lmomkur: L-moments of the Kumaraswamy Distribution

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

L-moments of the Kumaraswamy Distribution

Description

This function estimates the L-moments of the Kumaraswamy distribution given the parameters (\alpha and \beta) from parkur. The L-moments in terms of the parameters with \eta = 1 + 1/\alpha are

\lambda_1 = \beta B(\eta, \beta) \mbox{,}

\lambda_2 = \beta [B(\eta, \beta) - 2B(\eta, 2\beta)] \mbox{,}

\tau_3 = \frac{B(\eta,\beta) - 6B(\eta,2\beta) + 6B(\eta,3\beta)}{B(\eta,\beta) - 2B(\eta,2\beta)} \mbox{,}

\tau_4 = \frac{B(\eta,\beta) - 12B(\eta,2\beta) + 30B(\eta,3\beta) - 40B(\eta,4\beta)}{B(\eta,\beta) - 2B(\eta,2\beta)} \mbox{, and}

\tau_5 = \frac{B(\eta,\beta) - 20B(\eta,2\beta) + 90B(\eta,3\beta) - 140B(\eta,4\beta) + 70B(\eta,5\beta)}{B(\eta,\beta) - 2B(\eta,2\beta)} \mbox{.}

where B(a,b) is the complete beta function or beta().

Usage

lmomkur(para)

Arguments

para	The parameters of the distribution.

Value

An R list is returned.

lambdas	Vector of the L-moments. First element is \lambda_1, second element is \lambda_2, and so on.
ratios	Vector of the L-moment ratios. Second element is \tau, third element is \tau_3 and so on.
trim	Level of symmetrical trimming used in the computation, which is 0.
leftrim	Level of left-tail trimming used in the computation, which is NULL.
rightrim	Level of right-tail trimming used in the computation, which is NULL.
source	An attribute identifying the computational source of the L-moments: “lmomkur”.

Author(s)

W.H. Asquith

References

Jones, M.C., 2009, Kumaraswamy's distribution—A beta-type distribution with some tractability advantages: Statistical Methodology, v. 6, pp. 70–81.

See Also

parkur, cdfkur, pdfkur, quakur

Examples

lmr <- lmoms(c(0.25, 0.4, 0.6, 0.65, 0.67, 0.9))
lmomkur(parkur(lmr))
## Not run: 
A <- B <- exp(seq(-3,5, by=.05))
logA <- logB <- T3 <- T4 <- c();
i <- 0
for(a in A) {
  for(b in B) {
    i <- i + 1
    parkur <- list(para=c(a,b), type="kur");
    lmr <- lmomkur(parkur)
    logA[i] <- log(a); logB[i] <- log(b)
    T3[i] <- lmr$ratios[3]; T4[i] <- lmr$ratios[4]
  }
}
library(lattice)
contourplot(T3~logA+logB, cuts=20, lwd=0.5, label.style="align",
            xlab="LOG OF ALPHA", ylab="LOG OF BETA",
            xlim=c(-3,5), ylim=c(-3,5),
            main="L-SKEW FOR KUMARASWAMY DISTRIBUTION")
contourplot(T4~logA+logB, cuts=10, lwd=0.5, label.style="align",
            xlab="LOG OF ALPHA", ylab="LOG OF BETA",
            xlim=c(-3,5), ylim=c(-3,5),
            main="L-KURTOSIS FOR KUMARASWAMY DISTRIBUTION")

## End(Not run)

lmomco documentation built on May 29, 2024, 10:06 a.m.