statistics v0.4.0 Statistics.Math.Functions

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

beta(x, y)

Specs

beta(number, number) :: number

The Beta function

Examples

iex> Statistics.Math.Functions.beta(2, 0.5)
1.3333333333333324
erf(x)

Specs

erf(number) :: number

The ‘error’ function

Formula 7.1.26 given in Abramowitz and Stegun. Formula appears as 1 – (a1t1 + a2t2 + a3t3 + a4t4 + a5t5)exp(-x2)

gamma(x)

Specs

gamma(number) :: number

The Gamma function

This implementation uses the Lanczos approximation

Examples

iex> Statistics.Math.Functions.gamma(0.5)
1.7724538509055159
gammainc(a, x)

Specs

gammainc(number, number) :: number

Lower incomplete Gamma function

Examples

iex> Statistics.Math.Functions.gammainc(1,1)
0.63212055882855778
hyp2f1(a, b, c, x)

Specs

hyp2f1(number, number, number, number) :: number

Hypergeometrc 2F1 functiono

WARNING: the implementation is incomplete, and should not be used

inv_erf(x)

Specs

inv_erf(number) :: number

The inverse ‘error’ function

simpson(f, a, b, n)

Specs

simpson((... -> any), number, number, number) :: number

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