_jordan:function gauss_jordan(a,b){var m=jStat.aug(a,b);var h=m.length;var w=m[0].length;var c=0;var x,y,y2;for(y=0;y<h;y++){var maxrow=y;for(y2=y+1;y2<h;y2++){if(Math.abs(m[y2][y])>Math.abs(m[maxrow][y]))maxrow=y2}var tmp=m[y];m[y]=m[maxrow];m[maxrow]=tmp;for(y2=y+1;y2<h;y2++){c=m[y2][y]/m[y][y];for(x=y;x<w;x++){m[y2][x]-=m[y][x]*c}}}for(y=h-1;y>=0;y--){c=m[y][y];for(y2=0;y2<y;y2++){for(x=w-1;x>y-1;x--){m[y2][x]-=m[y][x]*m[y2][y]/c}}m[y][y]/=c;for(x=h;x<w;x++){m[y][x]/=c}}return m},triaUpSolve:function triaUpSolve(A,b){var size=A[0].length;var x=jStat.zeros(1,size)[0];var parts;var matrix_mode=false;if(b[0].length!=undefined){b=b.map(function(i){return i[0]});matrix_mode=true}jStat.arange(size-1,-1,-1).forEach(function(i){parts=jStat.arange(i+1,size).map(function(j){return x[j]*A[i][j]});x[i]=(b[i]-jStat.sum(parts))/A[i][i]});if(matrix_mode)return x.map(function(i){return[i]});return x},triaLowSolve:function triaLowSolve(A,b){var size=A[0].length;var x=jStat.zeros(1,size)[0];var parts;var matrix_mode=false;if(b[0].length!=undefined){b=b.map(function(i){return i[0]});matrix_mode=true}jStat.arange(size).forEach(function(i){parts=jStat.arange(i).map(function(j){return A[i][j]*x[j]});x[i]=(b[i]-jStat.sum(parts))/A[i][i]});if(matrix_mode)return x.map(function(i){return[i]});return x},lu:function lu(A){var size=A.length;var L=jStat.identity(size);var R=jStat.zeros(A.length,A[0].length);var parts;jStat.arange(size).forEach(function(t){R[0][t]=A[0][t]});jStat.arange(1,size).forEach(function(l){jStat.arange(l).forEach(function(i){parts=jStat.arange(i).map(function(jj){return L[l][jj]*R[jj][i]});L[l][i]=(A[l][i]-jStat.sum(parts))/R[i][i]});jStat.arange(l,size).forEach(function(j){parts=jStat.arange(l).map(function(jj){return L[l][jj]*R[jj][j]});R[l][j]=A[parts.length][j]-jStat.sum(parts)})});return[L,R]},cholesky:function cholesky(A){var size=A.length;var T=jStat.zeros(A.length,A[0].length);var parts;jStat.arange(size).forEach(function(i){parts=jStat.arange(i).map(function(t){return Math.pow(T[i][t],2)});T[i][i]=Math.sqrt(A[i][i]-jStat.sum(parts));jStat.arange(i+1,size).forEach(function(j){parts=jStat.arange(i).map(function(t){return T[i][t]*T[j][t]});T[j][i]=(A[i][j]-jStat.sum(parts))/T[i][i]})});return T},gauss_jacobi:function gauss_jacobi(a,b,x,r){var i=0;var j=0;var n=a.length;var l=[];var u=[];var d=[];var xv,c,h,xk;for(;i<n;i++){l[i]=[];u[i]=[];d[i]=[];for(j=0;j<n;j++){if(i>j){l[i][j]=a[i][j];u[i][j]=d[i][j]=0}else if(i<j){u[i][j]=a[i][j];l[i][j]=d[i][j]=0}else{d[i][j]=a[i][j];l[i][j]=u[i][j]=0}}}h=jStat.multiply(jStat.multiply(jStat.inv(d),jStat.add(l,u)),-1);c=jStat.multiply(jStat.inv(d),b);xv=x;xk=jStat.add(jStat.multiply(h,x),c);i=2;while(Math.abs(jStat.norm(jStat.subtract(xk,xv)))>r){xv=xk;xk=jStat.add(jStat.multiply(h,xv),c);i++}return xk},gauss_seidel:function gauss_seidel(a,b,x,r){var