Probabilities::StudentCDF Function

Overload List

#SignatureDescription
1double StudentCDF(double x, int Nu);Student's t cumulative distribution function (CDF).
2void StudentCDF(TDenseMtxVec *X, int Nu, TDenseMtxVec *Res);Student(T) distribution CDF (vectorized).

Overload 1: double StudentCDF(double x, int Nu);

Student's t cumulative distribution function (CDF).

#NameTypeDescription
1xdoubleFunction domain, any real value.
2NuintDegrees of freedom, integer >= 1.

Returns: the Student's t cumulative distribution function (CDF) at x with Nu degrees of freedom. Returns NAN when Nu < 1.

Remarks:

Computes the Student's t CDF

CDF(x| nu)= (Gamma ( (nu +1)/2))/(Gamma (nu/2)) 1/(sqrt(nu pi)) integral _(-inf) ^x 1/((1+t^2/nu)^((nu +1)/2)) dt

The implementation uses the regularized incomplete beta function (and the closed form 1/2+1/piarctan x for nu=1). The result is the probability that an observation falls in (-inf,x], lies in [0,1][0,1], is monotone non-decreasing and equals 0.5 at x=0. Domain: x in R, integer nu >= 1. If nu < 1 the result is NAN.

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

Overload 2: void StudentCDF(TDenseMtxVec *X, int Nu, TDenseMtxVec *Res);

Student(T) distribution CDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Distribution domain, real values.
2NuintDefines distribution degrees of freedom, positive integer.
3ResTDenseMtxVec *After calculation stores the CDF calculated from X and Nu. 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