lmomco (version 2.4.14)

lmomgov: L-moments of the Govindarajulu Distribution

Description

This function estimates the L-moments of the Govindarajulu distribution given the parameters (\(\xi\), \(\alpha\), and \(\beta\)) from pargov. The L-moments in terms of the parameters are $$\lambda_1 = \xi + \frac{2\alpha}{\beta+2} \mbox{,}$$ $$\lambda_2 = \frac{2\alpha\beta}{(\beta+2)(\beta+3)} \mbox{,}$$ $$\tau_3 = \frac{\beta-2}{\beta+4} \mbox{, and}$$ $$\tau_4 = \frac{(\beta-5)(\beta-1)}{(\beta+4)(\beta+5)} \mbox{.}$$

The limits of \(\tau_3\) are \((-1/2, 1)\) for \(\beta \rightarrow 0\) and \(\beta \rightarrow \infty\).

Usage

lmomgov(para)

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: “lmomgov”.

Arguments

para

The parameters of the distribution.

Author

W.H. Asquith

References

Gilchrist, W.G., 2000, Statistical modelling with quantile functions: Chapman and Hall/CRC, Boca Raton.

Nair, N.U., Sankaran, P.G., Balakrishnan, N., 2013, Quantile-based reliability analysis: Springer, New York.

Nair, N.U., Sankaran, P.G., and Vineshkumar, B., 2012, The Govindarajulu distribution---Some Properties and applications: Communications in Statistics, Theory and Methods, v. 41, no. 24, pp. 4391--4406.

See Also

pargov, cdfgov, pdfgov, quagov

Examples

lmr <- lmoms(c(123,34,4,654,37,78))
lmorph(lmr)
lmomgov(pargov(lmr))
if (FALSE) {
Bs <- exp(seq(log(.01),log(10000),by=.05))
T3 <- (Bs-2)/(Bs+4)
T4 <- (Bs-5)*(Bs-1)/((Bs+4)*(Bs+5))
plotlmrdia(lmrdia(), autolegend=TRUE)
points(T3, T4)
T3s <- c(-0.5,T3,1)
T4s  <- c(0.25,T4,1)
the.lm <- lm(T4s~T3s+I(T3s^2)+I(T3s^3)+I(T3s^4)+I(T3s^5))
lines(T3s, predict(the.lm), col=2)
max(residuals(the.lm))
summary(the.lm)
}