i=0;var n=a.length;var l=[];var u=[];var d=[];var j,xv,c,h,xk;for(;i<n;i++){l[i]=[];u[i]=[];d[i]=[];for(j=0;j<n;j++){if(i>j){l[i][j]=a[i][j];u[i][j]=d[i][j]=0}else if(i<j){u[i][j]=a[i][j];l[i][j]=d[i][j]=0}else{d[i][j]=a[i][j];l[i][j]=u[i][j]=0}}}h=jStat.multiply(jStat.multiply(jStat.inv(jStat.add(d,l)),u),-1);c=jStat.multiply(jStat.inv(jStat.add(d,l)),b);xv=x;xk=jStat.add(jStat.multiply(h,x),c);i=2;while(Math.abs(jStat.norm(jStat.subtract(xk,xv)))>r){xv=xk;xk=jStat.add(jStat.multiply(h,xv),c);i=i+1}return xk},SOR:function SOR(a,b,x,r,w){var i=0;var n=a.length;var l=[];var u=[];var d=[];var j,xv,c,h,xk;for(;i<n;i++){l[i]=[];u[i]=[];d[i]=[];for(j=0;j<n;j++){if(i>j){l[i][j]=a[i][j];u[i][j]=d[i][j]=0}else if(i<j){u[i][j]=a[i][j];l[i][j]=d[i][j]=0}else{d[i][j]=a[i][j];l[i][j]=u[i][j]=0}}}h=jStat.multiply(jStat.inv(jStat.add(d,jStat.multiply(l,w))),jStat.subtract(jStat.multiply(d,1-w),jStat.multiply(u,w)));c=jStat.multiply(jStat.multiply(jStat.inv(jStat.add(d,jStat.multiply(l,w))),b),w);xv=x;xk=jStat.add(jStat.multiply(h,x),c);i=2;while(Math.abs(jStat.norm(jStat.subtract(xk,xv)))>r){xv=xk;xk=jStat.add(jStat.multiply(h,xv),c);i++}return xk},householder:function householder(a){var m=a.length;var n=a[0].length;var i=0;var w=[];var p=[];var alpha,r,k,j,factor;for(;i<m-1;i++){alpha=0;for(j=i+1;j<n;j++)alpha+=a[j][i]*a[j][i];factor=a[i+1][i]>0?-1:1;alpha=factor*Math.sqrt(alpha);r=Math.sqrt((alpha*alpha-a[i+1][i]*alpha)/2);w=jStat.zeros(m,1);w[i+1][0]=(a[i+1][i]-alpha)/(2*r);for(k=i+2;k<m;k++)w[k][0]=a[k][i]/(2*r);p=jStat.subtract(jStat.identity(m,n),jStat.multiply(jStat.multiply(w,jStat.transpose(w)),2));a=jStat.multiply(p,jStat.multiply(a,p))}return a},QR:function(){var sum=jStat.sum;var range=jStat.arange;function qr2(x){var n=x.length;var p=x[0].length;var r=jStat.zeros(p,p);x=jStat.copy(x);var i,j,k;for(j=0;j<p;j++){r[j][j]=Math.sqrt(sum(range(n).map(function(i){return x[i][j]*x[i][j]})));for(i=0;i<n;i++){x[i][j]=x[i][j]/r[j][j]}for(k=j+1;k<p;k++){r[j][k]=sum(range(n).map(function(i){return x[i][j]*x[i][k]}));for(i=0;i<n;i++){x[i][k]=x[i][k]-x[i][j]*r[j][k]}}}return[x,r]}return qr2}(),lstsq:function(){function R_I(A){A=jStat.copy(A);var size=A.length;var I=jStat.identity(size);jStat.arange(size-1,-1,-1).forEach(function(i){jStat.sliceAssign(I,{row:i},jStat.divide(jStat.slice(I,{row:i}),A[i][i]));jStat.sliceAssign(A,{row:i},jStat.divide(jStat.slice(A,{row:i}),A[i][i]));jStat.arange(i).forEach(function(j){var c=jStat.multiply(A[j][i],-1);var Aj=jStat.slice(A,{row:j});var cAi=jStat.multiply(jStat.slice(A,{row:i}),c);jStat.sliceAssign(A,{row:j},jStat.add(Aj,cAi));var Ij=jStat.slice(I,{row:j});var cIi=jStat.multiply(jStat.slice(I,{row:i}),c);jStat.sliceAssign(I,{row:j},jStat.add(Ij,cIi))})});return I}function qr_solve(A,b){var array_mode=false;if(b[0].length===undefined){b=b.map(function(x){return[x]});array_mode=true}var