pwm: Unbiased Sample Probability-Weighted Moments

Description Usage Arguments Value Author(s) References See Also Examples

Description

Unbiased sample probability-weighted moments (PWMs) are computed from a sample. The β_r's are computed using

β_r = n^{-1}∑^n_{j=1} {j-1 \choose r} x_{j:n}\mbox{.}

Usage

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pwm(x, nmom=5, sort=TRUE)

Arguments

x

A vector of data values.

nmom

Number of PWMs to return (r = nmom - 1).

sort

Do the data need sorting? The computations require sorted data. This option is provided to optimize processing speed if presorted data already exists.

Value

An R list is returned.

betas

The PWMs. Note that convention is the have a β_0, but this is placed in the first index i=1 of the betas vector.

source

Source of the PWMs: “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, v. 15, pp. 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, v. 52, pp. 105–124.

See Also

lmoms, pwm2lmom, pwm

Examples

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# Data listed in Hosking (1995, table 29.2, p. 551)
H <- c(3,4,5,6,6,7,8,8,9,9,9,10,10,11,11,11,13,13,13,13,13,
       17,19,19,25,29,33,42,42,51.9999,52,52,52)
# 51.9999 was really 52, but a real non censored data point.
z <-  pwmRC(H,52,checkbetas=TRUE)
str(z)
# Hosking(1995) reports that A-type L-moments for this sample are
# lamA1=15.7 and lamAL-CV=.389, and lamAL-skew=.393
pwm2lmom(z$Abetas)
# WHA gets 15.666, 0.3959, and 0.4030

# See p. 553 of Hosking (1995)
# Data listed in Hosking (1995, table 29.3, p. 553)
D <- c(-2.982, -2.849, -2.546, -2.350, -1.983, -1.492, -1.443,
       -1.394, -1.386, -1.269, -1.195, -1.174, -0.854, -0.620,
       -0.576, -0.548, -0.247, -0.195, -0.056, -0.013,  0.006,
        0.033,  0.037,  0.046,  0.084,  0.221, 0.245, 0.296)
D <- c(D,rep(.2960001,40-28)) # 28 values, but Hosking mentions
                              # 40 values in total
z <-  pwmRC(D,.2960001)
# Hosking reports B-type L-moments for this sample are
# lamB1 = -.516 and lamB2 = 0.523
pwm2lmom(z$Bbetas)
# WHA gets -.5162 and 0.5218

Example output

Betas: 18.9696939393939 13.5880654356061 10.9387194159335 9.25512362292278 8.04940980289547 
checkBbetas: 18.9696939393939 13.5880654356061 10.9387194159335 9.25512362292278 8.04940980289547 
List of 8
 $ Abetas           : num [1:5] 15.67 10.93 8.74 7.41 6.49
 $ Bbetas           : num [1:5] 18.97 13.59 10.94 9.26 8.05
 $ source           : chr "pwmRC"
 $ threshold        : num 52
 $ zeta             : num 0.909
 $ numabovethreshold: int 3
 $ observedsize     : int 30
 $ samplesize       : int 33
$lambdas
[1] 15.666663  6.202296  2.499668  1.513826  0.377672

$ratios
[1]         NA 0.39589129 0.40302308 0.24407516 0.06089229

$source
[1] "pwm2lmom"

$lambdas
[1] -0.516299970  0.521805150 -0.191875497  0.025479444 -0.003476176

$ratios
[1]           NA -1.010662754 -0.367714840  0.048829422 -0.006661828

$source
[1] "pwm2lmom"

lmomco documentation built on Aug. 4, 2021, 9:06 a.m.