nbdtr.c

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/*                                                     nbdtr.c
 *
 *     Negative binomial distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * int k, n;
 * double p, y, nbdtr();
 *
 * y = nbdtr( k, n, p );
 *
 * DESCRIPTION:
 *
 * Returns the sum of the terms 0 through k of the negative
 * binomial distribution:
 *
 *   k
 *   --  ( n+j-1 )   n      j
 *   >   (       )  p  (1-p)
 *   --  (   j   )
 *  j=0
 *
 * In a sequence of Bernoulli trials, this is the probability
 * that k or fewer failures precede the nth success.
 *
 * The terms are not computed individually; instead the incomplete
 * beta integral is employed, according to the formula
 *
 * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
 *
 * The arguments must be positive, with p ranging from 0 to 1.
 *
 * ACCURACY:
 *
 * Tested at random points (a,b,p), with p between 0 and 1.
 *
 *               a,b                     Relative error:
 * arithmetic  domain     # trials      peak         rms
 *    IEEE     0,100       100000      1.7e-13     8.8e-15
 * See also incbet.c.
 *
 */
/*                                                     nbdtrc.c
 *
 *      Complemented negative binomial distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * int k, n;
 * double p, y, nbdtrc();
 *
 * y = nbdtrc( k, n, p );
 *
 * DESCRIPTION:
 *
 * Returns the sum of the terms k+1 to infinity of the negative
 * binomial distribution:
 *
 *   inf
 *   --  ( n+j-1 )   n      j
 *   >   (       )  p  (1-p)
 *   --  (   j   )
 *  j=k+1
 *
 * The terms are not computed individually; instead the incomplete
 * beta integral is employed, according to the formula
 *
 * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
 *
 * The arguments must be positive, with p ranging from 0 to 1.
 *
 * ACCURACY:
 *
 * Tested at random points (a,b,p), with p between 0 and 1.
 *
 *               a,b                     Relative error:
 * arithmetic  domain     # trials      peak         rms
 *    IEEE     0,100       100000      1.7e-13     8.8e-15
 * See also incbet.c.
 */

/*                                                     nbdtrc
 *
 *     Complemented negative binomial distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * int k, n;
 * double p, y, nbdtrc();
 *
 * y = nbdtrc( k, n, p );
 *
 * DESCRIPTION:
 *
 * Returns the sum of the terms k+1 to infinity of the negative
 * binomial distribution:
 *
 *   inf
 *   --  ( n+j-1 )   n      j
 *   >   (       )  p  (1-p)
 *   --  (   j   )
 *  j=k+1
 *
 * The terms are not computed individually; instead the incomplete
 * beta integral is employed, according to the formula
 *
 * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
 *
 * The arguments must be positive, with p ranging from 0 to 1.
 *
 * ACCURACY:
 *
 * See incbet.c.
 */
/*                                                     nbdtri
 *
 *      Functional inverse of negative binomial distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * int k, n;
 * double p, y, nbdtri();
 *
 * p = nbdtri( k, n, y );
 *
 * DESCRIPTION:
 *
 * Finds the argument p such that nbdtr(k,n,p) is equal to y.
 *
 * ACCURACY:
 *
 * Tested at random points (a,b,y), with y between 0 and 1.
 *
 *               a,b                     Relative error:
 * arithmetic  domain     # trials      peak         rms
 *    IEEE     0,100       100000      1.5e-14     8.5e-16
 * See also incbi.c.
 */

/*
 * Cephes Math Library Release 2.3:  March, 1995
 * Copyright 1984, 1987, 1995 by Stephen L. Moshier
 */
 
#include "mconf.h"
 
double nbdtrc(int k, int n, double p)
{
    double dk, dn;
 
    if ((p < 0.0) || (p > 1.0))
        goto domerr;
    if (k < 0) {
      domerr:
        sf_error("nbdtr", SF_ERROR_DOMAIN, NULL);
        return (NAN);
    }
 
    dk = k + 1;
    dn = n;
    return (incbet(dk, dn, 1.0 - p));
}
 
 
 
double nbdtr(int k, int n, double p)
{
    double dk, dn;
 
    if ((p < 0.0) || (p > 1.0))
        goto domerr;
    if (k < 0) {
      domerr:
        sf_error("nbdtr", SF_ERROR_DOMAIN, NULL);
        return (NAN);
    }
    dk = k + 1;
    dn = n;
    return (incbet(dn, dk, p));
}
 
 
 
double nbdtri(int k, int n, double p)
{
    double dk, dn, w;
 
    if ((p < 0.0) || (p > 1.0))
        goto domerr;
    if (k < 0) {
      domerr:
        sf_error("nbdtri", SF_ERROR_DOMAIN, NULL);
        return (NAN);
    }
    dk = k + 1;
    dn = n;
    w = incbi(dn, dk, p);
    return (w);
}