91 lines
2.5 KiB
Markdown
91 lines
2.5 KiB
Markdown
## Special Functions
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### betafn( x, y )
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Evaluates the Beta function at `(x,y)`.
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### betaln( x, y )
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Evaluates the log Beta function at `(x,y)`.
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### betacf( x, a, b )
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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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### ibetainv( p, a, b)
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Returns the inverse of the incomplete Beta function evaluated at `(p,a,b)`.
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### ibeta( x, a, b)
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Returns the incomplete Beta function evaluated at `(x,a,b)`.
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### gammafn( x )
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Returns the Gamma function evaluated at `x`. This is sometimes called the 'complete' gamma function.
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This function is tested against Mathematica's Gamma[x].
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### gammaln( x )
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Returns the Log-Gamma function evaluated at `x`.
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### gammap( a, x )
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Returns the lower incomplete gamma function evaluated at `(a,x)`.
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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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This function is tested against Mathematica's Gamma[a, 0, x].
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It is additionally tested against gammainc(a,x)'s 'lowinc' output from teh 'pracma' library for R.
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### lowRegGamma(a, x)
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Returns the lower regularized incomplete gamma function evaluated at `(a,x)`.
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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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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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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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### gammapinv( p, a )
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Returns the inverse of the lower regularized incomplete Gamma function evaluated at `(p,a)`.
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This function is the inverse of lowerRegularizedGamma(x, a).
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### factorialln( n )
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Returns the natural log factorial of `n`.
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### factorial( n )
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Returns the factorial of `n`.
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### combination( n, m )
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Returns the number of combinations of `n`, `m`.
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### permutation( n, m )
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Returns the number of permutations of `n`, `m`.
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### erf( x )
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Returns the error function evaluated at `x`.
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### erfc( x )
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Returns the complementary error function evaluated at `x`.
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### erfcinv( p )
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Returns the inverse of the complementary error function evaluated at `p`.
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### randn( n, m )
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Returns a normal deviate (mean 0 and standard deviation 1).
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### randg( shape, n, m )
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Returns a Gamma deviate by the method of Marsaglia and Tsang.
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