cdfrice {lmomco}

Cumulative Distribution Function of the Rice Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Rice distribution given parameters (\nu and \mathrm{SNR}) computed by parrice. The cumulative distribution function is complex and numerical integration of the probability density function pdfrice is used.

F(x) = 1 - Q\biggl(\frac{\nu}{\alpha}, \frac{x}{\alpha}\biggr)\mbox{,}

where F(x) is the nonexceedance probability for quantile x, Q(a,b) is the Marcum Q-function, and \nu/\alpha is a form of signal-to-noise ratio \mathrm{SNR}. If \nu=0, then the Rayleigh distribution results and pdfray is used. The Marcum Q-function is difficult to work with and the lmomco uses the integrate function on pdfrice (however, see the Note).

Usage

cdfrice(x, para)

Arguments

x

A real value vector.

para

The parameters from parrice or vec2par.

Value

Nonexceedance probability (F) for x.

Note

A user of lmomco reported that the Marcum Q function can be computed using R functions. An implementation is shown in this note.

See NEWS file and entries for version 2.0.1 for this "R Marcum"
"marcumq" <- function(a, b, nu=1) {
      pchisq(b^2, df=2*nu, ncp=a^2, lower.tail=FALSE) }

Author(s)

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.

See Also

pdfrice, quarice, lmomrice, parrice

Examples

lmr <- vec2lmom(c(45,0.27), lscale=FALSE)
cdfrice(35,parrice(lmr))