lmomray {lmomco}

L-moments of the Rayleigh Distribution

Description

This function estimates the L-moments of the Rayleigh distribution given the parameters (\xi and \alpha) from parray. The L-moments in terms of the parameters are

\lambda_1 = \xi + \alpha\sqrt{\pi/2} \mbox{,}

\lambda_2 = \frac{1}{2} \alpha(\sqrt{2} - 1)\sqrt{\pi}\mbox{,}

\tau_3 = \frac{1 - 3/\sqrt{2} + 2/\sqrt{3}}{1 - 1/\sqrt{2}} = 0.1140 \mbox{, and}

\tau_4 = \frac{1 - 6/\sqrt{2} + 10/\sqrt{3} - 5\sqrt{4}}{1 - 1/\sqrt{2}} = 0.1054 \mbox{.}

Usage

lmomray(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: “lmomray”.

Author(s)

W.H. Asquith

References

Hosking, J.R.M., 1986, The theory of probability weighted moments: Research Report RC12210, IBM Research Division, Yorkton Heights, N.Y.

See Also

parray, cdfray, pdfray, quaray

Examples

lmr <- lmoms(c(123,34,4,654,37,78))
lmr
lmomray(parray(lmr))