lmomco (version 2.2.5)

lmomrice: L-moments of the Rice Distribution

Description

This function estimates the L-moments of the Rice distribution given the parameters ($\nu$ and $\alpha$) from parrice. The L-moments in terms of the parameters are complex. They are computed here by the system of maximum order statistic expectations from theoLmoms.max.ostat, which uses expect.max.ostat. The connection between $\tau_2$ and $\nu/\alpha$ and a special function (the Laguerre polynomial, LaguerreHalf) of $\nu^2/\alpha^2$ and additional algebraic terms is tabulated in the R data.frame located within .lmomcohash$RiceTable. The file ‘SysDataBuilder.R’ provides additional details.

Usage

lmomrice(para, ...)

Arguments

para

The parameters of the distribution.

...

Additional arguments passed to theoLmoms.max.ostat.

Value

An R list is returned.

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

parrice, cdfrice, cdfrice, quarice

Examples

## Not run: 
# lmomrice(vec2par(c(65,34), type="rice"))
# 
# # Use the additional arguments to show how to avoid unnecessary overhead
# # when using the Rice, which only has two parameters.
#   rice <- vec2par(c(15,14), type="rice")
#   system.time(lmomrice(rice, nmom=2)); system.time(lmomrice(rice, nmom=6))
# 
#   lcvs <- vector(mode="numeric"); i <- 0
#   SNR  <- c(seq(7,0.25, by=-0.25), 0.1)
#   for(snr in SNR) {
#     i <- i + 1
#     rice    <- vec2par(c(10,10/snr), type="rice")
#     lcvs[i] <- lmomrice(rice, nmom=2)$ratios[2]
#   }
#   plot(lcvs, SNR,
#        xlab="COEFFICIENT OF L-VARIATION",
#        ylab="LOCAL SIGNAL TO NOISE RATIO (NU/ALPHA)")
#   lines(.lmomcohash$RiceTable$LCV,
#         .lmomcohash$RiceTable$SNR)
#   abline(1,0, lty=2)
#   mtext("Rice Distribution")
#   text(0.15,0.5, "More noise than signal")
#   text(0.15,1.5, "More signal than noise")
# ## End(Not run)
## Not run: 
# # A polynomial expression for the relation between L-skew and 
# # L-kurtosis for the Rice distribution can be readily constructed.
# T3 <- .lmomcohash$RiceTable$TAU3
# T4 <- .lmomcohash$RiceTable$TAU4
# LM <- lm(T4~T3+I(T3^2)+I(T3^3)+I(T3^4)+
#                I(T3^5)+I(T3^6)+I(T3^7)+I(T3^8))
# summary(LM) # note shown## End(Not run)