Probabilities.BetaPDF Method

Overload List

#	Signature	Description
1	procedure BetaPDF(const X: TDenseMtxVec; A: Double; B: Double; const Res: TDenseMtxVec);	Beta PDF (vectorized).
2	function BetaPDF(x: Double; a: Double; b: Double): Double;	Beta distribution probability density function (PDF).

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

Beta PDF (vectorized).

#	Name	Description
1	X	Defines distribution domain, real vector or matrix with integer values on open interval (0,1).
2	A	Distribution scale parameter, real positive value.
3	B	Distribution shape parameter, real positive value.
4	Res	After calculation stores the PDF 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 BetaPDF(x: Double; a: Double; b: Double): Double;

Beta distribution probability density function (PDF).

#	Name	Description
1	x	Function domain, real value on the closed interval [0,1].
2	a	First shape parameter, real value > 0.
3	b	Second shape parameter, real value > 0.

Returns: Double - the beta distribution probability density function (PDF) at x for shape parameters a and b. Returns NAN when a <= 0, b <= 0, x < 0 or x > 1; returns +INF at x=0 when a < 1 and at x=1 when b < 1.

Remarks:

Computes the beta PDF

PDF(x|a,b)=1/B(a,b) x^(a-1)(1-x)^(b-1)* I_([0,1])(x)

where $B(a,b)$ is the Probabilities.Beta function and the density is nonzero only on $[0,1]$ . Domain: x in [0,1], a > 0, b > 0. Behaviour: NAN for invalid parameters or x not in [0,1]; at the boundary x=0 (with a < 1) and x=1 (with b < 1) the density diverges and +INF is returned. A scalar form (this one) and a vectorized TDenseMtxVec overload are provided.

Examples

Uses Probabilities;

procedure Example;
var pdf,cdf: double;
begin
    pdf := BetaPDF(0.55, 3.0, 2.1);
    cdf := BetaCDF(0.55, 3.0, 2.1);
end;

See Also: Probabilities.BetaCDF, Probabilities.BetaCDFInv