Probabilities.GammaCDF Method

Overload List

#SignatureDescription
1procedure GammaCDF(const X: TDenseMtxVec; A: Double; B: Double; const Res: TDenseMtxVec);Gamma distribution CDF (vectorized).
2function GammaCDF(x: Double; a: Double; b: Double): Double;Gamma distribution cumulative distribution function (CDF).

Overload 1: procedure GammaCDF(const X: TDenseMtxVec; A: Double; B: Double; const Res: TDenseMtxVec);

Gamma distribution CDF (vectorized).

#NameDescription
1XDefines distribution domain, real vector or matrix with real positive real values.
2ADefines distribution scale parameter. A must be a positive scalar.
3BDefines distribution shape parameter. B must be a positive scalar.
4ResAfter 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.

Result: stored in self (calling object)

Overload 2: function GammaCDF(x: Double; a: Double; b: Double): Double;

Gamma distribution cumulative distribution function (CDF).

#NameDescription
1xDistribution domain, real value > 0.
2aShape parameter, real value > 0.
3bScale parameter, real value > 0.

Returns: Double - 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