lmomco (version 2.0.1)

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)

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.
• source
  An attribute identifying the computational source of the L-moments: lmomgov.

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.

See Also

pargov, cdfgov, pdfgov, quagov

Examples

lmr <- lmom.ub(c(123,34,4,654,37,78))
lmorph(lmr)
lmomgov(pargov(lmr))

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())
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)