pwm.ub {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} {n-1 choose r}^{-1} sum^n_{j=1} (j-1 choose r)x_{j:n}
pwm.ub(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.ub” |
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.
pwm <- pwm.ub(rnorm(20))