lmomco (version 2.2.5)

lmomsla: Trimmed L-moments of the Slash Distribution

Description

This function estimates the trimmed L-moments of the Slash distribution given the parameters ($\xi$ and $\alpha$) from parsla. The relation between the TL-moments (trim=1) and the parameters have been numerically determined and are $\lambda^{(1)}_1 = \xi$, $\lambda^{(1)}_2 = 0.9368627\alpha$, $\tau^{(1)}_3 = 0$, $\tau^{(1)}_4 = 0.3042045$, $\tau^{(1)}_5 = 0$, and $\tau^{(1)}_6 = 0.1890072$. These TL-moments (trim=1) are symmetrical for the first L-moments defined because $\mathrm{E}[X_{1:n}]$ and $\mathrm{E}[X_{n:n}]$ are undefined expectations for the Slash.

Usage

lmomsla(para)

Arguments

para

The parameters of the distribution.

Value

An R list is returned.

References

Rogers, W.H., and Tukey, J.W., 1972, Understanding some long-tailed symmetrical distributions: Statistica Neerlandica, v. 26, no. 3, pp. 211--226.

See Also

parsla, cdfsla, pdfsla, quasla

Examples

## Not run: 
# # This example was used to numerically back into the TL-moments and the 
# # relation between \alpha and \lambda_2.
# "lmomtrim1" <- function(para) {
#     bigF <- 0.999
#     minX <- para$para[1] - para$para[2]*qnorm(1 - bigF) / qunif(1 - bigF)
#     maxX <- para$para[1] + para$para[2]*qnorm(    bigF) / qunif(1 - bigF)
#     minF <- cdfsla(minX, para); maxF <- cdfsla(maxX, para)
#     lmr <- theoTLmoms(para, nmom = 6, leftrim = 1, rightrim = 1)
# }
# 
# U <- -10; i <- 0
# As <- seq(.1,abs(10),by=.2)
# L1s <- L2s <- T3s <- T4s <- T5s <- T6s <- vector(mode="numeric", length=length(As))
# for(A in As) {
#    i <- i + 1
#    lmr <- lmomtrim1(vec2par(c(U, A), type="sla"))
#    L1s[i] <- lmr$lambdas[1]; L2s[i] <- lmr$lambdas[2]
#    T3s[i] <- lmr$ratios[3];  T4s[i] <- lmr$ratios[4]
#    T5s[i] <- lmr$ratios[5];  T6s[i] <- lmr$ratios[6]
# }
# print(summary(lm(L2s~As-1))$coe)
# print(mean(T4s))
# print(mean(T6s))
# ## End(Not run)