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lmomco (version 0.6)

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. The plotting-position formula for the Generalized Extreme Value distribution is

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

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 $0, 1, 2, \dots$. Finally, pwm.gev dispatches to pwm.pp(data,A=-0.35,B=0) and does not have its own logic.

Usage

pwm.gev(x)

Arguments

x
A vector of data values.

Value

  • An R list is returned.
  • BETA0The first PWM---equal to the arithmetic mean.
  • BETA1The second PWM.
  • BETA2The third PWM.
  • BETA3The fourth PWM.
  • BETA4The fifth PWM.

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.pp, pwm2lmom

Examples

Run this code
pwm <- pwm.gev(rnorm(20))

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