GenExtrVal: The Generalized Extreme Value Distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Density function, distribution function, quantile function and random generation for the generalized Extreme value (GenExtrVal) distribution with location, scale and shape parameters.

Usage

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dGenExtrVal(x, loc=0, scale=1, shape=0, log = FALSE)
pGenExtrVal(q, loc=0, scale=1, shape=0, lower.tail = TRUE)
qGenExtrVal(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
rGenExtrVal(n, loc=0, scale=1, shape=0)

Arguments

x, q

Vector of quantiles.

p

Vector of probabilities.

n

Number of observations.

loc, scale, shape

Location, scale and shape parameters; the shape argument cannot be a vector (must have length one).

log

Logical; if TRUE, the log density is returned.

lower.tail

Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The GenExtrVal distribution function with parameters loc = a, scale = b and shape = s is

G(x) = exp[-{1+s(z-a)/b}^(-1/s)]

for 1+s(z-a)/b > 0, where b > 0. If s = 0 the distribution is defined by continuity. If 1+s(z-a)/b <= 0, the value z is either greater than the upper end point (if s < 0), or less than the lower end point (if s > 0).

The parametric form of the GenExtrVal encompasses that of the Gumbel, Frechet and reverse Weibull distributions, which are obtained for s = 0, s > 0 and s < 0 respectively. It was first introduced by Jenkinson (1955).

Value

dGenExtrVal gives the density function, pGenExtrVal gives the distribution function, qGenExtrVal gives the quantile function, and rGenExtrVal generates random deviates.

Author(s)

Alec Stephenson <alec_stephenson@hotmail.com>

References

Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158–171.

See Also

rFrechet, rGumbel, rRevWeibull

Examples

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dGenExtrVal(2:4, 1, 0.5, 0.8)
pGenExtrVal(2:4, 1, 0.5, 0.8)
qGenExtrVal(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
rGenExtrVal(6, 1, 0.5, 0.8)
p <- (1:9)/10
pGenExtrVal(qGenExtrVal(p, 1, 2, 0.8), 1, 2, 0.8)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

DescTools documentation built on June 17, 2021, 5:12 p.m.