Quantile Function of the Gamma Distribution

Description

This function computes the quantiles of the Gamma distribution given parameters (α and β) computed by pargam. The quantile function has no explicit form. See the qgamma function of R and cdfgam. The parameters have the following interpretations: α is a shape parameter and β is a scale parameter in the R syntax of the qgamma() function.

Alternatively, a three-parameter version is available following the parameterization of the Generalized Gamma distribution used in the gamlss.dist package and for lmomco is documented under pdfgam. The three parameter version is automatically triggered if the length of the para element is three and not two.

Usage

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quagam(f, para, paracheck=TRUE)

Arguments

f

Nonexceedance probability (0 ≤ F ≤ 1).

para

The parameters from pargam or vec2par.

paracheck

A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

Value

Quantile value for nonexceedance probability F.

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, v. 52, pp. 105–124.

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

See Also

cdfgam, pdfgam, lmomgam, pargam

Examples

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  lmr <- lmoms(c(123,34,4,654,37,78))
  g <- pargam(lmr)
  quagam(0.5,g)
## Not run: 
  # generate 50 random samples from this fitted parent
  Qsim <- rlmomco(5000,g)
  # compute the apparent gamma parameter for this parent
  gsim <- pargam(lmoms(Qsim))

## End(Not run)

## Not run: 
# 3-p Generalized Gamma Distribution and gamlss.dist package parameterization
gg <- vec2par(c(2, 4, 3), type="gam")
X <- gamlss.dist::rGG(1000, mu=2, sigma=4, nu=3); FF <- nonexceeds(sig6=TRUE)
plot(qnorm(lmomco::pp(X)), sort(X), pch=16, col=8) # lets compare the two quantiles
lines(qnorm(FF), gamlss.dist::qGG(FF, mu=2, sigma=4, nu=3), lwd=6, col=3)
lines(qnorm(FF), quagam(FF, gg), col=2, lwd=2) # 
## End(Not run)

## Not run: 
# 3-p Generalized Gamma Distribution and gamlss.dist package parameterization
gg <- vec2par(c(7.4, 0.2, -3), type="gam")
X <- gamlss.dist::rGG(1000, mu=7.4, sigma=0.2, nu=-3); FF <- nonexceeds(sig6=TRUE)
plot(qnorm(lmomco::pp(X)), sort(X), pch=16, col=8) # lets compare the two quantiles
lines(qnorm(FF), gamlss.dist::qGG(FF, mu=7.4, sigma=0.2, nu=-3), lwd=6, col=3)
lines(qnorm(FF), quagam(FF, gg), col=2, lwd=2) # 
## End(Not run)

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