jStat/doc/md/distributions.md

## Distributions


### jStat.beta( alpha, beta )

#### jStat.beta.pdf( x, alpha, beta )

Returns the value of `x` in the Beta distribution with parameters `alpha` and `beta`.

#### jStat.beta.cdf( x, alpha, beta )

Returns the value of `x` in the cdf for the Beta distribution with parameters `alpha` and `beta`.

#### jStat.beta.inv( p, alpha, beta )

Returns the value of `p` in the inverse of the cdf for the Beta distribution with parameters `alpha` and `beta`.

#### jStat.beta.mean( alpha, beta )

Returns the mean of the Beta distribution with parameters `alpha` and `beta`.

#### jStat.beta.median( alpha, beta )

Returns the median of the Beta distribution with parameters `alpha` and `beta`.

#### jStat.beta.mode( alpha, beta )

Returns the mode of the Beta distribution with parameters `alpha` and `beta`.

#### jStat.beta.sample( alpha, beta )

Returns a random number whose distribution is the Beta distribution with parameters `alpha` and `beta`.

#### jStat.beta.variance( alpha, beta )

Returns the variance of the Beta distribution with parameters `alpha` and `beta`.

### jStat.centralF( df1, df2 )

The F Distrbution is used frequently in analyses of variance. The distribution is parameterized by two degrees of freedom (`df1` and `df2`). It is defined continuously on x in [0, infinity).

In all cases, `df1` is the "numerator degrees of freedom" and `df2` is the "denominator degrees of freedom", which parameterize the distribtuion.

#### jStat.centralF.pdf( x, df1, df2 )

Given `x` in the range [0, infinity), returns the probability density of the (central) F distribution at `x`.

This function corresponds to the `df(x, df1, df2)` function in R.

#### jStat.centralF.cdf( x, df1, df2 )

Given x in the range [0, infinity), returns the cumulative probability density of the central F distribution. That is, `jStat.centralF.cdf(2.5, 10, 20)` will return the probability that a number randomly selected from the central F distribution with `df1 = 10` and `df2 = 20` will be less than 2.5.

This function corresponds to the `pf(q, df1, df2)` function in R.

#### jStat.centralF.inv( p, df1, df2 )

Given `p` in [0, 1), returns the value of x for which the cumulative probability density of the central F distribution is p. That is, `jStat.centralF.inv(p, df1, df2) = x` if and only if `jStat.centralF.inv(x, df1, df2) = p`.

This function corresponds to the `qf(p, df1, df2)` function in R.

#### jStat.centralF.mean( df1, df2 )

Returns the mean of the (Central) F distribution.

#### jStat.centralF.mode( df1, df2 )

Returns the mode of the (Central) F distribution.

#### jStat.centralF.sample( df1, df2 )

Returns a random number whose distribution is the (Central) F distribution.

This function corresponds to the `rf(n, df1, df2)` function in R.

#### jStat.centralF.variance( df1, df2 )

Returns the variance of the (Central) F distribution.

### jStat.cauchy( local, scale )

#### jStat.cauchy.pdf( x, local, scale )

Returns the value of `x` in the pdf of the Cauchy distribution with a location (median) of `local` and scale factor of `scale`.

#### jStat.cauchy.cdf( x, local, scale )

Returns the value of `x` in the cdf of the Cauchy distribution with a location (median) of `local` and scale factor of `scale`.

#### jStat.cauchy.inv( p, local, scale )

Returns the value of `p` in the inverse of the cdf for the Cauchy distribution with a location (median) of `local` and scale factor of `scale`.

#### jStat.cauchy.median( local, scale )

Returns the value of the median for the Cauchy distribution with a location (median) of `local` and scale factor of `scale`.

#### jStat.cauchy.mode( local, scale )

Returns the value of the mode for the Cauchy distribution with a location (median) of `local` and scale factor of `scale`.

#### jStat.cauchy.sample( local, scale )

Returns a random number whose distribution is the Cauchy distribution with a location (median) of `local` and scale factor of `scale`.

#### jStat.cauchy.variance( local, scale )

Returns the value of the variance for the Cauchy distribution with a location (median) of `local` and scale factor of `scale`.

### jStat.chisquare( dof )

#### jStat.chisquare.pdf( x, dof )

Returns the value of `x` in the pdf of the Chi Square distribution with `dof` degrees of freedom.

#### jStat.chisquare.cdf( x, dof )

Returns the value of `x` in the cdf of the Chi Square distribution with `dof` degrees of freedom.

