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
Specs
beta(number, number) :: number
The Beta function
Examples
iex> Statistics.Math.Functions.beta(2, 0.5)
1.3333333333333324
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)
Specs
gamma(number) :: number
The Gamma function
This implementation uses the Lanczos approximation
Examples
iex> Statistics.Math.Functions.gamma(0.5)
1.7724538509055159
Specs
gammainc(number, number) :: number
Lower incomplete Gamma function
Examples
iex> Statistics.Math.Functions.gammainc(1,1)
0.63212055882855778
Specs
hyp2f1(number, number, number, number) :: number
Hypergeometrc 2F1 functiono
WARNING: the implementation is incomplete, and should not be used
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