Generate a vector of variates \(V \sim F\) from the distribution
function \(F\) with Laplace-Stieltjes transform
$$(1-(1-\exp(-t)(1-e^{-\theta_1}))^\alpha)/(1-e^{-\theta_0}),
$$
for Frank, or
$$1-(1-\exp(-t))^\alpha,$$ for Joe, respectively,
where \(\theta_0\) and \(\theta_1\) denote two parameters
of Frank (that is, \(\theta_0,\theta_1\in(0,\infty)\)) and Joe (that is, \(\theta_0,\theta_1\in[1,\infty)\)) satisfying
\(\theta_0\le\theta_1\)
and \(\alpha=\theta_0/\theta_1\).