pbeta.cpp

/*
 *  Mathlib : A C Library of Special Functions
 *  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/
 *
 *  SYNOPSIS
 *
 * #include <Rmath.h>
 *
 * double pbeta_raw(double x, double a, double b, int lower_tail, int log_p)
 * double pbeta    (double x, double a, double b, int lower_tail, int log_p)
 *
 *  DESCRIPTION
 *
 *      Returns distribution function of the beta distribution.
 *      ( = The incomplete beta ratio I_x(p,q) ).
 *
 *  NOTES
 *
 *      As from R 2.3.0, a wrapper for TOMS708
 *      as from R 2.6.0, 'log_p' partially improved over log(p..)
 */

#include "nmath.h"
#include "dpq.h"

template<class Float>
attribute_hidden
Float pbeta_raw(Float x, Float a, Float b, int lower_tail, int log_p)
{
    // treat limit cases correctly here:
    if(a == 0 || b == 0 || !R_FINITE(a) || !R_FINITE(b)) {
        // NB:  0 < x < 1 :
        if(a == 0 && b == 0) // point mass 1/2 at each of {0,1} :
            return (log_p ? -M_LN2 : 0.5);
        if (a == 0 || a/b == 0) // point mass 1 at 0 ==> P(X <= x) = 1, all x > 0
            return R_DT_1;
        if (b == 0 || b/a == 0) // point mass 1 at 1 ==> P(X <= x) = 0, all x < 1
            return R_DT_0;
        // else, remaining case:  a = b = Inf : point mass 1 at 1/2
        if (x < 0.5) return R_DT_0; else return R_DT_1;
    }
    // Now:  0 < a < Inf;  0 < b < Inf

    Float x1 = 0.5 - x + 0.5, w, wc;
    int ierr;
    //====
    bratio(a, b, x, x1, &w, &wc, &ierr, log_p); /* -> ./toms708.c */
    //====
    // ierr in {10,14} <==> bgrat() error code ierr-10 in 1:4; for 1 and 4, warned *there*
    if(ierr && ierr != 11 && ierr != 14)
        MATHLIB_WARNING4(_("pbeta_raw(%g, a=%g, b=%g, ..) -> bratio() gave error code %d"),
                        x, a,b, ierr);
    return lower_tail ? w : wc;
} /* pbeta_raw() */

template<class Float>
Float pbeta(Float x, Float a, Float b, int lower_tail, int log_p)
{
#ifdef IEEE_754
    if (ISNAN(x) || ISNAN(a) || ISNAN(b)) return x + a + b;
#endif

    if (a < 0 || b < 0) ML_ERR_return_NAN;
    // allowing a==0 and b==0  <==> treat as one- or two-point mass

    if (x <= 0)
        return R_DT_0;
    if (x >= 1)
        return R_DT_1;

    return pbeta_raw(x, a, b, lower_tail, log_p);
}