gev {evd} | R Documentation |
Density function, distribution function, quantile function and random generation for the generalized extreme value (GEV) distribution with location, scale and shape parameters.
dgev(x, loc=0, scale=1, shape=0, log = FALSE) pgev(q, loc=0, scale=1, shape=0, lower.tail = TRUE) qgev(p, loc=0, scale=1, shape=0, lower.tail = TRUE) rgev(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
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] |
The GEV 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 GEV encompasses that of the Gumbel, Frechet and reversed Weibull distributions, which are obtained for s = 0, s > 0 and s < 0 respectively. It was first introduced by Jenkinson (1955).
dgev
gives the density function, pgev
gives the
distribution function, qgev
gives the quantile function,
and rgev
generates random deviates.
Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158–171.
fgev
, rfrechet
,
rgumbel
, rrweibull
dgev(2:4, 1, 0.5, 0.8) pgev(2:4, 1, 0.5, 0.8) qgev(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8) rgev(6, 1, 0.5, 0.8) p <- (1:9)/10 pgev(qgev(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