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. 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,B)
x |
A vector of data values. |
A |
A value for the plotting-position formula. |
B |
Another value for the plotting-position formula. |
An R list
is returned.
BETA0 |
The first PWM—equal to the arithmetic mean. |
BETA1 |
The second PWM. |
BETA2 |
The third PWM. |
BETA3 |
The fourth PWM. |
BETA4 |
The fifth 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., 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)