pwm.gev {lmomco}

Generalized Extreme Value Plotting-Position Probability-Weighted Moments

Description

Generalized Extreme Value plotting-position probability-weighted moments (PWMs) are computed from a sample. The first five \beta_r's are computed by default. The plotting-position formula for the Generalized Extreme Value distribution is

pp_i = \frac{i-0.35}{n} \mbox{,}

where pp_i is the nonexceedance probability F of the ith ascending values of the sample of size n. The PWMs are computed by

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

where x_{j:n} is the jth 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. Finally, pwm.gev dispatches to pwm.pp(data,A=-0.35,B=0) and does not have its own logic.

Usage

pwm.gev(x, nmom=5, sort=TRUE)

Arguments

x

A vector of data values.

nmom

Number of PWMs to return.

sort

Do 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.gev”.

Author(s)

W.H. Asquith

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, v. 15, pp. 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, v. 52, pp. 105–124.

See Also

pwm.ub, pwm.pp, pwm2lmom

Examples

pwm <- pwm.gev(rnorm(20))