gevUC: The Generalized Extreme Value Distribution

In VGAM: Vector Generalized Linear and Additive Models

The Generalized Extreme Value Distribution

Description

Density, distribution function, quantile function and random generation for the generalized extreme value distribution (GEV) with location parameter location, scale parameter scale and shape parameter shape.

Usage

dgev(x, location = 0, scale = 1, shape = 0, log = FALSE,
     tolshape0 = sqrt(.Machine$double.eps))
pgev(q, location = 0, scale = 1, shape = 0, lower.tail = TRUE, log.p = FALSE)
qgev(p, location = 0, scale = 1, shape = 0, lower.tail = TRUE, log.p = FALSE)
rgev(n, location = 0, scale = 1, shape = 0)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1 then the length is taken to be the number required.
location	the location parameter \mu.
scale	the (positive) scale parameter \sigma. Must consist of positive values.
shape	the shape parameter \xi.
log	Logical. If log = TRUE then the logarithm of the density is returned.
lower.tail, log.p	Same meaning as in punif or qunif.
tolshape0	Positive numeric. Threshold/tolerance value for resting whether \xi is zero. If the absolute value of the estimate of \xi is less than this value then it will be assumed zero and a Gumbel distribution will be used.

Details

See gev, the VGAM family function for estimating the 3 parameters by maximum likelihood estimation, for formulae and other details. Apart from n, all the above arguments may be vectors and are recyled to the appropriate length if necessary.

Value

dgev gives the density, pgev gives the distribution function, qgev gives the quantile function, and rgev generates random deviates.

Note

The default value of \xi = 0 means the default distribution is the Gumbel.

Currently, these functions have different argument names compared with those in the evd package.

Author(s)

T. W. Yee

References

Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.

See Also

gev, gevff, vglm.control.

Examples

 loc <- 2; sigma <- 1; xi <- -0.4
pgev(qgev(seq(0.05, 0.95, by = 0.05), loc, sigma, xi), loc, sigma, xi)
## Not run:  x <- seq(loc - 3, loc + 3, by = 0.01)
plot(x, dgev(x, loc, sigma, xi), type = "l", col = "blue", ylim = c(0, 1),
     main = "Blue is density, orange is the CDF",
     sub = "Purple are 10,...,90 percentiles", ylab = "", las = 1)
abline(h = 0, col = "blue", lty = 2)
lines(qgev(seq(0.1, 0.9, by = 0.1), loc, sigma, xi),
      dgev(qgev(seq(0.1, 0.9, by = 0.1), loc, sigma, xi), loc, sigma, xi),
      col = "purple", lty = 3, type = "h")
lines(x, pgev(x, loc, sigma, xi), type = "l", col = "orange")
abline(h = (0:10)/10, lty = 2, col = "gray50")

## End(Not run)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.