Probabilities::GammaCDF Function

Probabilities Namespace

Overload List

#SignatureDescription
1double GammaCDF(double x, double a, double b);Gamma distribution cumulative distribution function (CDF).
2void GammaCDF(TDenseMtxVec *X, double A, double B, TDenseMtxVec *Res);Gamma distribution CDF (vectorized).

Overload 1: double GammaCDF(double x, double a, double b);

Gamma distribution cumulative distribution function (CDF).

#NameTypeDescription
1xdoubleDistribution domain, real value > 0.
2adoubleShape parameter, real value > 0.
3bdoubleScale parameter, real value > 0.

Returns: the Gamma cumulative distribution function (CDF) at x for SHAPE parameter a and SCALE parameter b. Returns NAN when a <= 0, b <= 0 or x <= 0.

Remarks:

Computes the Gamma CDF, the regularized lower incomplete gamma function P(a,x/b)P(a,x/b):

CDF(x| a,b )= 1/(b^a Gamma (a)) integral _0 ^x t^(a-1)* exp (-t/b) dt = P(a,x/b)

(clamped to at most 1). Domain: x > 0, a > 0, b > 0; the result lies in [0,1][0,1] and is monotone non-decreasing. The implementation evaluates the CDF only for x > 0; for x <= 0 (and for a <= 0 or b <= 0) the result is NAN.

See Also: Probabilities::GammaPDF, Probabilities::GammaCDFInv
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler

Overload 2: void GammaCDF(TDenseMtxVec *X, double A, double B, TDenseMtxVec *Res);

Gamma distribution CDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, real vector or matrix with real positive real values.
2AdoubleDefines distribution scale parameter. A must be a positive scalar.
3BdoubleDefines distribution shape parameter. B must be a positive scalar.
4ResTDenseMtxVec *After calculation stores the CDF calculated from X, a and b. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of X.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler