R: Maxima of Two Gumbel Distributions

gumbelx {evd} | R Documentation

## 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

[Package evd version 2.3-5 Index]