| /* |
| * AUTHOR |
| * Catherine Loader, catherine@research.bell-labs.com. |
| * October 23, 2000. |
| * |
| * Merge in to R: |
| * Copyright (C) 2000, 2005 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 density function of the F distribution. |
| * To evaluate it, write it as a Binomial probability with p = x*m/(n+x*m). |
| * For m >= 2, we use the simplest conversion. |
| * For m < 2, (m-2)/2 < 0 so the conversion will not work, and we must use |
| * a second conversion. |
| * Note the division by p; this seems unavoidable |
| * for m < 2, since the F density has a singularity as x (or p) -> 0. |
| */ |
| |
| #include "nmath.h" |
| #include "dpq.h" |
| |
| double df(double x, double m, double n, int give_log) |
| { |
| double p, q, f, dens; |
| |
| #ifdef IEEE_754 |
| if (ISNAN(x) || ISNAN(m) || ISNAN(n)) |
| return x + m + n; |
| #endif |
| if (m <= 0 || n <= 0) ML_ERR_return_NAN; |
| if (x < 0.) return(R_D__0); |
| if (x == 0.) return(m > 2 ? R_D__0 : (m == 2 ? R_D__1 : ML_POSINF)); |
| if (!R_FINITE(m) && !R_FINITE(n)) { /* both +Inf */ |
| if(x == 1.) return ML_POSINF; else return R_D__0; |
| } |
| if (!R_FINITE(n)) /* must be +Inf by now */ |
| return(dgamma(x, m/2, 2./m, give_log)); |
| if (m > 1e14) {/* includes +Inf: code below is inaccurate there */ |
| dens = dgamma(1./x, n/2, 2./n, give_log); |
| return give_log ? dens - 2*log(x): dens/(x*x); |
| } |
| |
| f = 1./(n+x*m); |
| q = n*f; |
| p = x*m*f; |
| |
| if (m >= 2) { |
| f = m*q/2; |
| dens = dbinom_raw((m-2)/2, (m+n-2)/2, p, q, give_log); |
| } |
| else { |
| f = m*m*q / (2*p*(m+n)); |
| dens = dbinom_raw(m/2, (m+n)/2, p, q, give_log); |
| } |
| return(give_log ? log(f)+dens : f*dens); |
| } |