pdfgov {lmomco}

Probability Density Function of the Govindarajulu Distribution

Description

This function computes the probability density of the Govindarajulu distribution given parameters (\xi, \alpha, and \beta) computed by pargov. The probability density function is

f(x) = [\alpha\beta(\beta+1)]^{-1} [F(x)]^{1-\beta} [1 - F(x)]^{-1} \mbox{,}

where f(x) is the probability density for quantile x, F(x) the cumulative distribution function or nonexceedance probability at x, \xi is a location parameter, \alpha is a scale parameter, and \beta is a shape parameter.

Usage

pdfgov(x, para)

Arguments

x

A real value vector.

para

The parameters from pargov or vec2par.

Value

Probability density (f) for x.

Author(s)

W.H. Asquith

References

Gilchrist, W.G., 2000, Statistical modelling with quantile functions: Chapman and Hall/CRC, Boca Raton.

Nair, N.U., Sankaran, P.G., Balakrishnan, N., 2013, Quantile-based reliability analysis: Springer, New York.

Nair, N.U., Sankaran, P.G., and Vineshkumar, B., 2012, The Govindarajulu distribution—Some Properties and applications: Communications in Statistics, Theory and Methods, v. 41, no. 24, pp. 4391–4406.

See Also

cdfgov, quagov, lmomgov, pargov

Examples

  lmr <- lmoms(c(123,34,4,654,37,78))
  gov <- pargov(lmr)
  x <- quagov(0.5,gov)
  pdfgov(x,gov)