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/*
* Mathlib : A C Library of Special Functions
* Copyright (C) 1998 Ross Ihaka
* Copyright (C) 2000-2016 The R Core Team
*
* 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 2 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, a copy is available at
* https://www.R-project.org/Licenses/
*
* DESCRIPTION
*
* The distribution function of the negative binomial distribution.
*
* NOTES
*
* x = the number of failures before the n-th success
*/
#include "nmath.h"
#include "dpq.h"
double pnbinom(double x, double size, double prob, int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(size) || ISNAN(prob))
return x + size + prob;
if(!R_FINITE(size) || !R_FINITE(prob)) ML_ERR_return_NAN;
#endif
if (size < 0 || prob <= 0 || prob > 1) ML_ERR_return_NAN;
/* limiting case: point mass at zero */
if (size == 0)
return (x >= 0) ? R_DT_1 : R_DT_0;
if (x < 0) return R_DT_0;
if (!R_FINITE(x)) return R_DT_1;
x = floor(x + 1e-7);
return pbeta(prob, size, x + 1, lower_tail, log_p);
}
double pnbinom_mu(double x, double size, double mu, int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(size) || ISNAN(mu))
return x + size + mu;
if(!R_FINITE(mu)) ML_ERR_return_NAN;
#endif
if (size < 0 || mu < 0) ML_ERR_return_NAN;
/* limiting case: point mass at zero */
if (size == 0)
return (x >= 0) ? R_DT_1 : R_DT_0;
if (x < 0) return R_DT_0;
if (!R_FINITE(x)) return R_DT_1;
if (!R_FINITE(size)) // limit case: Poisson
return(ppois(x, mu, lower_tail, log_p));
x = floor(x + 1e-7);
/* return
* pbeta(pr, size, x + 1, lower_tail, log_p); pr = size/(size + mu), 1-pr = mu/(size+mu)
*
*= pbeta_raw(pr, size, x + 1, lower_tail, log_p)
* x. pin qin
*= bratio (pin, qin, x., 1-x., &w, &wc, &ierr, log_p), and return w or wc ..
*= bratio (size, x+1, pr, 1-pr, &w, &wc, &ierr, log_p) */
{
int ierr;
double w, wc;
bratio(size, x+1, size/(size+mu), mu/(size+mu), &w, &wc, &ierr, log_p);
if(ierr)
MATHLIB_WARNING(_("pnbinom_mu() -> bratio() gave error code %d"), ierr);
return lower_tail ? w : wc;
}
}