Statistics.Math.Functions (statistics v0.6.3)
Summary
Functions
The Beta function
The 'error' function
The Gamma function
Lower incomplete Gamma function
Hypergeometrc 2F1 functiono
The inverse 'error' function
Simpsons rule for numerical integration of a function
Functions
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beta(x, y)
The Beta function
Examples
iex> Statistics.Math.Functions.beta(2, 0.5)
1.3333333333333324
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erf(x)
The 'error' function
Formula 7.1.26 given in Abramowitz and Stegun. Formula appears as 1 – (a1t1 + a2t2 + a3t3 + a4t4 + a5t5)exp(-x2)
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gamma(x)
The Gamma function
This implementation uses the Lanczos approximation
Examples
iex> Statistics.Math.Functions.gamma(0.5)
1.7724538509055159
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gammainc(a, x)
Lower incomplete Gamma function
Examples
iex> Statistics.Math.Functions.gammainc(1,1)
0.63212055882855778
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hyp2f1(a, b, c, x)
Hypergeometrc 2F1 functiono
WARNING: the implementation is incomplete, and should not be used
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inv_erf(x)
The inverse 'error' function
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simpson(f, a, b, n)
Simpsons rule for numerical integration of a function
see: http://en.wikipedia.org/wiki/Simpson's_rule
Examples
iex> Statistics.Math.Functions.simpson(fn x -> x*x*x end, 0, 20, 100000)
40000.00000000011