lmomco (version 2.3.1)

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 $${\lambda }_1=\mu \text{,}$$ $${\lambda }_2=(\alpha +3\mu )/6\text{,}$$ $${\lambda }_3=0\text{,}$$ $${\lambda }_4=(\alpha +\mu )/12\text{,}$$ $${\lambda }_5=(\alpha +\mu )/20\text{, and}$$ $${\lambda }_6=(\alpha +\mu )/30\text{.}$$

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)

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: “lmomlmrq”.

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.

See Also

parlmrq, cdflmrq, pdflmrq, qualmrq

Examples

# NOT RUN {
lmr <- lmoms(c(3, 0.05, 1.6, 1.37, 0.57, 0.36, 2.2))
lmr
lmomlmrq(parlmrq(lmr))
# }