lmomco (version 1.7.3)

pdfgam: Probability Density Function of the Gamma Distribution

Description

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

$$f(x) = \frac{1}{\beta^\alpha\Gamma(\alpha)} x^{\alpha - 1} e^{-x/\beta} \mbox{,}$$

where $f(x)$ is the probability density for the quantile $x$. The parameters have the following interpretation in the R syntax; $\alpha$ is a shape parameter and $\beta$ 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 $x$.

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)