pwm.ub {lmomco}R Documentation

Unbiased Sample Probability-Weighted Moments

Description

Unbiased sample Probability-Weighted Moments (PWMs) are computed from a sample. The first five β_r's are computed. The unbiased PWMs are computed by the the plotting-position formula by a call to pwm.pp{data,A=0,B=0}. The plotting-position formula is

p_i = frac{i+A}{n+B} mbox{,}

where p_i is the nonexceedance probability F of the ith ascending data values. The parameters A and B together specify the plotting position type, and n is the sample size. The PWMs are computed by

β_r = n^{-1}sum_{i=1}^{n}p_i^r times x_{j:n} mbox{,}

where x_{j:n} is the jth order statistic x_{1:n} <= x_{2:n} <= x_{j:n} ... <= x_{n:n} of random variable X, and r is 0, 1, 2, ....

Usage

pwm.ub(x)

Arguments

x A vector of data values.

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

pwm.pp, pwm.gev, pwm2lmom

Examples

pwm <- pwm.ub(rnorm(20))

[Package lmomco version 0.6 Index]