rFFrankJoe {copula}

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.

Details

rFFrank(n, theta0, theta1, rej) calls rF01Frank(rep(1,n), theta0, theta1, rej, 1) and rFJoe(n, alpha) calls rSibuya(n, alpha).

Value

numeric vector of random variates V of length n.

See Also

rF01Frank, rF01Joe, also for references. rSibuya, and rnacopula.

Examples

## Simple definition of the functions:
rFFrank
rFJoe