QR=jStat.QR(A);var Q=QR[0];var R=QR[1];var attrs=A[0].length;var Q1=jStat.slice(Q,{col:{end:attrs}});var R1=jStat.slice(R,{row:{end:attrs}});var RI=R_I(R1);var Q2=jStat.transpose(Q1);if(Q2[0].length===undefined){Q2=[Q2]}var x=jStat.multiply(jStat.multiply(RI,Q2),b);if(x.length===undefined){x=[[x]]}if(array_mode)return x.map(function(i){return i[0]});return x}return qr_solve}(),jacobi:function jacobi(a){var condition=1;var n=a.length;var e=jStat.identity(n,n);var ev=[];var b,i,j,p,q,maxim,theta,s;while(condition===1){maxim=a[0][1];p=0;q=1;for(i=0;i<n;i++){for(j=0;j<n;j++){if(i!=j){if(maxim<Math.abs(a[i][j])){maxim=Math.abs(a[i][j]);p=i;q=j}}}}if(a[p][p]===a[q][q])theta=a[p][q]>0?Math.PI/4:-Math.PI/4;else theta=Math.atan(2*a[p][q]/(a[p][p]-a[q][q]))/2;s=jStat.identity(n,n);s[p][p]=Math.cos(theta);s[p][q]=-Math.sin(theta);s[q][p]=Math.sin(theta);s[q][q]=Math.cos(theta);e=jStat.multiply(e,s);b=jStat.multiply(jStat.multiply(jStat.inv(s),a),s);a=b;condition=0;for(i=1;i<n;i++){for(j=1;j<n;j++){if(i!=j&&Math.abs(a[i][j])>.001){condition=1}}}}for(i=0;i<n;i++)ev.push(a[i][i]);return[e,ev]},rungekutta:function rungekutta(f,h,p,t_j,u_j,order){var k1,k2,u_j1,k3,k4;if(order===2){while(t_j<=p){k1=h*f(t_j,u_j);k2=h*f(t_j+h,u_j+k1);u_j1=u_j+(k1+k2)/2;u_j=u_j1;t_j=t_j+h}}if(order===4){while(t_j<=p){k1=h*f(t_j,u_j);k2=h*f(t_j+h/2,u_j+k1/2);k3=h*f(t_j+h/2,u_j+k2/2);k4=h*f(t_j+h,u_j+k3);u_j1=u_j+(k1+2*k2+2*k3+k4)/6;u_j=u_j1;t_j=t_j+h}}return u_j},romberg:function romberg(f,a,b,order){var i=0;var h=(b-a)/2;var x=[];var h1=[];var g=[];var m,a1,j,k,I;while(i<order/2){I=f(a);for(j=a,k=0;j<=b;j=j+h,k++)x[k]=j;m=x.length;for(j=1;j<m-1;j++){I+=(j%2!==0?4:2)*f(x[j])}I=h/3*(I+f(b));g[i]=I;h/=2;i++}a1=g.length;m=1;while(a1!==1){for(j=0;j<a1-1;j++)h1[j]=(Math.pow(4,m)*g[j+1]-g[j])/(Math.pow(4,m)-1);a1=h1.length;g=h1;h1=[];m++}return g},richardson:function richardson(X,f,x,h){function pos(X,x){var i=0;var n=X.length;var p;for(;i<n;i++)if(X[i]===x)p=i;return p}var h_min=Math.abs(x-X[pos(X,x)+1]);var i=0;var g=[];var h1=[];var y1,y2,m,a,j;while(h>=h_min){y1=pos(X,x+h);y2=pos(X,x);g[i]=(f[y1]-2*f[y2]+f[2*y2-y1])/(h*h);h/=2;i++}a=g.length;m=1;while(a!=1){for(j=0;j<a-1;j++)h1[j]=(Math.pow(4,m)*g[j+1]-g[j])/(Math.pow(4,m)-1);a=h1.length;g=h1;h1=[];m++}return g},simpson:function simpson(f,a,b,n){var h=(b-a)/n;var I=f(a);var x=[];var j=a;var k=0;var i=1;var m;for(;j<=b;j=j+h,k++)x[k]=j;m=x.length;for(;i<m-1;i++){I+=(i%2!==0?4:2)*f(x[i])}return h/3*(I+f(b))},hermite:function hermite(X,F,dF,value){var n=X.length;var p=0;var i=0;var l=[];var dl=[];var A=[];var B=[];var j;for(;i<n;i++){l[i]=1;for(j=0;j<n;j++){if(i!=j)l[i]*=(value-X[j])/(X[i]-X[j])}dl[i]=0;for(j=0;j<n;j++){if(i!