Unbiased sample probability-weighted moments (PWMs) are computed from a sample. The \(\beta_r\)'s are computed using $$\beta_r = n^{-1} {n-1 \choose r}^{-1} \sum^n_{j=1} {j-1 \choose r} x_{j:n}\mbox{.}$$
pwm.ub(x, nmom=5, sort=TRUE)An R
list is returned.
The PWMs. Note that convention is the have a \(\beta_0\), but this is placed in the first index i=1 of the betas vector.
Source of the PWMs: “pwm.ub”.
A vector of data values.
Number of PWMs to return (\(r =\) nmom - 1).
Do the data need sorting? The computations require sorted data. This option is provided to optimize processing speed if presorted data already exists.
W.H. Asquith
Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978--146350841--8.
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.
Stedinger, J.R., Vogel, R.M., Foufoula-Georgiou, E., 1993, Frequency analysis of extreme events: in Handbook of Hydrology, ed. Maidment, D.R., McGraw-Hill, Section 18.6 Partial duration series, mixtures, and censored data, pp. 18.37--18.39.
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.
pwm.pp, pwm.gev, pwm2lmom