# quagam: 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

 `1` ```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.

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.

`cdfgam`, `pdfgam`, `lmomgam`, `pargam`

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ``` 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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