=j)dl[i]+=1/(X[i]-X[j])}A[i]=(1-2*(value-X[i])*dl[i])*(l[i]*l[i]);B[i]=(value-X[i])*(l[i]*l[i]);p+=A[i]*F[i]+B[i]*dF[i]}return p},lagrange:function lagrange(X,F,value){var p=0;var i=0;var j,l;var n=X.length;for(;i<n;i++){l=F[i];for(j=0;j<n;j++){if(i!=j)l*=(value-X[j])/(X[i]-X[j])}p+=l}return p},cubic_spline:function cubic_spline(X,F,value){var n=X.length;var i=0,j;var A=[];var B=[];var alpha=[];var c=[];var h=[];var b=[];var d=[];for(;i<n-1;i++)h[i]=X[i+1]-X[i];alpha[0]=0;for(i=1;i<n-1;i++){alpha[i]=3/h[i]*(F[i+1]-F[i])-3/h[i-1]*(F[i]-F[i-1])}for(i=1;i<n-1;i++){A[i]=[];B[i]=[];A[i][i-1]=h[i-1];A[i][i]=2*(h[i-1]+h[i]);A[i][i+1]=h[i];B[i][0]=alpha[i]}c=jStat.multiply(jStat.inv(A),B);for(j=0;j<n-1;j++){b[j]=(F[j+1]-F[j])/h[j]-h[j]*(c[j+1][0]+2*c[j][0])/3;d[j]=(c[j+1][0]-c[j][0])/(3*h[j])}for(j=0;j<n;j++){if(X[j]>value)break}j-=1;return F[j]+(value-X[j])*b[j]+jStat.sq(value-X[j])*c[j]+(value-X[j])*jStat.sq(value-X[j])*d[j]},gauss_quadrature:function gauss_quadrature(){throw new Error("gauss_quadrature not yet implemented")},PCA:function PCA(X){var m=X.length;var n=X[0].length;var i=0;var j,temp1;var u=[];var D=[];var result=[];var temp2=[];var Y=[];var Bt=[];var B=[];var C=[];var V=[];var Vt=[];for(i=0;i<m;i++){u[i]=jStat.sum(X[i])/n}for(i=0;i<n;i++){B[i]=[];for(j=0;j<m;j++){B[i][j]=X[j][i]-u[j]}}B=jStat.transpose(B);for(i=0;i<m;i++){C[i]=[];for(j=0;j<m;j++){C[i][j]=jStat.dot([B[i]],[B[j]])/(n-1)}}result=jStat.jacobi(C);V=result[0];D=result[1];Vt=jStat.transpose(V);for(i=0;i<D.length;i++){for(j=i;j<D.length;j++){if(D[i]<D[j]){temp1=D[i];D[i]=D[j];D[j]=temp1;temp2=Vt[i];Vt[i]=Vt[j];Vt[j]=temp2}}}Bt=jStat.transpose(B);for(i=0;i<m;i++){Y[i]=[];for(j=0;j<Bt.length;j++){Y[i][j]=jStat.dot([Vt[i]],[Bt[j]])}}return[X,D,Vt,Y]}});(function(funcs){for(var i=0;i<funcs.length;i++)(function(passfunc){jStat.fn[passfunc]=function(arg,func){var tmpthis=this;if(func){setTimeout(function(){func.call(tmpthis,jStat.fn[passfunc].call(tmpthis,arg))},15);return this}if(typeof jStat[passfunc](this,arg)==="number")return jStat[passfunc](this,arg);else return jStat(jStat[passfunc](this,arg))}})(funcs[i])})("add divide multiply subtract dot pow exp log abs norm angle".split(" "))})(jStat,Math);(function(jStat,Math){var slice=[].slice;var isNumber=jStat.utils.isNumber;var isArray=jStat.utils.isArray;jStat.extend({zscore:function zscore(){var args=slice.call(arguments);if(isNumber(args[1])){return(args[0]-args[1])/args[2]}return(args[0]-jStat.mean(args[1]))/jStat.stdev(args[1],args[2])},ztest:function ztest(){var args=slice.call(arguments);var z;if(isArray(args[1])){z=jStat.zscore(args[0],args[1],args[3]);return args[2]===1?jStat.normal.cdf(-Math.abs(z),0,1):jStat.normal.cdf(-Math.abs(z),0,1)*2}else{if(args.length>2){z=jStat.zscore(args[0],args[1],args[2]);return args[3]===1?jStat.normal.cdf(-Math.abs(z),0,1):jStat.normal.cdf(-Math.abs(z),0,1)*2}else{z=args[0];return args[1]===1?jStat.normal.cdf(-Math.abs(z),0,1):jStat.normal.cdf(-Math.abs(z),0,1)*2}}}});jStat.extend(jStat.fn,{zscore:function zscore(value,flag){return(value-this.mean())/this.stdev(flag)},ztest:function ztest(value,sides,flag){var zscore=Math.abs(this.zscore(value,flag));return sides===1?jStat.normal.cdf(-zscore,0,1):jStat.normal.cdf(-zscore,0,1)*2}});jStat.extend({tscore:function tscore(){var args=slice.call(arguments);return args.length===4?