Beta (FSharp.Stats) | FSharp.Stats

FSharp.Stats

Beta Module

Namespace: FSharp.Stats.SpecialFunctions
Assembly: FSharp.Stats.dll

The beta function B(p,q), or the beta integral (also called the Eulerian integral of the first kind) is defined by B(p, q) = (Γ(p) * Γ(q)) / Γ(p+q)

Functions and values

Function or value	Description
`_beta z w` Full Usage: `_beta z w` Parameters: z : `'T` - The function input for approximating B(z, w) w : `'T` - The function input for approximating B(z, w) Returns: `'T` Modifiers: inline Type parameters: 'T	Computes an approximation of the real value of the beta function using approximations for the gamma function using Lanczos Coefficients described in Numerical Recipes (Press et al) The caller is responsible to handle edge cases such as nan, infinity, and -infinity in the input z : `'T` The function input for approximating B(z, w) w : `'T` The function input for approximating B(z, w) Returns: `'T`
`_betaLn z w` Full Usage: `_betaLn z w` Parameters: z : `^T` - The function input for approximating ln(B(z, w)) w : `^T` - The function input for approximating ln(B(z, w)) Returns: `^T` Modifiers: inline Type parameters: ^T	Computes an approximation of the real value of the log beta function using approximations for the gamma function using Lanczos Coefficients described in Numerical Recipes (Press et al) The caller is responsible to handle edge cases such as nan, infinity, and -infinity in the input z : `^T` The function input for approximating ln(B(z, w)) w : `^T` The function input for approximating ln(B(z, w)) Returns: `^T`
`beta z w` Full Usage: `beta z w` Parameters: z : `'T` - The function input for approximating B(z, w) w : `'T` - The function input for approximating B(z, w) Returns: `'T` Modifiers: inline Type parameters: 'T	Computes an approximation of the real value of the beta function using approximations for the gamma function using Lanczos Coefficients described in Numerical Recipes (Press et al) Edge cases in the input (nan, infinity, and -infinity) are catched and handled. This might be slower than the unchecked version `_beta` but does not require input sanitation to get expected results for these cases. z : `'T` The function input for approximating B(z, w) w : `'T` The function input for approximating B(z, w) Returns: `'T`
`betaLn z w` Full Usage: `betaLn z w` Parameters: z : `^T` - The function input for approximating ln(B(z, w)) w : `^T` - The function input for approximating ln(B(z, w)) Returns: `^T` Modifiers: inline Type parameters: ^T	Computes an approximation of the real value of the log beta function using approximations for the gamma function using Lanczos Coefficients described in Numerical Recipes (Press et al) Edge cases in the input (nan, infinity, and -infinity) are catched and handled. This might be slower than the unchecked version `_betaLn` but does not require input sanitation to get expected results for these cases. z : `^T` The function input for approximating ln(B(z, w)) w : `^T` The function input for approximating ln(B(z, w)) Returns: `^T`
`lowerIncomplete (a, b, x)` Full Usage: `lowerIncomplete (a, b, x)` Parameters: a : `float` - The first Beta parameter, a positive real number. b : `float` - The second Beta parameter, a positive real number. x : `float` - The upper limit of the integral. Returns: `float`	Returns the lower incomplete (unregularized) beta function a : `float` The first Beta parameter, a positive real number. b : `float` The second Beta parameter, a positive real number. x : `float` The upper limit of the integral. Returns: `float`
`lowerIncompleteRegularized a b x` Full Usage: `lowerIncompleteRegularized a b x` Parameters: a : `float` - The first Beta parameter, a positive real number. b : `float` - The second Beta parameter, a positive real number. x : `float` - The upper limit of the integral. Returns: `float`	Returns the regularized lower incomplete beta function a : `float` The first Beta parameter, a positive real number. b : `float` The second Beta parameter, a positive real number. x : `float` The upper limit of the integral. Returns: `float`
`powerSeries a b x` Full Usage: `powerSeries a b x` Parameters: a : `float` b : `float` x : `float` Returns: `float`	Power series for incomplete beta integral. Use when b*x is small and x not too close to 1. a : `float` b : `float` x : `float` Returns: `float`