lmomco (version 2.2.5)

quarice: Quantile Function of the Rice Distribution

Description

This function computes the quantiles of the Rice distribution given parameters ($\nu$ and $\alpha$) computed by parrice. The quantile function is complex and numerical rooting of the cumulative distribution function cdfrice is used.

Usage

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

Arguments

f

Nonexceedance probability ($0 \le F \le 1$).

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 $F$.

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.

See Also

cdfrice, pdfrice, lmomrice, parrice

Examples

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)