The Generalized Extreme Value Distribution
Density function, distribution function, quantile function and random generation for the generalized Extreme value (GenExtrVal) distribution with location, scale and shape parameters.
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)
x, q |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
loc, scale, shape |
Location, scale and shape parameters; the
|
log |
Logical; if |
lower.tail |
Logical; if |
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).
dGenExtrVal gives the density function, pGenExtrVal gives the
distribution function, qGenExtrVal gives the quantile function,
and rGenExtrVal generates random deviates.
Alec Stephenson <alec_stephenson@hotmail.com>
Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158–171.
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
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