Probabilities.StudentCDF Method

Overload List

#SignatureDescription
1procedure StudentCDF(const X: TDenseMtxVec; Nu: Integer; const Res: TDenseMtxVec);Student(T) distribution CDF (vectorized).
2function StudentCDF(x: Double; Nu: Integer): Double;Student's t cumulative distribution function (CDF).

Overload 1: procedure StudentCDF(const X: TDenseMtxVec; Nu: Integer; const Res: TDenseMtxVec);

Student(T) distribution CDF (vectorized).

#NameDescription
1XDistribution domain, real values.
2NuDefines distribution degrees of freedom, positive integer.
3ResAfter 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.

Result: stored in self (calling object)

Overload 2: function StudentCDF(x: Double; Nu: Integer): Double;

Student's t cumulative distribution function (CDF).

#NameDescription
1xFunction domain, any real value.
2NuDegrees of freedom, integer >= 1.

Returns: Double - 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