copula (version 0.999-19)

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

Run this code
# NOT RUN {
## Simple definition of the functions:
rFFrank
rFJoe
# }

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