| /* |
| * AUTHOR |
| * Peter Ruckdeschel, peter.ruckdeschel@uni-bayreuth.de. |
| * April 13, 2006. |
| * |
| * Merge in to R: |
| * Copyright (C) 2006 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 non-central F distribution --- |
| * obtained by differentiating the corresp. cumulative distribution function |
| * using dnbeta. |
| * For df1 < 2, since the F density has a singularity as x -> Inf. |
| */ |
| |
| #include "nmath.h" |
| #include "dpq.h" |
| |
| double dnf(double x, double df1, double df2, double ncp, int give_log) |
| { |
| double y, z, f; |
| |
| #ifdef IEEE_754 |
| if (ISNAN(x) || ISNAN(df1) || ISNAN(df2) || ISNAN(ncp)) |
| return x + df2 + df1 + ncp; |
| #endif |
| |
| /* want to compare dnf(ncp=0) behavior with df() one, hence *NOT* : |
| * if (ncp == 0) |
| * return df(x, df1, df2, give_log); */ |
| |
| if (df1 <= 0. || df2 <= 0. || ncp < 0) ML_ERR_return_NAN; |
| if (x < 0.) return(R_D__0); |
| if (!R_FINITE(ncp)) /* ncp = +Inf -- FIXME?: in some cases, limit exists */ |
| ML_ERR_return_NAN; |
| |
| /* This is not correct for df1 == 2, ncp > 0 - and seems unneeded: |
| * if (x == 0.) return(df1 > 2 ? R_D__0 : (df1 == 2 ? R_D__1 : ML_POSINF)); |
| */ |
| if (!R_FINITE(df1) && !R_FINITE(df2)) { /* both +Inf */ |
| /* PR: not sure about this (taken from ncp==0) -- FIXME ? */ |
| if(x == 1.) return ML_POSINF; else return R_D__0; |
| } |
| if (!R_FINITE(df2)) /* i.e. = +Inf */ |
| return df1* dnchisq(x*df1, df1, ncp, give_log); |
| /* == dngamma(x, df1/2, 2./df1, ncp, give_log) -- but that does not exist */ |
| if (df1 > 1e14 && ncp < 1e7) { |
| /* includes df1 == +Inf: code below is inaccurate there */ |
| f = 1 + ncp/df1; /* assumes ncp << df1 [ignores 2*ncp^(1/2)/df1*x term] */ |
| z = dgamma(1./x/f, df2/2, 2./df2, give_log); |
| return give_log ? z - 2*log(x) - log(f) : z / (x*x) / f; |
| } |
| |
| y = (df1 / df2) * x; |
| z = dnbeta(y/(1 + y), df1 / 2., df2 / 2., ncp, give_log); |
| return give_log ? |
| z + log(df1) - log(df2) - 2 * log1p(y) : |
| z * (df1 / df2) /(1 + y) / (1 + y); |
| } |
| |
| |
| |