Probabilities::ParetoPDF Function

Overload List

#SignatureDescription
1double ParetoPDF(double x, double a, double b);Pareto probability density function (PDF).
2void ParetoPDF(TDenseMtxVec *X, double a, double b, TDenseMtxVec *Res);Pareto distribution PDF (vectorized).

Overload 1: double ParetoPDF(double x, double a, double b);

Pareto probability density function (PDF).

#NameTypeDescription
1xdoubleFunction domain, real value >= b.
2adoubleDistribution shape parameter, real positive value.
3bdoubleDistribution scale parameter (lower bound of the support), real positive value.

Returns: the Pareto probability density function (PDF) for value x using the parameters a and b. x must be >= b, otherwise the result is NAN.

Remarks:

The Pareto probability density function is

PDF(x| a,b)=(a b^a)/(x^(a+1)), x >= b

where a is the shape (tail) parameter and b the scale parameter equal to the minimum value of the support. Domain: x >= b, a > 0, b > 0. For x < b the result is NAN.

See Also: Probabilities::ParetoCDF, Probabilities::ParetoCDFInv
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler

Overload 2: void ParetoPDF(TDenseMtxVec *X, double a, double b, TDenseMtxVec *Res);

Pareto distribution PDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, real vector or matrix.
2adoubleDistribution scale parameter, real positive value.
3bdoubleDistribution shape parameter, real positive value, smaller than x.
4ResTDenseMtxVec *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.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler