Density, distribution function, quantile function and
random generation for the LEV distribution with location
loc and scale scale.
qlev(p, loc = 0, scale = 1)plev(q, loc = 0, scale = 1)
dlev(x, loc = 0, scale = 1)
rlev(n, loc = 0, scale = 1)
Vector of probabilities
Location parameter
Scale parameter
Vector of quantiles
Vector of quantiles
Number of observations
dlev gives the density,
plev gives the distribution function,
qlev gives the quantile function, and
rlev generates random observations.
The length of the result is determined by n
for rlev, 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 largest extreme value distribution with location parameter \(\mu\) and scale \(\sigma\) has density
$$f(x;\mu,\sigma) = \frac{1}{\sigma}\phi_{_{LEV}}\left(\frac{x-\mu}{\sigma}\right),\quad -\infty < x < \infty $$
where \(\phi_{_{LEV}}(z)\) exp[-z - exp(-z)] is the density of the standard LEV distribution.