extreme value {smoothSurv}R Documentation

Density of the Extreme Value Distribution of a Minimum.

Description

Density function of the extreme value distribution of a minimum with location alpha and scale beta and the density of the standardized version (with zero mean and unit variance).

Usage

dextreme(x, alpha=0, beta=1)
dstextreme(x)

Arguments

x

Vector of quantiles.

alpha

Vector of location parameters.

beta

Vector of scale parameters.

Details

Extreme value distribution of a minimum with the location alpha and the scale beta has a density

f(x) = (1/beta)*exp((x-alpha)/beta - exp((x-alpha)/beta))

the mean equal to alpha - beta*e, where e is approximately 0.5772 and the variance equal to beta^2 pi^2/6. Its standardized version is obtained with alpha = (sqrt(6)/pi)*e and beta = (sqrt(6)/pi).

Value

The value of the density.

Author(s)

Arnošt Komárek arnost.komarek[AT]mff.cuni.cz

Examples

dextreme(1, (sqrt(6)/pi)*0.5772, sqrt(6)/pi)
dstextreme(1)        ## approximately same result as on the previous row

[Package smoothSurv version 2.0.1 Index]