#### jStat.chisquare.inv( p, dof )

Returns the value of `x` in the inverse of the cdf for the Chi Square distribution with `dof` degrees of freedom.

#### jStat.chisquare.mean( dof )

Returns the value of the mean for the Chi Square distribution with `dof` degrees of freedom.

#### jStat.chisquare.median( dof )

Returns the value of the median for the Chi Square distribution with `dof` degrees of freedom.

#### jStat.chisquare.mode( dof )

Returns the value of the mode for the Chi Square distribution with `dof` degrees of freedom.

#### jStat.chisquare.sample( dof )

Returns a random number whose distribution is the Chi Square distribution with `dof` degrees of freedom.

#### jStat.chisquare.variance( dof )

Returns the value of the variance for the Chi Square distribution with `dof` degrees of freedom.


### jStat.exponential( rate )

#### jStat.exponential.pdf( x, rate )

Returns the value of `x` in the pdf of the Exponential distribution with the parameter `rate` (lambda).

#### jStat.exponential.cdf( x, rate )

Returns the value of `x` in the cdf of the Exponential distribution with the parameter `rate` (lambda).

#### jStat.exponential.inv( p, rate )

Returns the value of `p` in the inverse of the cdf for the Exponential distribution with the parameter `rate` (lambda).

#### jStat.exponential.mean( rate )

Returns the value of the mean for the Exponential distribution with the parameter `rate` (lambda).

#### jStat.exponential.median( rate )

Returns the value of the median for the Exponential distribution with the parameter `rate` (lambda)

#### jStat.exponential.mode( rate )

Returns the value of the mode for the Exponential distribution with the parameter `rate` (lambda).

#### jStat.exponential.sample( rate )

Returns a random number whose distribution is the Exponential distribution with the parameter `rate` (lambda).

#### jStat.exponential.variance( rate )

Returns the value of the variance for the Exponential distribution with the parameter `rate` (lambda).

### jStat.gamma( shape, scale )

#### jStat.gamma.pdf( x, shape, scale )

Returns the value of `x` in the pdf of the Gamma distribution with the parameters `shape` (k) and `scale` (theta). Notice that if using the alpha beta convention, `scale = 1/beta`.

#### jStat.gamma.cdf( x, shape, scale )

Returns the value of `x` in the cdf of the Gamma distribution with the parameters `shape` (k) and `scale` (theta). Notice that if using the alpha beta convention, `scale = 1/beta`.

This function is checked against R's `pgamma` function.

#### jStat.gamma.inv( p, shape, scale )

Returns the value of `p` in the inverse of the cdf for the Gamma distribution with the parameters `shape` (k) and `scale` (theta). Notice that if using the alpha beta convention, `scale = 1/beta`.

This function is checked against R's `qgamma` function.

#### jStat.gamma.mean( shape, scale )

Returns the value of the mean for the Gamma distribution with the parameters `shape` (k) and `scale` (theta). Notice that if using the alpha beta convention, `scale = 1/beta`.

#### jStat.gamma.mode( shape, scale )

Returns the value of the mode for the Gamma distribution with the parameters `shape` (k) and `scale` (theta). Notice that if using the alpha beta convention, `scale = 1/beta`.

#### jStat.gamma.sample( shape, scale )

Returns a random number whose distribution is the Gamma distribution with the parameters `shape` (k) and `scale` (theta). Notice that if using the alpha beta convention, `scale = 1/beta`.

#### jStat.gamma.variance( shape, scale )

Returns the value of the variance for the Gamma distribution with the parameters `shape` (k) and `scale` (theta). Notice that if using the alpha beta convention, `scale = 1/beta`.

### jStat.invgamma( shape, scale )

#### jStat.invgamma.pdf( x, shape, scale )

Returns the value of `x` in the pdf of the Inverse-Gamma distribution with parametres `shape` (alpha) and `scale` (beta).

#### jStat.invgamma.cdf( x, shape, scale )

Returns the value of `x` in the cdf of the Inverse-Gamma distribution with parametres `shape` (alpha) and `scale` (beta).

#### jStat.invgamma.inv( p, shape, scale )

Returns the value of `p` in the inverse of the cdf for the Inverse-Gamma distribution with parametres `shape` (alpha) and `scale` (beta).

#### jStat.invgamma.mean( shape, scale )

Returns the value of the mean for the Inverse-Gamma distribution with parametres `shape` (alpha) and `scale` (beta).

#### jStat.invgamma.mode( shape, scale )

Returns the value of the mode for the Inverse-Gamma distribution with parametres `shape` (alpha) and `scale` (beta).