(args[0]-args[1])/(args[2]/Math.sqrt(args[3])):(args[0]-jStat.mean(args[1]))/(jStat.stdev(args[1],true)/Math.sqrt(args[1].length))},ttest:function ttest(){var args=slice.call(arguments);var tscore;if(args.length===5){tscore=Math.abs(jStat.tscore(args[0],args[1],args[2],args[3]));return args[4]===1?jStat.studentt.cdf(-tscore,args[3]-1):jStat.studentt.cdf(-tscore,args[3]-1)*2}if(isNumber(args[1])){tscore=Math.abs(args[0]);return args[2]==1?jStat.studentt.cdf(-tscore,args[1]-1):jStat.studentt.cdf(-tscore,args[1]-1)*2}tscore=Math.abs(jStat.tscore(args[0],args[1]));return args[2]==1?jStat.studentt.cdf(-tscore,args[1].length-1):jStat.studentt.cdf(-tscore,args[1].length-1)*2}});jStat.extend(jStat.fn,{tscore:function tscore(value){return(value-this.mean())/(this.stdev(true)/Math.sqrt(this.cols()))},ttest:function ttest(value,sides){return sides===1?1-jStat.studentt.cdf(Math.abs(this.tscore(value)),this.cols()-1):jStat.studentt.cdf(-Math.abs(this.tscore(value)),this.cols()-1)*2}});jStat.extend({anovafscore:function anovafscore(){var args=slice.call(arguments),expVar,sample,sampMean,sampSampMean,tmpargs,unexpVar,i,j;if(args.length===1){tmpargs=new Array(args[0].length);for(i=0;i<args[0].length;i++){tmpargs[i]=args[0][i]}args=tmpargs}sample=new Array;for(i=0;i<args.length;i++){sample=sample.concat(args[i])}sampMean=jStat.mean(sample);expVar=0;for(i=0;i<args.length;i++){expVar=expVar+args[i].length*Math.pow(jStat.mean(args[i])-sampMean,2)}expVar/=args.length-1;unexpVar=0;for(i=0;i<args.length;i++){sampSampMean=jStat.mean(args[i]);for(j=0;j<args[i].length;j++){unexpVar+=Math.pow(args[i][j]-sampSampMean,2)}}unexpVar/=sample.length-args.length;return expVar/unexpVar},anovaftest:function anovaftest(){var args=slice.call(arguments),df1,df2,n,i;if(isNumber(args[0])){return 1-jStat.centralF.cdf(args[0],args[1],args[2])}var anovafscore=jStat.anovafscore(args);df1=args.length-1;n=0;for(i=0;i<args.length;i++){n=n+args[i].length}df2=n-df1-1;return 1-jStat.centralF.cdf(anovafscore,df1,df2)},ftest:function ftest(fscore,df1,df2){return 1-jStat.centralF.cdf(fscore,df1,df2)}});jStat.extend(jStat.fn,{anovafscore:function anovafscore(){return jStat.anovafscore(this.toArray())},anovaftes:function anovaftes(){var n=0;var i;for(i=0;i<this.length;i++){n=n+this[i].length}return jStat.ftest(this.anovafscore(),this.length-1,n-this.length)}});jStat.extend({qscore:function qscore(){var args=slice.call(arguments);var