Statistics.Math.Functions
Summary↑
beta(x, y) | The Beta function |
erf(x) | The ‘error’ function |
gamma(x) | The Gamma function |
gammainc(a, x) | Lower incomplete Gamma function |
hyp2f1(a, b, c, x) | Hypergeometrc 2F1 functiono |
inv_erf(x) | The inverse ‘error’ function |
simpson(f, a, b, n) | Simpsons rule for numerical intergation of a function |
Functions
The Beta function
Examples
iex> Statistics.Math.Functions.beta(2, 0.5)
1.3333333333333324
The ‘error’ function
Formula 7.1.26 given in Abramowitz and Stegun. Formula appears as 1 – (a1t1 + a2t2 + a3t3 + a4t4 + a5t5)exp(-x2)
The Gamma function
This implementation uses the Lanczos approximation
Examples
iex> Statistics.Math.Functions.gamma(0.5)
1.7724538509055159
Lower incomplete Gamma function
Examples
iex> Statistics.Math.Functions.gammainc(1,1)
0.63212055882855778
Hypergeometrc 2F1 functiono
WARNING: the implementation is incomplete, and should not be used
The inverse ‘error’ function
Simpsons rule for numerical intergation 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