lmom2pwm {lmomco}R Documentation

L-moments to Probability-Weighted Moments

Description

Converts the L-moments to the Probability-Weighted Moments (PWMs) given the L-moments. The conversion is linear so procedures based on L-moments are identical to those based on PWMs. The relation between L-moments and PWMs is shown with pwm2lmom.

Usage

lmom2pwm(lmom)

Arguments

lmom An L-moment object created by lmom.ub or similar.

Details

PWMs are linear combinations of the L-moments and therefore contain the same statistical information of the data as the L-moments. However, the PWMs are harder to interpret as measures of probability distributions. The PWMs are included here for theoretical completeness and are not intended for use with the majority of the other functions implementing the various probability distributions. The relation between L-moments (λ_r)and PWMs (β_{r-1}) for 1 <= r <= 5 order is

λ_1 = β_0 mbox{,}

λ_2 = 2β_1 - β_0 mbox{,}

λ_3 = 6β_2 - 6β_1 + β_0 mbox{,}

λ_4 = 20β_3 - 30β_2 + 12β_1 - β_0mbox{, and}

λ_5 = 70β_4 - 140β_3 + 90β_2 - 20β_1 + β_0mbox{.}

The linearity between L-moments and PWMs means that procedures based on one are equivalent to the other.

Value

An R list is returned.

BETA0 The first PWM—equal to the arithmetic mean.
BETA1 The second PWM.
BETA2 The third PWM.
BETA3 The fourth PWM.
BETA4 The fifth PWM.

Author(s)

W.H. Asquith

References

Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, J.R., 1979, Probability weighted moments—Definition and relation to parameters of several distributions expressable in inverse form: Water Resources Research, vol. 15, p. 1,049–1,054.

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

See Also

lmom.ub, pwm.ub, pwm2lmom

Examples

pwm <- lmom2pwm(lmom.ub(c(123,34,4,654,37,78)))

lmom2pwm(lmom.ub(rnorm(100)))

[Package lmomco version 0.84 Index]