Density, distribution function, quantile function and
random generation for the SEV distribution with location
loc and scale scale.
qsev(p, loc = 0, scale = 1)psev(q, loc = 0, scale = 1)
dsev(x, loc = 0, scale = 1)
rsev(n, loc = 0, scale = 1)
ssev(x, loc = 0, scale = 1)
Vector of probabilities
Location parameter
Scale parameter
Vector of quantiles
Vector of quantiles
Number of observations
dsev gives the density,
psev gives the distribution function,
qsev gives the quantile function, and
rsev generates random observations.
The length of the result is determined by n
for rsev, and is the maximum of the lengths
of the numerical arguments for the other functions.
The numerical arguments other than n are
recycled to the length of the result.
If loc is not specified, a default
value of 0 is used. If scale is not
specified, a default value of 1 is used.
The smallest extreme value distribution with location parameter \(\mu\) and scale \(\sigma\) has density
$$f(x;\mu,\sigma) = \frac{1}{\sigma}\phi_{_{SEV}}\left(\frac{x-\mu}{\sigma}\right),\quad -\infty < x < \infty $$
where \(\phi_{_{SEV}}(z)\) exp[z - exp(z)] is the density of the standard LEV distribution.