pwm {lmomco} | R Documentation |
Unbiased sample Probability-Weighted Moments (PWMs) are computed from a sample. The first five β_r's are computed by default.
β_r = n^{-1}sum^n_{j=1} (j-1 choose r)x_{j:n}
pwm(x,nmom=5,sort=TRUE)
x |
A vector of data values. |
nmom |
Number of PWMs to return. |
sort |
Does the data need sorting? The computations require sorted data. This option is provided to optimize processing speed if presorted data already exists. |
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” |
W.H. Asquith
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. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.
# 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$Abetas) # My version of R reports 15.666, 0.3959, and 0.4030 # See p. 553 of Hosking (1995) # Data listed in Hosking (1995, table 29.3, p. 553) D <- c(-2.982, -2.849, -2.546, -2.350, -1.983, -1.492, -1.443, -1.394, -1.386, -1.269, -1.195, -1.174, -0.854, -0.620, -0.576, -0.548, -0.247, -0.195, -0.056, -0.013, 0.006, 0.033, 0.037, 0.046, 0.084, 0.221, 0.245, 0.296) D <- c(D,rep(.2960001,40-28)) # 28 values, but Hosking mentions 40 values in total z <- pwmRC(D,.2960001) # Hosking reports B-type L-moments for this sample are # lamB1 = -.516 and lamB2 = 0.523 pwm2lmom(z$Bbetas) # My version of R reports -.5162 and 0.5218