#### jStat.invgamma.sample( shape, scale )

Returns a random number whose distribution is the Inverse-Gamma distribution with parametres `shape` (alpha) and `scale` (beta).

#### jStat.invgamma.variance( shape, scale )

Returns the value of the variance for the Inverse-Gamma distribution with parametres `shape` (alpha) and `scale` (beta).

### jStat.kumaraswamy( alpha, beta )

#### jStat.kumaraswamy.pdf( x, a, b )

Returns the value of `x` in the pdf of the Kumaraswamy distribution with parameters `a` and `b`.

#### jStat.kumaraswamy.cdf( x, alpha, beta )

Returns the value of `x` in the cdf of the Kumaraswamy distribution with parameters `alpha` and `beta`.

#### jStat.kumaraswamy.inv( p, alpha, beta )

Returns the value of `p` in the inverse of the pdf for the Kumaraswamy distribution with parametres `alpha` and `beta`.

This function corresponds to `qkumar(p, alpha, beta)` in R's VGAM package.

#### jStat.kumaraswamy.mean( alpha, beta )

Returns the value of the mean of the Kumaraswamy distribution with parameters `alpha` and `beta`.

#### jStat.kumaraswamy.median( alpha, beta )

Returns the value of the median of the Kumaraswamy distribution with parameters `alpha` and `beta`.

#### jStat.kumaraswamy.mode( alpha, beta )

Returns the value of the mode of the Kumaraswamy distribution with parameters `alpha` and `beta`.

#### jStat.kumaraswamy.variance( alpha, beta )

Returns the value of the variance of the Kumaraswamy distribution with parameters `alpha` and `beta`.

### jStat.lognormal( mu, sigma )

#### jStat.lognormal.pdf( x, mu, sigma )

Returns the value of `x` in the pdf of the Log-normal distribution with paramters `mu` (mean) and `sigma` (standard deviation).

#### jStat.lognormal.cdf( x, mu, sigma )

Returns the value of `x` in the cdf of the Log-normal distribution with paramters `mu` (mean) and `sigma` (standard deviation).

#### jStat.lognormal.inv( p, mu, sigma )

Returns the value of `x` in the inverse of the cdf for the Log-normal distribution with paramters `mu` (mean of the Normal distribution) and `sigma` (standard deviation of the Normal distribution).

#### jStat.lognormal.mean( mu, sigma )

Returns the value of the mean for the Log-normal distribution with paramters `mu` (mean of the Normal distribution) and `sigma` (standard deviation of the Normal distribution).

#### jStat.lognormal.median( mu, sigma )

Returns the value of the median for the Log-normal distribution with paramters `mu` (mean of the Normal distribution) and `sigma` (standard deviation of the Normal distribution).

#### jStat.lognormal.mode( mu, sigma )

Returns the value of the mode for the Log-normal distribution with paramters `mu` (mean of the Normal distribution) and `sigma` (standard deviation of the Normal distribution).

#### jStat.lognormal.sample( mu, sigma )

Returns a random number whose distribution is the Log-normal distribution with paramters `mu` (mean of the Normal distribution) and `sigma` (standard deviation of the Normal distribution).

#### jStat.lognormal.variance( mu, sigma )

Returns the value of the variance for the Log-normal distribution with paramters `mu` (mean of the Normal distribution) and `sigma` (standard deviation of the Normal distribution).

### jStat.normal( mean, std )

#### jStat.normal.pdf( x, mean, std )

Returns the value of `x` in the pdf of the Normal distribution with parameters `mean` and `std` (standard deviation).

#### jStat.normal.cdf( x, mean, std )

Returns the value of `x` in the cdf of the Normal distribution with parameters `mean` and `std` (standard deviation).

#### jStat.normal.inv( p, mean, std )

Returns the value of `p` in the inverse cdf for the Normal distribution with parameters `mean` and `std` (standard deviation).

#### jStat.normal.mean( mean, std )

Returns the value of the mean for the Normal distribution with parameters `mean` and `std` (standard deviation).

#### jStat.normal.median( mean, std )

Returns the value of the median for the Normal distribution with parameters `mean` and `std` (standard deviation).

#### jStat.normal.mode( mean, std )

Returns the value of the mode for the Normal distribution with parameters `mean` and `std` (standard deviation).

#### jStat.normal.sample( mean, std )

Returns a random number whose distribution is the Normal distribution with parameters `mean` and `std` (standard deviation).

#### jStat.normal.variance( mean, std )

Returns the value of the variance for the Normal distribution with parameters `mean` and `std` (standard deviation).

