L-moments of the Rayleigh Distribution

Description

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

λ_1 = ξ + α√{π/2} \mbox{,}

λ_2 = \frac{1}{2} α(√{2} - 1)√{π}\mbox{,}

τ_3 = \frac{1 - 3/√{2} + 2/√{3}}{1 - 1/√{2}} = 0.1140 \mbox{, and}

τ_4 = \frac{1 - 6/√{2} + 10/√{3} - 5√{4}}{1 - 1/√{2}} = 0.1054 \mbox{.}

Usage

1
lmomray(para)

Arguments

para

The parameters of the distribution.

Value

An R list is returned.

lambdas

Vector of the L-moments. First element is λ_1, second element is λ_2, and so on.

ratios

Vector of the L-moment ratios. Second element is τ, third element is τ_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

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

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