chdtr.c

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/*                                                     chdtr.c
 *
 *     Chi-square distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * double df, x, y, chdtr();
 *
 * y = chdtr( df, x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the area under the left hand tail (from 0 to x)
 * of the Chi square probability density function with
 * v degrees of freedom.
 *
 *
 *                                  inf.
 *                                    -
 *                        1          | |  v/2-1  -t/2
 *  P( x | v )   =   -----------     |   t      e     dt
 *                    v/2  -       | |
 *                   2    | (v/2)   -
 *                                   x
 *
 * where x is the Chi-square variable.
 *
 * The incomplete Gamma integral is used, according to the
 * formula
 *
 *     y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
 *
 *
 * The arguments must both be positive.
 *
 *
 *
 * ACCURACY:
 *
 * See igam().
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * chdtr domain   x < 0 or v < 1        0.0
 */
/*                                                     chdtrc()
 *
 *      Complemented Chi-square distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * double v, x, y, chdtrc();
 *
 * y = chdtrc( v, x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the area under the right hand tail (from x to
 * infinity) of the Chi square probability density function
 * with v degrees of freedom:
 *
 *
 *                                  inf.
 *                                    -
 *                        1          | |  v/2-1  -t/2
 *  P( x | v )   =   -----------     |   t      e     dt
 *                    v/2  -       | |
 *                   2    | (v/2)   -
 *                                   x
 *
 * where x is the Chi-square variable.
 *
 * The incomplete Gamma integral is used, according to the
 * formula
 *
 *      y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
 *
 *
 * The arguments must both be positive.
 *
 *
 *
 * ACCURACY:
 *
 * See igamc().
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * chdtrc domain  x < 0 or v < 1        0.0
 */
/*                                                     chdtri()
 *
 *      Inverse of complemented Chi-square distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * double df, x, y, chdtri();
 *
 * x = chdtri( df, y );
 *
 *
 *
 *
 * DESCRIPTION:
 *
 * Finds the Chi-square argument x such that the integral
 * from x to infinity of the Chi-square density is equal
 * to the given cumulative probability y.
 *
 * This is accomplished using the inverse Gamma integral
 * function and the relation
 *
 *    x/2 = igamci( df/2, y );
 *
 *
 *
 *
 * ACCURACY:
 *
 * See igami.c.
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * chdtri domain   y < 0 or y > 1        0.0
 *                     v < 1
 *
 */

/*                                                             chdtr() */
 
 
/*
 * Cephes Math Library Release 2.0:  April, 1987
 * Copyright 1984, 1987 by Stephen L. Moshier
 * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
 */
 
#include "mconf.h"
 
double chdtrc(double df, double x)
{
 
    if (x < 0.0)
        return 1.0;             /* modified by T. Oliphant */
    return (igamc(df / 2.0, x / 2.0));
}
 
 
 
double chdtr(double df, double x)
{
 
    if ((x < 0.0)) {            /* || (df < 1.0) ) */
        sf_error("chdtr", SF_ERROR_DOMAIN, NULL);
        return (NAN);
    }
    return (igam(df / 2.0, x / 2.0));
}
 
 
 
double chdtri(double df, double y)
{
    double x;
 
    if ((y < 0.0) || (y > 1.0)) {       /* || (df < 1.0) ) */
        sf_error("chdtri", SF_ERROR_DOMAIN, NULL);
        return (NAN);
    }
 
    x = igamci(0.5 * df, y);
    return (2.0 * x);
}