Probabilities.TriangularCDF Method

Overload List

#SignatureDescription
1procedure TriangularCDF(const X: TDenseMtxVec; a: Double; b: Double; c: Double; const Res: TDenseMtxVec);Triangular distribution CDF (vectorized).
2function TriangularCDF(x: Double; a: Double; b: Double; c: Double): Double;Triangular cumulative distribution function (CDF).

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

Triangular distribution CDF (vectorized).

#NameDescription
1XDistribution domain, real value on closed interval [a,b].
2aDistribution location 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 CDF 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 TriangularCDF(x: Double; a: Double; b: Double; c: Double): Double;

Triangular cumulative distribution function (CDF).

#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 cumulative distribution 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 cumulative distribution function is

CDF(x| a,b,c)={ ((x-a)^2)/((b-a)(c-a)),  if amp; a <= x <= c
              { [6pt] 1-((b-x)^2)/((b-a)(b-c)),  if amp; c

It is the probability that an observation falls in (a, x]. Domain: b > a, a <= c <= b, a <= x <= b; the result rises monotonically from 0 to 1. Outside the support, or when the parameter ordering is violated, the result is NAN.

See Also: Probabilities.TriangularPDF, Probabilities.TriangularCDFInv