### jStat.pareto( scale, shape )

#### jStat.pareto.pdf( x, scale, shape )

Returns the value of `x` in the pdf of the Pareto distribution with parameters `scale` (x<sub>m</sub>) and `shape` (alpha).

#### jStat.pareto.inv( p, scale, shape )

Returns the inverse of the Pareto distribution with probability `p`, `scale`, `shape`.

This coresponds to `qpareto(p, scale, shape)` in R's VGAM package, and generally corresponds to the `q`<dist> function pattern in R.

#### jStat.pareto.cdf( x, scale, shape )

Returns the value of `x` in the cdf of the Pareto distribution with parameters `scale` (x<sub>m</sub>) and `shape` (alpha).

#### jStat.pareto.mean( scale, shape )

Returns the value of the mean of the Pareto distribution with parameters `scale` (x<sub>m</sub>) and `shape` (alpha).

#### jStat.pareto.median( scale, shape )

Returns the value of the median of the Pareto distribution with parameters `scale` (x<sub>m</sub>) and `shape` (alpha).

#### jStat.pareto.mode( scale, shape )

Returns the value of the mode of the Pareto distribution with parameters `scale` (x<sub>m</sub>) and `shape` (alpha).

#### jStat.pareto.variance( scale, shape )

Returns the value of the variance of the Pareto distribution with parameters `scale` (x<sub>m</sub>) and `shape` (alpha).

### jStat.studentt( dof )

#### jStat.studentt.pdf( x, dof )

Returns the value of `x` in the pdf of the Student's T distribution with `dof` degrees of freedom.

#### jStat.studentt.cdf( x, dof )

Returns the value of `x` in the cdf of the Student's T distribution with `dof` degrees of freedom.

#### jStat.studentt.inv( p, dof )

Returns the value of `p` in the inverse of the cdf for the Student's T distribution with `dof` degrees of freedom.

#### jStat.studentt.mean( dof )

Returns the value of the mean of the Student's T distribution with `dof` degrees of freedom.

#### jStat.studentt.median( dof )

Returns the value of the median of the Student's T distribution with `dof` degrees of freedom.

#### jStat.studentt.mode( dof )

Returns the value of the mode of the Student's T distribution with `dof` degrees of freedom.

#### jStat.studentt.sample( dof )

Returns a random number whose distribution is the Student's T distribution with `dof` degrees of freedom.

#### jStat.studentt.variance( dof )

Returns the value of the variance for the Student's T distribution with `dof` degrees of freedom.

### jStat.tukey( nmeans, dof )

#### jStat.tukey.cdf( q, nmeans, dof )

Returns the value of q in the cdf of the Studentized range distribution with `nmeans` number of groups nmeans and `dof` degrees of freedom.

#### jStat.tukey.inv( p, nmeans, dof )

Returns the value of `p` in the inverse of the cdf for the Studentized range distribution with `nmeans` number of groups and `dof` degrees of freedom.
Only accurate to 4 decimal places.

### jStat.weibull( scale, shape )

#### jStat.weibull.pdf( x, scale, shape )

Returns the value `x` in the pdf for the Weibull distribution with parameters `scale` (lambda) and `shape` (k).

#### jStat.weibull.cdf( x, scale, shape )

Returns the value `x` in the cdf for the Weibull distribution with parameters `scale` (lambda) and `shape` (k).

#### jStat.weibull.inv( p, scale, shape )

Returns the value of `x` in the inverse of the cdf for the Weibull distribution with parameters `scale` (lambda) and `shape` (k).

#### jStat.weibull.mean( scale, shape )

Returns the value of the mean of the Weibull distribution with parameters `scale` (lambda) and `shape` (k).

#### jStat.weibull.median( scale, shape )

Returns the value of the median of the Weibull distribution with parameters `scale` (lambda) and `shape` (k).

#### jStat.weibull.mode( scale, shape )

Returns the mode of the Weibull distribution with parameters `scale` (lambda) and `shape` (k).

#### jStat.weibull.sample( scale, shape )

Returns a random number whose distribution is the Weibull distribution with parameters `scale` (lambda) and `shape` (k).

#### jStat.weibull.variance( scale, shape )

Returns the variance of the Weibull distribution with parameters `scale` (lambda) and `shape` (k).

### jStat.uniform( a, b )

#### jStat.uniform.pdf( x, a, b )

Returns the value of `x` in the pdf of the Uniform distribution from `a` to `b`.