mean1,mean2,n1,n2,sd;if(isNumber(args[0])){mean1=args[0];mean2=args[1];n1=args[2];n2=args[3];sd=args[4]}else{mean1=jStat.mean(args[0]);mean2=jStat.mean(args[1]);n1=args[0].length;n2=args[1].length;sd=args[2]}return Math.abs(mean1-mean2)/(sd*Math.sqrt((1/n1+1/n2)/2))},qtest:function qtest(){var args=slice.call(arguments);var qscore;if(args.length===3){qscore=args[0];args=args.slice(1)}else if(args.length===7){qscore=jStat.qscore(args[0],args[1],args[2],args[3],args[4]);args=args.slice(5)}else{qscore=jStat.qscore(args[0],args[1],args[2]);args=args.slice(3)}var n=args[0];var k=args[1];return 1-jStat.tukey.cdf(qscore,k,n-k)},tukeyhsd:function tukeyhsd(arrays){var sd=jStat.pooledstdev(arrays);var means=arrays.map(function(arr){return jStat.mean(arr)});var n=arrays.reduce(function(n,arr){return n+arr.length},0);var results=[];for(var i=0;i<arrays.length;++i){for(var j=i+1;j<arrays.length;++j){var p=jStat.qtest(means[i],means[j],arrays[i].length,arrays[j].length,sd,n,arrays.length);results.push([[i,j],p])}}return results}});jStat.extend({normalci:function normalci(){var args=slice.call(arguments),ans=new Array(2),change;if(args.length===4){change=Math.abs(jStat.normal.inv(args[1]/2,0,1)*args[2]/Math.sqrt(args[3]))}else{change=Math.abs(jStat.normal.inv(args[1]/2,0,1)*jStat.stdev(args[2])/Math.sqrt(args[2].length))}ans[0]=args[0]-change;ans[1]=args[0]+change;return ans},tci:function tci(){var args=slice.call(arguments),ans=new Array(2),change;if(args.length===4){change=Math.abs(jStat.studentt.inv(args[1]/2,args[3]-1)*args[2]/Math.sqrt(args[3]))}else{change=Math.abs(jStat.studentt.inv(args[1]/2,args[2].length-1)*jStat.stdev(args[2],true)/Math.sqrt(args[2].length))}ans[0]=args[0]-change;ans[1]=args[0]+change;return ans},significant:function significant(pvalue,alpha){return pvalue<alpha}});jStat.extend(jStat.fn,{normalci:function normalci(value,alpha){return jStat.normalci(value,alpha,this.toArray())},tci:function tci(value,alpha){return jStat.tci(value,alpha,this.toArray())}});function differenceOfProportions(p1,n1,p2,n2){if(p1>1||p2>1||p1<=0||p2<=0){throw new Error("Proportions should be greater than 0 and less than 1")}var pooled=(p1*n1+p2*n2)/(n1+n2);var se=Math.sqrt(pooled*(1-pooled)*(1/n1+1/n2));return(p1-p2)/se}jStat.extend(jStat.fn,{oneSidedDifferenceOfProportions:function oneSidedDifferenceOfProportions(p1,n1,p2,n2){var z=differenceOfProportions(p1,n1,p2,n2);return jStat.ztest(z,1)},twoSidedDifferenceOfProportions:function twoSidedDifferenceOfProportions(p1,n1,p2,n2){var z=differenceOfProportions(p1,n1,p2,n2);return jStat.ztest(z,2)}})})(jStat,Math);jStat.models=function(){function sub_regress(exog){var var_count=exog[0].length;var modelList=jStat.arange(var_count).map(function(endog_index){var exog_index=jStat.arange(var_count).filter(function(i){return i!