Probabilities.TriangularPDF Method

Overload List

#SignatureDescription
1procedure TriangularPDF(const X: TDenseMtxVec; a: Double; b: Double; c: Double; const Res: TDenseMtxVec);Triangular distribution PDF (vectorized).
2function TriangularPDF(x: Double; a: Double; b: Double; c: Double): Double;Triangular probability density function (PDF).

Overload 1: procedure TriangularPDF(const X: TDenseMtxVec; a: Double; b: Double; c: Double; const Res: TDenseMtxVec);

Triangular distribution PDF (vectorized).

#NameDescription
1XDistribution domain, real value on closed interval [a,b].
2aDistribution locagtion parameter, real value, smaller than parameter b.
3bDistribution scale parameter, real value, greater than parameter a.
4cDistribution shape parameter, real value on closed interval [a,b].
5ResAfter calculation stores the PDF calculated from X, a, b and c. 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 TriangularPDF(x: Double; a: Double; b: Double; c: Double): Double;

Triangular probability density function (PDF).

#NameDescription
1xDistribution domain, real value on closed interval [a,b].
2aLower bound, real value, smaller than b.
3bUpper bound, real value, greater than a.
4cMode (peak), real value on closed interval [a,b].

Returns: Double - the Triangular probability density function for value x using parameters a, b and c. Requires b > a and a <= c <= b and a <= x <= b, otherwise the result is NAN.

Remarks:

The triangular probability density function is

PDF(x| a,b,c)={ (2(x-a))/((b-a)(c-a)),  if amp; a <= x <= c
              { [6pt] (2(b-x))/((b-a)(b-c)),  if amp; c

where a is the lower bound, b the upper bound and c the mode (peak). Domain: b > a, a <= c <= b, and a <= x <= b. Outside the support, or when the parameter ordering is violated, the result is NAN.

See Also: Probabilities.TriangularCDF, Probabilities.TriangularCDFInv