| /* |
| * Mathlib : A C Library of Special Functions |
| * Copyright (C) 2000-2021 The R Core Team |
| * Copyright (C) 2005-2021 The R Foundation |
| * Copyright (C) 1998 Ross Ihaka |
| * |
| * 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/ |
| * |
| * SYNOPSIS |
| * |
| * #include <Rmath.h> |
| * double qnbinom(double p, double size, double prob, |
| * int lower_tail, int log_p) |
| * |
| * DESCRIPTION |
| * |
| * The quantile function of the negative binomial distribution, |
| * for the (size, prob) parametrizations |
| * |
| * NOTES |
| * |
| * x = the number of failures before the n-th success |
| * |
| * METHOD |
| * |
| * Uses the Cornish-Fisher Expansion to include a skewness |
| * correction to a normal approximation. This gives an |
| * initial value which never seems to be off by more than |
| * 1 or 2. A search is then conducted of values close to |
| * this initial start point. |
| */ |
| |
| #include "nmath.h" |
| #include "dpq.h" |
| |
| /*-------- DEBUGGING ------------- make CFLAGS='-DDEBUG_qnbinom ...' |
| */ |
| #ifdef DEBUG_qnbinom |
| # define R_DBG_printf(...) REprintf(__VA_ARGS__) |
| #else |
| # define R_DBG_printf(...) |
| #endif |
| |
| #define _thisDIST_ nbinom |
| #define _dist_PARS_DECL_ double size, double prob |
| #define _dist_PARS_ size, prob |
| |
| #include "qDiscrete_search.h" |
| // ------------------> do_search() and all called by q_DISCRETE_*() below |
| |
| double qnbinom(double p, double size, double prob, int lower_tail, int log_p) |
| { |
| #ifdef IEEE_754 |
| if (ISNAN(p) || ISNAN(size) || ISNAN(prob)) |
| return p + size + prob; |
| #endif |
| |
| /* this happens if specified via mu, size, since |
| prob == size/(size+mu) |
| */ |
| if (prob == 0 && size == 0) return 0; |
| if (prob <= 0 || prob > 1 || size < 0) ML_WARN_return_NAN; |
| if (prob == 1 || size == 0) return 0; |
| |
| R_Q_P01_boundaries(p, 0, ML_POSINF); |
| |
| double |
| Q = 1.0 / prob, |
| P = (1.0 - prob) * Q, // = (1 - prob) / prob = Q - 1 |
| mu = size * P, |
| sigma = sqrt(size * P * Q), |
| gamma = (Q + P)/sigma; |
| |
| R_DBG_printf("qnbinom(p=%.12g, size=%.15g, prob=%g, l.t.=%d, log=%d):" |
| " mu=%g, sigma=%g, gamma=%g;\n", |
| p, size, prob, lower_tail, log_p, mu, sigma, gamma); |
| |
| q_DISCRETE_01_CHECKS(); |
| q_DISCRETE_BODY(); |
| } |