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 $$\lambda_1 = \mu \mbox{,}$$ $$\lambda_2 = (\alpha + 3\mu)/6 \mbox{,}$$ $$\lambda_3 = 0 \mbox{,}$$ $$\lambda_4 = (\alpha + \mu)/12 \mbox{,}$$ $$\lambda_5 = (\alpha + \mu)/20 \mbox{, and}$$ $$\lambda_6 = (\alpha + \mu)/30 \mbox{.}$$

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)

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))
# }