pdfgam {lmomco}R Documentation

Probability Density Function of the Gamma Distribution

Description

This function computes the probability density function of the Gamma distribution given parameters (α, shape, and β, scale) of the distribution computed by pargam. The probability density function of the distribution has no explicit form, but is expressed as an integral.

f(x) = frac{1}{β^αΓ(α)} x^{α - 1} e^{-x/β} mbox{,}

where f(x) is the probability density for the quantile x. The parameters have the following interpretation in the R syntax; α is a shape parameter and β is a scale parameter.

Usage

pdfgam(x, para)

Arguments

x A real value.
para The parameters from pargam or similar.

Value

Probability density (f) for x.

Author(s)

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, vol. 52, p. 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

cdfgam, quagam, pargam

Examples

  lmr <- lmoms(c(123,34,4,654,37,78))
  gam <- pargam(lmr)
  x <- quagam(0.5,gam)
  pdfgam(x,gam)

[Package lmomco version 0.96.3 Index]