| /* |
| * AUTHOR |
| * Catherine Loader, catherine@research.bell-labs.com. |
| * October 23, 2000. |
| * |
| * Merge in to R: |
| * Copyright (C) 2000, The R Core Team |
| * Changes to case a, b < 2, use logs to avoid underflow |
| * Copyright (C) 2006-2014 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 |
| * Beta density, |
| * (a+b-1)! a-1 b-1 |
| * p(x;a,b) = ------------ x (1-x) |
| * (a-1)!(b-1)! |
| * |
| * = (a+b-1) dbinom(a-1; a+b-2,x) |
| * |
| * The basic formula for the log density is thus |
| * (a-1) log x + (b-1) log (1-x) - lbeta(a, b) |
| * If either a or b <= 2 then 0 < lbeta(a, b) < 710 and so no |
| * term is large. We use Loader's code only if both a and b > 2. |
| */ |
| |
| #include "nmath.h" |
| #include "dpq.h" |
| |
| double dbeta(double x, double a, double b, int give_log) |
| { |
| #ifdef IEEE_754 |
| /* NaNs propagated correctly */ |
| if (ISNAN(x) || ISNAN(a) || ISNAN(b)) return x + a + b; |
| #endif |
| |
| if (a < 0 || b < 0) ML_ERR_return_NAN; |
| if (x < 0 || x > 1) return(R_D__0); |
| |
| // limit cases for (a,b), leading to point masses |
| if(a == 0 || b == 0 || !R_FINITE(a) || !R_FINITE(b)) { |
| if(a == 0 && b == 0) { // point mass 1/2 at each of {0,1} : |
| if (x == 0 || x == 1) return(ML_POSINF); else return(R_D__0); |
| } |
| if (a == 0 || a/b == 0) { // point mass 1 at 0 |
| if (x == 0) return(ML_POSINF); else return(R_D__0); |
| } |
| if (b == 0 || b/a == 0) { // point mass 1 at 1 |
| if (x == 1) return(ML_POSINF); else return(R_D__0); |
| } |
| // else, remaining case: a = b = Inf : point mass 1 at 1/2 |
| if (x == 0.5) return(ML_POSINF); else return(R_D__0); |
| } |
| |
| if (x == 0) { |
| if(a > 1) return(R_D__0); |
| if(a < 1) return(ML_POSINF); |
| /* a == 1 : */ return(R_D_val(b)); |
| } |
| if (x == 1) { |
| if(b > 1) return(R_D__0); |
| if(b < 1) return(ML_POSINF); |
| /* b == 1 : */ return(R_D_val(a)); |
| } |
| |
| double lval; |
| if (a <= 2 || b <= 2) |
| lval = (a-1)*log(x) + (b-1)*log1p(-x) - lbeta(a, b); |
| else |
| lval = log(a+b-1) + dbinom_raw(a-1, a+b-2, x, 1-x, TRUE); |
| |
| return R_D_exp(lval); |
| } |