pwm.pp {lmomco} | R Documentation |
The sample Probability-Weighted Moments (PWMs) are computed from the plotting positions of the data. The first five β_r's are computed by default. The plotting-position formula is
p_i = frac{i+A}{n+B} mbox{,}
where pp_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, ....
pwm.pp(x,A=0,B=0,nmom=5,sort=TRUE)
x |
A vector of data values. |
A |
A value for the plotting-position formula. If A and B are both zero then the unbiased PWMs are computed through pwm.ub |
B |
Another value for the plotting-position formula. If A and B are both zero then the unbiased PWMs are computed through pwm.ub |
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.pp” |
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., 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.
pwm <- pwm.pp(rnorm(20),A=-0.35,B=0)