Probabilities.ParetoPDF Method

Overload List

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

Overload 1: void ParetoPDF(TDenseMtxVec X, Double a, Double b, TDenseMtxVec Res)

Pareto distribution PDF (vectorized).

#NameDescription
1XDefines distribution domain, real vector or matrix.
2aDistribution scale parameter, real positive value.
3bDistribution shape parameter, real positive value, smaller than x.
4ResAfter 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: Double ParetoPDF(Double x, Double a, Double b)

Pareto probability density function (PDF).

#NameDescription
1xFunction domain, real value >= b.
2aDistribution shape parameter, real positive value.
3bDistribution scale parameter (lower bound of the support), real positive value.

Returns: Double - 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