| 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) = \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 arnost.komarek@mff.cuni.cz
Examples
dextreme(1, (sqrt(6)/pi)*0.5772, sqrt(6)/pi)
dstextreme(1) ## approximately same result as on the previous row