# Quantile Function of the Gamma Distribution This function computes the quantiles of the Gamma distribution given parameters ($\alpha$ and $\beta$) computed by `pargam`. The quantile function has no explicit form. See the `qgamma` function of and `cdfgam`. The parameters have the following interpretations: $\alpha$ is a shape parameter and $\beta$ is a scale parameter in the 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. ```r quagam(f, para, paracheck=TRUE) ``` ## Arguments - `f`: Nonexceedance probability ($0 \le F \le 1$). - `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. ## Returns Quantile value for nonexceedance probability $F$. ## 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. ## Author(s) W.H. Asquith ## See Also `cdfgam`, `pdfgam`, `lmomgam`, `pargam` ## Examples ```r 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) ```

quagam function