rFFrankJoe: Sampling Distribution F for Frank and Joe
Description
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 $\alpha=\theta_0/\theta_1$.
Usage
rFFrank(n, theta0, theta1, rej)
rFJoe(n, alpha)
Arguments
n
number of variates from $F$.
theta0
parameter $\theta_0$.
theta1
parameter $\theta_1$.
rej
method switch for rFFrank: if theta0 >
rej a rejection from Joe's family (Sibuya distribution) is
applied (otherwise, a logarithmic envelope is used).
alpha
parameter $\alpha=
\theta_0/\theta_1$ in $(0,1]$ for
rFJoe.
Value
numeric vector of random variates $V$ of length n.