lmomlmrq: L-moments of the Linear Mean Residual Quantile Function Distribution

Description

This function estimates the L-moments of the Linear Mean Residual Quantile Function distribution given the parameters ($\mu$ and $\alpha$) from parlmrq. The first six L-moments in terms of the parameters are $$\lambda_1 = \mu \mbox{,}$$ $$\lambda_2 = (\alpha + 3\mu)/6 \mbox{,}$$ $$\lambda_3 = 0 \mbox{,}$$ $$\lambda_4 = (\alpha + \mu)/12 \mbox{,}$$ $$\lambda_5 = (\alpha + \mu)/20 \mbox{, and}$$ $$\lambda_6 = (\alpha + \mu)/30 \mbox{.}$$

Because $\alpha + \mu > 0$, then $\tau_3 > 0$, so the distribution is positively skewed. The coefficient of L-variation is in the interval $(1/3, 2/3)$.

Usage

lmomlmrq(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: “lmomlmrq”.

Arguments

para: The parameters of the distribution.

Author

W.H. Asquith

References

Midhu, N.N., Sankaran, P.G., and Nair, N.U., 2013, A class of distributions with linear mean residual quantile function and it's generalizations: Statistical Methodology, v. 15, pp. 1--24.

Examples

Run this code

lmr <- lmoms(c(3, 0.05, 1.6, 1.37, 0.57, 0.36, 2.2))
lmr
lmomlmrq(parlmrq(lmr))

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