# quarice: Quantile Function of the Rice Distribution In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function computes the quantiles of the Rice distribution given parameters (ν and α) computed by `parrice`. The quantile function is complex and numerical rooting of the cumulative distribution function `cdfrice` is used.

## Usage

 `1` ```quarice(f, para, xmax=NULL, paracheck=TRUE) ```

## Arguments

 `f` Nonexceedance probability (0 ≤ F ≤ 1). `para` The parameters from `parrice` or `vec2par`. `xmax` The maximum x value used for integeration. `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

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

`cdfrice`, `pdfrice`, `lmomrice`, `parrice`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```lmr <- vec2lmom(c(125,0.20), lscale=FALSE) quarice(0.75,parrice(lmr)) # The quantile function of the Rice as implemented in lmomco # is slow because of rooting the CDF, which is created by # integration of the PDF. Rician random variates are easily created. # Thus, in speed applications the rlmomco() with a Rice parameter # object could be bypassed by the following function, rrice(). ## Not run: "rrice" = function(n, nu, alpha) { # from the VGAM package theta = 1 # any number X = rnorm(n, mean=nu * cos(theta), sd=alpha) Y = rnorm(n, mean=nu * sin(theta), sd=alpha) return(sqrt(X^2 + Y^2)) } n <- 5000; # suggest making it about 10,000 nu <- 100; alpha <- 10 set.seed(501); lmoms(rrice(n, nu, alpha)) set.seed(501); lmoms(rlmomco(n, vec2par(c(nu,alpha), type='rice'))) # There are slight numerical differences between the two? ## End(Not run) ```