dextreme: Density of the Extreme Value Distribution of a Minimum.

In smoothSurv: Survival Regression with Smoothed Error Distribution

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) = \frac{1}{\beta}\exp\left[\frac{x-\alpha}{\beta}-\exp\left(\frac{x-\alpha}{\beta}\right)\right]

the mean equal to \alpha - \beta\;e, where e is approximately 0.5772 and the variance equal to \beta^2\frac{\pi}{6}. Its standardized version is obtained with \alpha = \frac{\sqrt{6}}{\pi}\;e and \beta = \frac{\sqrt{6}}{\pi}

Value

The value of the density.

Author(s)

Arnošt Komárek [e-mail]

Examples

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

smoothSurv documentation built on June 22, 2024, 11:11 a.m.