==endog_index});return ols(jStat.col(exog,endog_index).map(function(x){return x[0]}),jStat.col(exog,exog_index))});return modelList}function ols(endog,exog){var nobs=endog.length;var df_model=exog[0].length-1;var df_resid=nobs-df_model-1;var coef=jStat.lstsq(exog,endog);var predict=jStat.multiply(exog,coef.map(function(x){return[x]})).map(function(p){return p[0]});var resid=jStat.subtract(endog,predict);var ybar=jStat.mean(endog);var SSE=jStat.sum(predict.map(function(f){return Math.pow(f-ybar,2)}));var SSR=jStat.sum(endog.map(function(y,i){return Math.pow(y-predict[i],2)}));var SST=SSE+SSR;var R2=SSE/SST;return{exog:exog,endog:endog,nobs:nobs,df_model:df_model,df_resid:df_resid,coef:coef,predict:predict,resid:resid,ybar:ybar,SST:SST,SSE:SSE,SSR:SSR,R2:R2}}function t_test(model){var subModelList=sub_regress(model.exog);var sigmaHat=Math.sqrt(model.SSR/model.df_resid);var seBetaHat=subModelList.map(function(mod){var SST=mod.SST;var R2=mod.R2;return sigmaHat/Math.sqrt(SST*(1-R2))});var tStatistic=model.coef.map(function(coef,i){return(coef-0)/seBetaHat[i]});var pValue=tStatistic.map(function(t){var leftppf=jStat.studentt.cdf(t,model.df_resid);return(leftppf>.5?1-leftppf:leftppf)*2});var c=jStat.studentt.inv(.975,model.df_resid);var interval95=model.coef.map(function(coef,i){var d=c*seBetaHat[i];return[coef-d,coef+d]});return{se:seBetaHat,t:tStatistic,p:pValue,sigmaHat:sigmaHat,interval95:interval95}}function F_test(model){var F_statistic=model.R2/model.df_model/((1-model.R2)/model.df_resid);var fcdf=function(x,n1,n2){return jStat.beta.cdf(x/(n2/n1+x),n1/2,n2/2)};var pvalue=1-fcdf(F_statistic,model.df_model,model.df_resid);return{F_statistic:F_statistic,pvalue:pvalue}}function ols_wrap(endog,exog){var model=ols(endog,exog);var ttest=t_test(model);var ftest=F_test(model);var adjust_R2=1-(1-model.R2)*((model.nobs-1)/model.df_resid);model.t=ttest;model.f=ftest;model.adjust_R2=adjust_R2;return model}return{ols:ols_wrap}}();jStat.extend({buildxmatrix:function buildxmatrix(){var matrixRows=new Array(arguments.length);for(var i=0;i<arguments.length;i++){var array=[1];matrixRows[i]=array.concat(arguments[i])}return jStat(matrixRows)},builddxmatrix:function builddxmatrix(){var matrixRows=new Array(arguments[0].length);for(var i=0;i<arguments[0].length;i++){var array=[1];matrixRows[i]=array.concat(arguments[0][i])}return jStat(matrixRows)},buildjxmatrix:function buildjxmatrix(jMat){var pass=new Array(jMat.length);for(var i=0;i<jMat.length;i++){pass[i]=jMat[i]}return jStat.builddxmatrix(pass)},buildymatrix:function buildymatrix(array){return jStat(array).transpose()},buildjymatrix:function buildjymatrix(jMat){return jMat.transpose()},matrixmult:function matrixmult(A,B){var i,j,k,result,sum;if(A.cols()==B.rows()){if(B.rows()>1){result=[];for(i=0;i<A.rows();i++){result[i]=[];for(j=0;j<B.cols();j++){sum=0;for(k=0;k<A.cols();k++){sum+=A.toArray()[i][k]*B.toArray()[k][j]}result[i][j]=sum}}return