lmomray {lmomco}R Documentation

L-moments of the Rayleigh Distribution

Description

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

λ_1 = xi + αsqrt{π/2} mbox{,}

λ_2 = frac{1}{2} α(sqrt{2} - 1)sqrt{π}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} - 5sqrt{4}}{1 - 1/sqrt{2}} = 0.1054 mbox{.}

Usage

lmomray(para)

Arguments

para The parameters of the distribution.

Value

An R list is returned.

L1 Arithmetic mean.
L2 L-scale—analogous to standard deviation.
LCV coefficient of L-variation—analogous to coe. of variation.
TAU3 The third L-moment ratio or L-skew–analogous to skew.
TAU4 The fourth L-moment ratio or L-kurtosis—analogous to kurtosis.
TAU5 The fifth L-moment ratio.
L3 The third L-moment.
L4 The fourth L-moment.
L5 The fifth L-moment.
source An attribute identifying the computational source of the L-moments: “lmomgum”.

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

pargum, quagum, cdfgum

Examples

lmr <- lmom.ub(c(123,34,4,654,37,78))
lmr
lmomray(parray(lmr))

[Package lmomco version 0.96.3 Index]