lmomlmrq {lmomco}

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”.

Author(s)

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.

See Also

parlmrq, cdflmrq, pdflmrq, qualmrq

Examples

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