jStat(result)}result=[];for(i=0;i<A.rows();i++){result[i]=[];for(j=0;j<B.cols();j++){sum=0;for(k=0;k<A.cols();k++){sum+=A.toArray()[i][k]*B.toArray()[j]}result[i][j]=sum}}return jStat(result)}},regress:function regress(jMatX,jMatY){var innerinv=jStat.xtranspxinv(jMatX);var xtransp=jMatX.transpose();var next=jStat.matrixmult(jStat(innerinv),xtransp);return jStat.matrixmult(next,jMatY)},regresst:function regresst(jMatX,jMatY,sides){var beta=jStat.regress(jMatX,jMatY);var compile={};compile.anova={};var jMatYBar=jStat.jMatYBar(jMatX,beta);compile.yBar=jMatYBar;var yAverage=jMatY.mean();compile.anova.residuals=jStat.residuals(jMatY,jMatYBar);compile.anova.ssr=jStat.ssr(jMatYBar,yAverage);compile.anova.msr=compile.anova.ssr/(jMatX[0].length-1);compile.anova.sse=jStat.sse(jMatY,jMatYBar);compile.anova.mse=compile.anova.sse/(jMatY.length-(jMatX[0].length-1)-1);compile.anova.sst=jStat.sst(jMatY,yAverage);compile.anova.mst=compile.anova.sst/(jMatY.length-1);compile.anova.r2=1-compile.anova.sse/compile.anova.sst;if(compile.anova.r2<0)compile.anova.r2=0;compile.anova.fratio=compile.anova.msr/compile.anova.mse;compile.anova.pvalue=jStat.anovaftest(compile.anova.fratio,jMatX[0].length-1,jMatY.length-(jMatX[0].length-1)-1);compile.anova.rmse=Math.sqrt(compile.anova.mse);compile.anova.r2adj=1-compile.anova.mse/compile.anova.mst;if(compile.anova.r2adj<0)compile.anova.r2adj=0;compile.stats=new Array(jMatX[0].length);var covar=jStat.xtranspxinv(jMatX);var sds,ts,ps;for(var i=0;i<beta.length;i++){sds=Math.sqrt(compile.anova.mse*Math.abs(covar[i][i]));ts=Math.abs(beta[i]/sds);ps=jStat.ttest(ts,jMatY.length-jMatX[0].length-1,sides);compile.stats[i]=[beta[i],sds,ts,ps]}compile.regress=beta;return compile},xtranspx:function xtranspx(jMatX){return jStat.matrixmult(jMatX.transpose(),jMatX)},xtranspxinv:function xtranspxinv(jMatX){var inner=jStat.matrixmult(jMatX.transpose(),jMatX);var innerinv=jStat.inv(inner);return innerinv},jMatYBar:function jMatYBar(jMatX,beta){var yBar=jStat.matrixmult(jMatX,beta);return new jStat(yBar)},residuals:function residuals(jMatY,jMatYBar){return jStat.matrixsubtract(jMatY,jMatYBar)},ssr:function ssr(jMatYBar,yAverage){var ssr=0;for(var i=0;i<jMatYBar.length;i++){ssr+=Math.pow(jMatYBar[i]-yAverage,2)}return ssr},sse:function sse(jMatY,jMatYBar){var sse=0;for(var i=0;i<jMatY.length;i++){sse+=Math.pow(jMatY[i]-jMatYBar[i],2)}return sse},sst:function sst(jMatY,yAverage){var sst=0;for(var i=0;i<jMatY.length;i++){sst+=Math.pow(jMatY[i]-yAverage,2)}return sst},matrixsubtract:function matrixsubtract(A,B){var ans=new Array(A.length);for(var i=0;i<A.length;i++){ans[i]=new Array(A[i].length);for(var j=0;j<A[i].length;j++){ans[i][j]=A[i][j]-B[i][j]}}return jStat(ans)}});jStat.jStat=jStat;return jStat});
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