/src/r-source/src/nmath/qbinom.c
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1 | | /* |
2 | | * Mathlib : A C Library of Special Functions |
3 | | * Copyright (C) 1999-2025 The R Core Team |
4 | | * Copyright (C) 2003-2021 The R Foundation |
5 | | * Copyright (C) 1998 Ross Ihaka |
6 | | * |
7 | | * This program is free software; you can redistribute it and/or modify |
8 | | * it under the terms of the GNU General Public License as published by |
9 | | * the Free Software Foundation; either version 2 of the License, or |
10 | | * (at your option) any later version. |
11 | | * |
12 | | * This program is distributed in the hope that it will be useful, |
13 | | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
14 | | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
15 | | * GNU General Public License for more details. |
16 | | * |
17 | | * You should have received a copy of the GNU General Public License |
18 | | * along with this program; if not, a copy is available at |
19 | | * https://www.R-project.org/Licenses/ |
20 | | * |
21 | | * DESCRIPTION |
22 | | * |
23 | | * The quantile function of the binomial distribution. |
24 | | * |
25 | | * METHOD |
26 | | * |
27 | | * Uses the Cornish-Fisher Expansion to include a skewness |
28 | | * correction to a normal approximation. This gives an |
29 | | * initial value which never seems to be off by more than |
30 | | * 1 or 2. A search is then conducted of values close to |
31 | | * this initial start point. |
32 | | */ |
33 | | #include "nmath.h" |
34 | | #include "dpq.h" |
35 | | |
36 | | // notably used in " ./qDiscrete_search.h ": |
37 | | #ifdef DEBUG_qbinom |
38 | | # define R_DBG_printf(...) REprintf(__VA_ARGS__) |
39 | | #else |
40 | | # define R_DBG_printf(...) |
41 | | #endif |
42 | | |
43 | | |
44 | | #define _thisDIST_ binom |
45 | | #define _dist_PARS_DECL_ double n, double pr |
46 | | #define _dist_PARS_ n, pr |
47 | 0 | #define _dist_MAX_y n |
48 | | // === Binomial Y <= n |
49 | | |
50 | | #include "qDiscrete_search.h" |
51 | | // ------------------> do_search() and all called by q_DISCRETE_*() below |
52 | | |
53 | | double qbinom(double p, double n, double pr, int lower_tail, int log_p) |
54 | 0 | { |
55 | 0 | #ifdef IEEE_754 |
56 | 0 | if (ISNAN(p) || ISNAN(n) || ISNAN(pr)) |
57 | 0 | return p + n + pr; |
58 | 0 | #endif |
59 | 0 | if(!R_FINITE(n) || !R_FINITE(pr)) |
60 | 0 | ML_WARN_return_NAN; |
61 | | /* if log_p is true, p = -Inf is a legitimate value */ |
62 | 0 | if(!R_FINITE(p) && !log_p) |
63 | 0 | ML_WARN_return_NAN; |
64 | |
|
65 | 0 | n = R_forceint(n); |
66 | |
|
67 | 0 | if (pr < 0 || pr > 1 || n < 0) |
68 | 0 | ML_WARN_return_NAN; |
69 | |
|
70 | 0 | R_Q_P01_boundaries(p, 0, n); |
71 | |
|
72 | 0 | if (pr == 0. || n == 0) return 0.; |
73 | 0 | if (pr == 1.) return n; /* covers the full range of the distribution */ |
74 | | |
75 | | // (NB: unavoidable cancellation for pr ~= 1) |
76 | 0 | double |
77 | 0 | q = 1 - pr, |
78 | 0 | mu = n * pr, |
79 | 0 | sigma = sqrt(n * pr * q), |
80 | 0 | gamma = (q - pr) / sigma; |
81 | |
|
82 | 0 | R_DBG_printf("qbinom(p=%.12g, n=%.15g, pr=%.7g, l.t.=%d, log=%d): sigma=%g, gamma=%g;\n", |
83 | 0 | p, n,pr, lower_tail, log_p, sigma, gamma); |
84 | |
|
85 | 0 | q_DISCRETE_01_CHECKS(); |
86 | | q_DISCRETE_BODY(); |
87 | 0 | } |