gumbelx {evd}

Maxima of Two Gumbel Distributions

Description

Density function, distribution function, quantile function and random generation for the maxima of two Gumbel distributions, each with different location and scale parameters.

Usage

dgumbelx(x, loc1=0, scale1=1, loc2=0, scale2=1, log = FALSE) 
pgumbelx(q, loc1=0, scale1=1, loc2=0, scale2=1, lower.tail = TRUE) 
qgumbelx(p, interval, loc1=0, scale1=1, loc2=0, scale2=1, lower.tail = TRUE, ...)
rgumbelx(n, loc1=0, scale1=1, loc2=0, scale2=1)

Arguments

x, q

Vector of quantiles.

p

Vector of probabilities.

n

Number of observations.

interval

A length two vector containing the end-points of the interval to be searched for the quantiles, passed to the uniroot function.

loc1, scale1, loc2, scale2

Location and scale parameters of the two Gumbel distributions. The second location parameter must be greater than or equal to the first location parameter.

log

Logical; if TRUE, the log density is returned.

lower.tail

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

...

Other arguments passed to uniroot.

Value

dgumbelx gives the density function, pgumbelx gives the distribution function, qgumbelx gives the quantile function, and rgumbelx generates random deviates.

See Also

fgev, rfrechet, rgumbel, rrweibull, uniroot

Examples

dgumbelx(2:4, 0, 1.1, 1, 0.5)
pgumbelx(2:4, 0, 1.1, 1, 0.5)
qgumbelx(seq(0.9, 0.6, -0.1), interval = c(0,10), 0, 1.2, 2, 0.5)
rgumbelx(6, 0, 1.1, 1, 0.5)
p <- (1:9)/10
pgumbelx(qgumbelx(p, interval = c(0,10), 0, 0.5, 1, 2), 0, 0.5, 1, 2)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9