#### jStat.uniform.cdf( x, a, b )

Returns the value of `x` in the cdf of the Uniform distribution from `a` to `b`.

#### jStat.uniform.inv( p, a, b)

Returns the inverse of the `uniform.cdf` function; i.e. the value of `x` for which `uniform.cdf(x, a, b) == p`.

#### jStat.uniform.mean( a, b )

Returns the value of the mean of the Uniform distribution from `a` to `b`.

#### jStat.uniform.median( a, b )

Returns the value of the median of the Uniform distribution from `a` to `b`.

#### jStat.uniform.mode( a, b )

Returns the value of the mode of the Uniform distribution from `a` to `b`.

#### jStat.uniform.sample( a, b )

Returns a random number whose distribution is the Uniform distribution from `a` to `b`.

#### jStat.uniform.variance( a, b )

Returns the variance of the Uniform distribution from `a` to `b`.

### jStat.binomial

#### jStat.binomial.pdf( k, n, p )

Returns the value of `k` in the pdf of the Binomial distribution with parameters `n` and `p`.

#### jStat.binomial.cdf( k, n, p )

Returns the value of `k` in the cdf of the Binomial distribution with parameters `n` and `p`.

### jStat.negbin

#### jStat.negbin.pdf( k, r, p )

Returns the value of `k` in the pdf of the Negative Binomial distribution with parameters `n` and `p`.

#### jStat.negbin.cdf( x, r, p )

Returns the value of `x` in the cdf of the Negative Binomial distribution with parameters `n` and `p`.

### jStat.hypgeom

#### jStat.hypgeom.pdf( k, N, m, n )

Returns the value of `k` in the pdf of the Hypergeometric distribution with parameters `N` (the population size), `m` (the success rate), and `n` (the number of draws).

#### jStat.hypgeom.cdf( x, N, m, n )

Returns the value of `x` in the cdf of the Hypergeometric distribution with parameters `N` (the population size), `m` (the success rate), and `n` (the number of draws).

### jStat.poisson

#### jStat.poisson.pdf( k, l )

Returns the value of `k` in the pdf of the Poisson distribution with parameter `l` (lambda).

#### jStat.poisson.cdf( x, l )

Returns the value of `x` in the cdf of the Poisson distribution with parameter `l` (lambda).

#### jStat.poisson.sample( l )

Returns a random number whose distribution is the Poisson distribution with rate parameter l (lamda)

### jStat.triangular

#### jStat.triangular.pdf( x, a, b, c )

Returns the value of `x` in the pdf of the Triangular distribution with the parameters `a`, `b`, and `c`.

#### jStat.triangular.cdf( x, a, b, c )

Returns the value of `x` in the cdf of the Triangular distribution with the parameters `a`, `b`, and `c`.

#### jStat.triangular.mean( a, b, c )

Returns the value of the mean of the Triangular distribution with the parameters `a`, `b`, and `c`.

#### jStat.triangular.median( a, b, c )

Returns the value of the median of the Triangular distribution with the parameters `a`, `b`, and `c`.

#### jStat.triangular.mode( a, b, c )

Returns the value of the mode of the Triangular distribution with the parameters `a`, `b`, and `c`.

#### jStat.triangular.sample( a, b, c )

Returns a random number whose distribution is the Triangular distribution with the parameters `a`, `b`, and `c`.

#### jStat.triangular.variance( a, b, c )

Returns the value of the variance of the Triangular distribution with the parameters `a`, `b`, and `c`.

### jStat.arcsine( a, b )

#### jStat.arcsine.pdf( x, a, b )

Returns the value of `x` in the pdf of the arcsine distribution from `a` to `b`.

#### jStat.arcsine.cdf( x, a, b )

Returns the value of `x` in the cdf of the arcsine distribution from `a` to `b`.

#### jStat.arcsine.inv(p, a, b)

Returns the inverse of the `arcsine.cdf` function; i.e. the value of `x` for which `arcsine.cdf(x, a, b) == p`.

#### jStat.arcsine.mean( a, b )

Returns the value of the mean of the arcsine distribution from `a` to `b`.

#### jStat.arcsine.median( a, b )

Returns the value of the median of the arcsine distribution from `a` to `b`.

#### jStat.arcsine.mode( a, b )

Returns the value of the mode of the arcsine distribution from `a` to `b`.

#### jStat.arcsine.sample( a, b )

Returns a random number whose distribution is the arcsine distribution from `a` to `b`.

#### jStat.arcsine.variance( a, b )

Returns the variance of the Uniform distribution from `a` to `b`.