| /* |
| * Mathlib : A C Library of Special Functions |
| * Copyright (C) 1998 Ross Ihaka |
| * Copyright (C) 2000-2016 The R Core Team |
| * Copyright (C) 2005-2016 The R Foundation |
| * |
| * 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. |
| * |
| * 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" |
| |
| static double |
| do_search(double y, double *z, double p, double n, double pr, double incr) |
| { |
| if(*z >= p) { /* search to the left */ |
| for(;;) { |
| if(y == 0 || |
| (*z = pnbinom(y - incr, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) < p) |
| return y; |
| y = fmax2(0, y - incr); |
| } |
| } |
| else { /* search to the right */ |
| for(;;) { |
| y = y + incr; |
| if((*z = pnbinom(y, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) >= p) |
| return y; |
| } |
| } |
| } |
| |
| |
| double qnbinom(double p, double size, double prob, int lower_tail, int log_p) |
| { |
| double P, Q, mu, sigma, gamma, z, y; |
| |
| #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_ERR_return_NAN; |
| |
| if (prob == 1 || size == 0) return 0; |
| |
| R_Q_P01_boundaries(p, 0, ML_POSINF); |
| |
| Q = 1.0 / prob; |
| P = (1.0 - prob) * Q; |
| mu = size * P; |
| sigma = sqrt(size * P * Q); |
| gamma = (Q + P)/sigma; |
| |
| /* Note : "same" code in qpois.c, qbinom.c, qnbinom.c -- |
| * FIXME: This is far from optimal [cancellation for p ~= 1, etc]: */ |
| if(!lower_tail || log_p) { |
| p = R_DT_qIv(p); /* need check again (cancellation!): */ |
| if (p == R_DT_0) return 0; |
| if (p == R_DT_1) return ML_POSINF; |
| } |
| /* temporary hack --- FIXME --- */ |
| if (p + 1.01*DBL_EPSILON >= 1.) return ML_POSINF; |
| |
| /* y := approx.value (Cornish-Fisher expansion) : */ |
| z = qnorm(p, 0., 1., /*lower_tail*/TRUE, /*log_p*/FALSE); |
| y = R_forceint(mu + sigma * (z + gamma * (z*z - 1) / 6)); |
| |
| z = pnbinom(y, size, prob, /*lower_tail*/TRUE, /*log_p*/FALSE); |
| |
| /* fuzz to ensure left continuity: */ |
| p *= 1 - 64*DBL_EPSILON; |
| |
| /* If the C-F value is not too large a simple search is OK */ |
| if(y < 1e5) return do_search(y, &z, p, size, prob, 1); |
| /* Otherwise be a bit cleverer in the search */ |
| { |
| double incr = floor(y * 0.001), oldincr; |
| do { |
| oldincr = incr; |
| y = do_search(y, &z, p, size, prob, incr); |
| incr = fmax2(1, floor(incr/100)); |
| } while(oldincr > 1 && incr > y*1e-15); |
| return y; |
| } |
| } |
| |
| double qnbinom_mu(double p, double size, double mu, int lower_tail, int log_p) |
| { |
| if (size == ML_POSINF) // limit case: Poisson |
| return(qpois(p, mu, lower_tail, log_p)); |
| /* FIXME! Implement properly!! (not losing accuracy for very large size (prob ~= 1)*/ |
| return qnbinom(p, size, /* prob = */ size/(size+mu), lower_tail, log_p); |
| } |