##### https://github.com/cran/nacopula

Revision

**161411bb86f97e5a8bd89091cd61d03a33c2761a**authored by Martin Maechler on**06 February 2012, 00:00:00 UTC**, committed by Gabor Csardi on**06 February 2012, 00:00:00 UTC****1 parent**5bc804b

Tip revision:

**161411bb86f97e5a8bd89091cd61d03a33c2761a**authored by**Martin Maechler**on**06 February 2012, 00:00:00 UTC****version 0.8-0** Tip revision:

**161411b** rF01Frank.c

```
/*
Copyright (C) 2010 Marius Hofert and Martin Maechler
This program is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation; either version 3 of the License, or (at your option) any later
version.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
details.
You should have received a copy of the GNU General Public License along with
this program; if not, see <http://www.gnu.org/licenses/>.
*/
#include <Rmath.h>
#include "nacopula.h"
/**
* Sample V01 ~ F01 with Laplace-Stieltjes transform
* Used, e.g., for sampling F01 for Joe and for sampling F01 for Frank.
* Note: The caller of this function must use GetRNGstate() and PutRNGstate().
* The commented part also includes the algorithm of Hofert (2011)
* "Efficiently sampling nested Archimedean copulas", but does not improve
* run time.
* @param V0 parameter V0
* @param theta_0 parameter theta0 in (0,infinity)
* @param theta_1 parameter theta1 in [theta0, infinity)
* @param p0 parameter 1-exp(-theta0)
* @param p1 parameter 1-exp(-theta1)
* @param gamma_1_a Gamma(1-alpha)
* @param rej method switch: if V0*theta_0*p0^(V0-1) > rej a rejection
* from F01 of Joe is applied (otherwise, the sum is
* sampled via a logarithmic envelope for the summands)
* @param approx largest number of summands before asymptotics is used
* @return a random variate from F01
* @author Marius Hofert, Martin Maechler
*/
double rF01Frank(double V0, double theta0, double theta1, double p0, double p1,
double gamma_1_a, double rej, int approx)
{
double alpha = theta0 / theta1, iAlpha = (theta1-theta0)/theta1, U, V;
if(V0*theta0*pow(p0,V0-1.) > rej) { /**< sample V01 via standard rejection from F01 for Joe */
do {
U = unif_rand();
V = rF01Joe(V0, alpha,gamma_1_a, approx);
} while(U > pow(p1, V));
} else { /**< sample V01 as the V0-fold sum where the summands are sampled
via rejection with a logarithmic envelope */
double Ip = exp(-theta1);
V = 0.;
double X;
/* if(theta0 <= theta1){ */
for(int j=0; j < (int) V0; j++){ /**< sample V01 as a sum */
do {
U = unif_rand();
X = rLog(p1,Ip);
} while (U*(X-alpha) > 1./beta(X, iAlpha)); /**< X is now one summand of the sum of V01 */
V += X;
}
/* }else{ */
/* for(int j=0; j < (int) V0; j++){ /\**< sample V01 as a sum *\/ */
/* do { */
/* U = unif_rand(); */
/* X = rSibuya(alpha,gamma_1_a); */
/* } while (U > pow(p1,X-1.)); /\**< X is now one summand of the sum of V01*\/ */
/* V += X; */
/* } */
/* } */
}
return V;
}
/**
* Generate a vector of variates V01 ~ F01 with Laplace-Stieltjes transform
* ((1-(1-exp(-t)*(1-e^(-theta1)))^alpha)/(1-e^(-theta0)))^V0. Vectorized version
* of rF01Frank.
* @param V01 vector of random variates from F01 (result)
* @param V0 vector of random variates from F0
* @param n length of the vectors V0 and V01
* @param theta0 parameter theta0 in (0,infinity)
* @param theta1 parameter theta1 in [theta0, infinity)
* @param rej method switch, see rF01Frank
* @param approx largest number of summands before asymptotics is used
* @return none
* @author Marius Hofert
*/
void rF01Frank_vec(double *V01, const double *V0, int n, double theta0,
double theta1, double rej, int approx){
double p0 = -expm1(-theta0), p1 = - expm1(-theta1),
iAlpha = (theta1 - theta0) / theta1, gamma_1_a = gammafn(iAlpha);
GetRNGstate();
for(int i=0; i < n; i++)
V01[i] = rF01Frank(V0[i], theta0, theta1, p0, p1, gamma_1_a, rej, approx);
PutRNGstate();
return;
}
/**
* Generate a vector of variates V01 ~ F01 with Laplace-Stieltjes transform
* ((1-(1-exp(-t)*(1-e^(-theta1)))^alpha)/(1-e^(-theta0)))^V0. Bridge to R. Used,
* e.g., to draw several variates from rF01Frank.
* @param V0_ vector of random variates from F0
* @param theta_0_ parameter theta0 in (0,infinity)
* @param theta_1_ parameter theta1 in [theta0, infinity)
* @param rej_ method switch, see rF01Frank
* @param approx_ largest number of summands before asymptotics is used
* @return vector of random variates V01
* @author Martin Maechler, Marius Hofert
*/
SEXP rF01Frank_vec_c(SEXP V0_, SEXP theta_0_, SEXP theta_1_, SEXP rej_, SEXP approx_){
double *V0 = REAL(V0_);
int n = length(V0_);
double theta_0 = asReal(theta_0_), theta_1 = asReal(theta_1_), rej = asReal(rej_);
int approx = asInteger(approx_);
SEXP res = PROTECT(allocVector(REALSXP, n));
if(n >= 1) rF01Frank_vec(REAL(res), V0, n, theta_0, theta_1, rej, approx);
UNPROTECT(1);
return res;
}
```

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