statistics v0.5.0 Statistics.Math.Functions
Link to this section 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
Link to this section Functions
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
Link to this function
simpson(f, a, b, n)
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