| /* |
| * 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 quantile function of the Poisson distribution. |
| * |
| * 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 lambda, double incr) |
| { |
| if(*z >= p) { |
| /* search to the left */ |
| for(;;) { |
| if(y == 0 || |
| (*z = ppois(y - incr, lambda, /*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 = ppois(y, lambda, /*l._t.*/TRUE, /*log_p*/FALSE)) >= p) |
| return y; |
| } |
| } |
| } |
| |
| double qpois(double p, double lambda, int lower_tail, int log_p) |
| { |
| double mu, sigma, gamma, z, y; |
| #ifdef IEEE_754 |
| if (ISNAN(p) || ISNAN(lambda)) |
| return p + lambda; |
| #endif |
| if(!R_FINITE(lambda)) |
| ML_ERR_return_NAN; |
| if(lambda < 0) ML_ERR_return_NAN; |
| R_Q_P01_check(p); |
| if(lambda == 0) return 0; |
| if(p == R_DT_0) return 0; |
| if(p == R_DT_1) return ML_POSINF; |
| |
| mu = lambda; |
| sigma = sqrt(lambda); |
| /* gamma = sigma; PR#8058 should be kurtosis which is mu^-0.5 */ |
| gamma = 1.0/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 == 0.) return 0; |
| if (p == 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 = nearbyint(mu + sigma * (z + gamma * (z*z - 1) / 6)); |
| |
| z = ppois(y, lambda, /*lower_tail*/TRUE, /*log_p*/FALSE); |
| |
| /* fuzz to ensure left continuity; 1 - 1e-7 may lose too much : */ |
| p *= 1 - 64*DBL_EPSILON; |
| |
| /* If the mean is not too large a simple search is OK */ |
| if(lambda < 1e5) return do_search(y, &z, p, lambda, 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, lambda, incr); |
| incr = fmax2(1, floor(incr/100)); |
| } while(oldincr > 1 && incr > lambda*1e-15); |
| return y; |
| } |
| } |