These functions provide information about the generalized Weibull
distribution, also called the exponentiated Weibull, with scale
parameter equal to m, shape equal to s, and family
parameter equal to f: density, cumulative distribution,
quantiles, log hazard, and random generation.
The generalized Weibull distribution has density
$$
f(y) = \frac{\sigma \nu y^{\sigma-1} (1-\exp(-(y/\mu)^\sigma))^{\nu-1}
\exp(-(y/\mu)^\sigma)}{\mu^\sigma}$$
where \(\mu\) is the scale parameter of the distribution,
\(\sigma\) is the shape, and \(\nu\) is the family
parameter.
\(\nu=1\) gives a Weibull distribution, for
\(\sigma=1\), \(\nu<0\) a generalized F distribution,
and for \(\sigma>0\), \(\nu\leq0\) a Burr type XII distribution.