pdfkur: Probability Density Function of the Kumaraswamy Distribution

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Probability Density Function of the Kumaraswamy Distribution

Description

This function computes the probability density of the Kumaraswamy distribution given parameters (\alpha and \beta) computed by parkur. The probability density function is

f(x) = \alpha\beta x^{\alpha - 1}(1-x^\alpha)^{\beta-1} \mbox{,}

where f(x) is the nonexceedance probability for quantile x, \alpha is a shape parameter, and \beta is a shape parameter.

Usage

pdfkur(x, para)

Arguments

x	A real value vector.
para	The parameters from parkur or vec2par.

Value

Probability density (f) for x.

Author(s)

W.H. Asquith

References

Jones, M.C., 2009, Kumaraswamy's distribution—A beta-type distribution with some tractability advantages: Statistical Methodology, v. 6, pp. 70–81.

See Also

cdfkur, quakur, lmomkur, parkur

Examples

  lmr <- lmoms(c(0.25, 0.4, 0.6, 0.65, 0.67, 0.9))
  kur <- parkur(lmr)
  x <- quakur(0.5,kur)
  pdfkur(x,kur)

lmomco documentation built on Nov. 7, 2025, 5:11 p.m.