Probabilities::BetaCDF Function

Probabilities Namespace

Overload List

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

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

Beta distribution cumulative distribution function (CDF).

#NameTypeDescription
1xdoubleFunction domain, real value on the closed interval [0,1].
2adoubleFirst shape parameter, real value > 0.
3bdoubleSecond shape parameter, real value > 0.

Returns: the beta cumulative distribution function (CDF) at x: the probability that an observation from a beta distribution with shape parameters a and b falls in [0,x]. Returns NAN when a <= 0 or b <= 0.

Remarks:

Computes the beta CDF, the regularized incomplete beta function I_x(a,b):

CDF(x|a,b)=1/B(a,b)integral _0 ^x t^(a-1)(1-t)^(b-1) dt = I_x(a,b)

where B(a,b)B(a,b) is the Probabilities::Beta function. Domain: x in [0,1], a > 0, b > 0; the result lies in [0,1][0,1], is monotone non-decreasing, equals 0 for x <= 0 and 1 for x >= 1. If a <= 0 or b <= 0 the result is NAN.

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

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

Beta CDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, real vector or matrix with integer values on open interval (0,1).
2AdoubleDistribution scale parameter, real positive value.
3BdoubleDistribution shape parameter, real positive value.
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