lmomco (version 0.88)

pwm.pp: Plotting-Position Sample Probability-Weighted Moments

Description

The sample Probability-Weighted Moments (PWMs) are computed from the plotting positions of the data. The first five $\beta_r$'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 $i$th 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

$$\beta_r = n^{-1}\sum_{i=1}^{n}p_i^r \times x_{j:n} \mbox{,}$$

where $x_{j:n}$ is the $j$th order statistic $x_{1:n} \le x_{2:n} \le x_{j:n} \dots \le x_{n:n}$ of random variable X, and $r$ is $0, 1, 2, \dots$.

Usage

pwm.pp(x,A=0,B=0,nmom=5,sort=TRUE)

Arguments

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.

Value

• An R list is returned.
• betas
  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
  Source of the PWMs: pwm.pp

References

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.

See Also

pwm.ub, pwm.gev, pwm2lmom

Examples

pwm <- pwm.pp(rnorm(20),A=-0.35,B=0)