copula (version 0.999-1)

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.

Details

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

See Also

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

Examples

## Simple definition of the functions:
rFFrank
rFJoe