lmomco (version 0.88)

pwm.gev: 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

$$p_i = \frac{i-0.35}{n} \mbox{,}$$

where $p_i$ is the nonexceedance probability $F$ of the $i$th ascending values of the sample of size $n$. 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 $0, 1, 2, \dots$. 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

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.gev

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. and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

See Also

pwm.ub, pwm.pp, pwm2lmom

Examples

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