lmomco (version 2.4.14)

pdfglo: Probability Density Function of the Generalized Logistic Distribution

Description

This function computes the probability density of the Generalized Logistic distribution given parameters (\(\xi\), \(\alpha\), and \(\kappa\)) computed by parglo. The probability density function is $$f(x) = \frac{\alpha^{-1} \exp(-(1-\kappa)Y)}{[1+\exp(-Y)]^2} \mbox{,}$$ where \(Y\) is $$Y = -\kappa^{-1} \log\left(1 - \frac{\kappa(x-\xi)}{\alpha}\right) \mbox{,}$$ for \(\kappa \ne 0\), and $$Y = (x-\xi)/\alpha\mbox{,}$$ for \(\kappa = 0\), and where \(f(x)\) is the probability density for quantile \(x\), \(\xi\) is a location parameter, \(\alpha\) is a scale parameter, and \(\kappa\) is a shape parameter.

Usage

pdfglo(x, para)

Value

Probability density (\(f\)) for \(x\).

Arguments

x

A real value vector.

para

The parameters from parglo or vec2par.

Author

W.H. Asquith

References

Hosking, J.R.M., 1990, L-moments---Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105--124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

See Also

cdfglo, quaglo, lmomglo, parglo

Examples

  lmr <- lmoms(c(123,34,4,654,37,78))
  glo <- parglo(lmr)
  x <- quaglo(0.5,glo)
  pdfglo(x,glo)