| 1 | ## Special Functions
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| 2 |
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| 3 | ### betafn( x, y )
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| 4 |
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| 5 | Evaluates the Beta function at `(x,y)`.
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| 6 |
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| 7 | ### betaln( x, y )
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| 8 |
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| 9 | Evaluates the log Beta function at `(x,y)`.
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| 10 |
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| 11 | ### betacf( x, a, b )
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| 12 |
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| 13 | Returns the continued fraction for the incomplete Beta function with parameters a and b modified by Lentz's method evaluated at `x`.
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| 14 |
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| 15 | ### ibetainv( p, a, b)
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| 16 |
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| 17 | Returns the inverse of the incomplete Beta function evaluated at `(p,a,b)`.
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| 18 |
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| 19 | ### ibeta( x, a, b)
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| 20 |
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| 21 | Returns the incomplete Beta function evaluated at `(x,a,b)`.
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| 22 |
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| 23 | ### gammafn( x )
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| 24 |
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| 25 | Returns the Gamma function evaluated at `x`. This is sometimes called the 'complete' gamma function.
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| 26 |
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| 27 | This function is tested against Mathematica's Gamma[x].
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| 28 |
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| 29 | ### gammaln( x )
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| 30 |
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| 31 | Returns the Log-Gamma function evaluated at `x`.
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| 32 |
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| 33 | ### gammap( a, x )
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| 34 |
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| 35 | Returns the lower incomplete gamma function evaluated at `(a,x)`.
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| 36 | This function is usually written with a lower case greek gamma character, and is one of the two [incomplete gamma functions](http://mathworld.wolfram.com/IncompleteGammaFunction.html).
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| 37 |
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| 38 | This function is tested against Mathematica's Gamma[a, 0, x].
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| 39 | It is additionally tested against gammainc(a,x)'s 'lowinc' output from teh 'pracma' library for R.
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| 40 |
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| 41 | ### lowRegGamma(a, x)
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| 42 |
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| 43 | Returns the lower regularized incomplete gamma function evaluated at `(a,x)`.
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| 44 | It is defined as the quotient of the lower incomplete gamma function evaluated at (a, x) and the upper incomplete gamma function ('the gamma function') evaluated at (a).
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| 45 | This function is usually written as P(x, a); and is one of the two [regularized gamma functions](http://mathworld.wolfram.com/RegularizedGammaFunction.html).
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| 46 |
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| 47 | This function is tested against gammainc(x, a)'s 'reginc' output from the 'pracma' library for R. Note that R and jStat switch the order of operators for this function.
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| 48 |
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| 49 | ### gammapinv( p, a )
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| 50 |
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| 51 | Returns the inverse of the lower regularized incomplete Gamma function evaluated at `(p,a)`.
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| 52 | This function is the inverse of lowerRegularizedGamma(x, a).
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| 53 |
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| 54 | ### factorialln( n )
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| 55 |
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| 56 | Returns the natural log factorial of `n`.
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| 57 |
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| 58 | ### factorial( n )
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| 59 |
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| 60 | Returns the factorial of `n`.
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| 61 |
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| 62 | ### combination( n, m )
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| 63 |
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| 64 | Returns the number of combinations of `n`, `m`.
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| 65 |
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| 66 | ### permutation( n, m )
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| 67 |
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| 68 | Returns the number of permutations of `n`, `m`.
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| 69 |
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| 70 |
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| 71 | ### erf( x )
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| 72 |
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| 73 | Returns the error function evaluated at `x`.
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| 74 |
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| 75 | ### erfc( x )
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| 76 |
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| 77 | Returns the complementary error function evaluated at `x`.
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| 78 |
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| 79 | ### erfcinv( p )
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| 80 |
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| 81 | Returns the inverse of the complementary error function evaluated at `p`.
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| 82 |
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| 83 | ### randn( n, m )
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| 84 |
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| 85 | Returns a normal deviate (mean 0 and standard deviation 1).
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| 86 |
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| 87 | ### randg( shape, n, m )
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| 88 |
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| 89 | Returns a Gamma deviate by the method of Marsaglia and Tsang.
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| 90 |
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