gdtr.c

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/*                                                     gdtr.c
 *
 *     Gamma distribution function
 *
 *
 *
 * SYNOPSIS:
 *
 * double a, b, x, y, gdtr();
 *
 * y = gdtr( a, b, x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the integral from zero to x of the Gamma probability
 * density function:
 *
 *
 *                x
 *        b       -
 *       a       | |   b-1  -at
 * y =  -----    |    t    e    dt
 *       -     | |
 *      | (b)   -
 *               0
 *
 *  The incomplete Gamma integral is used, according to the
 * relation
 *
 * y = igam( b, ax ).
 *
 *
 * ACCURACY:
 *
 * See igam().
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * gdtr domain         x < 0            0.0
 *
 */
/*                                                     gdtrc.c
 *
 *      Complemented Gamma distribution function
 *
 *
 *
 * SYNOPSIS:
 *
 * double a, b, x, y, gdtrc();
 *
 * y = gdtrc( a, b, x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the integral from x to infinity of the Gamma
 * probability density function:
 *
 *
 *               inf.
 *        b       -
 *       a       | |   b-1  -at
 * y =  -----    |    t    e    dt
 *       -     | |
 *      | (b)   -
 *               x
 *
 *  The incomplete Gamma integral is used, according to the
 * relation
 *
 * y = igamc( b, ax ).
 *
 *
 * ACCURACY:
 *
 * See igamc().
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * gdtrc domain         x < 0            0.0
 *
 */

/*                                                     gdtr()  */
 
 
/*
 * Cephes Math Library Release 2.3:  March,1995
 * Copyright 1984, 1987, 1995 by Stephen L. Moshier
 */
 
#include "mconf.h"
 
 
double gdtr(double a, double b, double x)
{
 
    if (x < 0.0) {
        sf_error("gdtr", SF_ERROR_DOMAIN, NULL);
        return (NAN);
    }
    return (igam(b, a * x));
}
 
 
double gdtrc(double a, double b, double x)
{
 
    if (x < 0.0) {
        sf_error("gdtrc", SF_ERROR_DOMAIN, NULL);
        return (NAN);
    }
    return (igamc(b, a * x));
}
 
 
double gdtri(double a, double b, double y)
{
 
    if ((y < 0.0) || (y > 1.0) || (a <= 0.0) || (b < 0.0)) {
        sf_error("gdtri", SF_ERROR_DOMAIN, NULL);
        return (NAN);
    }
 
    return (igamci(b, 1.0 - y) / a);
}