Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure StudentCDF(const X: TDenseMtxVec; Nu: Integer; const Res: TDenseMtxVec); | Student(T) distribution CDF (vectorized). |
| 2 | function 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).
| # | Name | Description |
|---|---|---|
| 1 | X | Distribution domain, real values. |
| 2 | Nu | Defines distribution degrees of freedom, positive integer. |
| 3 | Res | 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. |
Result: stored in self (calling object)
Overload 2: function StudentCDF(x: Double; Nu: Integer): Double;
Student's t cumulative distribution function (CDF).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, any real value. |
| 2 | Nu | Degrees 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 , 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.