# lmomray: 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”.

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.

parray, cdfray, pdfray, quaray

### Examples

 1 2 3 lmr <- lmoms(c(123,34,4,654,37,78)) lmr lmomray(parray(lmr)) 

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