The R Project SVN R

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *
 *  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, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA.
 *
 *  SYNOPSIS
 *
 *    #include "Mathlib.h"
 *    double qnbinom(double x, double n, double p);
 *
 *  DESCRIPTION
 *
 *    The distribution function of the negative binomial distribution.
 *
 *  NOTES
 *
 *    x = the number of failures before the n-th success
 *
 *  METHOD
 *
 *    Uses the Cornish-Fisher Expansion to include a skewness
 *    correction to a normal approximation.  This gives an
 *    initial value which never seems to be off by more than
 *    1 or 2.  A search is then conducted of values close to
 *    this initial start point.
 */

#include "Mathlib.h"

double qnbinom(double x, double n, double p)
{
    double P, Q, mu, sigma, gamma, z, y;

#ifdef IEEE_754
    if (ISNAN(x) || ISNAN(n) || ISNAN(p))
    return x + n + p;
    if (!R_FINITE(x)) {
    ML_ERROR(ME_DOMAIN);
    return ML_NAN;
    }
#endif
    if (x < 0 || x > 1 || p <= 0 || p >= 1 || n <= 0) {
    ML_ERROR(ME_DOMAIN);
    return ML_NAN;
    }
    if (x == 0) return 0;
#ifdef IEEE_754
    if (x == 1) return ML_POSINF;
#endif
    Q = 1.0 / p;
    P = (1.0 - p) * Q;
    mu = n * P;
    sigma = sqrt(n * P * Q);
    gamma = (Q + P)/sigma;
    z = qnorm(x, 0.0, 1.0);
    y = floor(mu + sigma * (z + gamma * (z*z - 1.0) / 6.0) + 0.5);

    z = pnbinom(y, n, p);
    if(z >= x) {

    /* search to the left */

    for(;;) {
        if((z = pnbinom(y - 1, n, p)) < x)
        return y;
        y = y - 1;
    }
    }
    else {

    /* search to the right */

    for(;;) {
        if((z = pnbinom(y + 1, n, p)) >= x)
        return y + 1;
        y = y + 1;
    }
    }
}