/*							pdtr.c
 *
 *	Poisson distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * int k;
 * double m, y, pdtr();
 *
 * y = pdtr( k, m );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the sum of the first k terms of the Poisson
 * distribution:
 *
 *   k         j
 *   --   -m  m
 *   >   e    --
 *   --       j!
 *  j=0
 *
 * The terms are not summed directly; instead the incomplete
 * gamma integral is employed, according to the relation
 *
 * y = pdtr( k, m ) = igamc( k+1, m ).
 *
 * The arguments must both be positive.
 *
 *
 *
 * ACCURACY:
 *
 * See igamc().
 *
 */
/*							pdtrc()
 *
 *	Complemented poisson distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * int k;
 * double m, y, pdtrc();
 *
 * y = pdtrc( k, m );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the sum of the terms k+1 to infinity of the Poisson
 * distribution:
 *
 *  inf.       j
 *   --   -m  m
 *   >   e    --
 *   --       j!
 *  j=k+1
 *
 * The terms are not summed directly; instead the incomplete
 * gamma integral is employed, according to the formula
 *
 * y = pdtrc( k, m ) = igam( k+1, m ).
 *
 * The arguments must both be positive.
 *
 *
 *
 * ACCURACY:
 *
 * See igam.c.
 *
 */
/*							pdtri()
 *
 *	Inverse Poisson distribution
 *
 *
 *
 * SYNOPSIS:
 *
 * int k;
 * double m, y, pdtr();
 *
 * m = pdtri( k, y );
 *
 *
 *
 *
 * DESCRIPTION:
 *
 * Finds the Poisson variable x such that the integral
 * from 0 to x of the Poisson density is equal to the
 * given probability y.
 *
 * This is accomplished using the inverse gamma integral
 * function and the relation
 *
 *    m = igami( k+1, y ).
 *
 *
 *
 *
 * ACCURACY:
 *
 * See igami.c.
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * pdtri domain    y < 0 or y >= 1       0.0
 *                     k < 0
 *
 */

/*
Cephes Math Library Release 2.3:  March, 1995
Copyright 1984, 1987, 1995 by Stephen L. Moshier
*/

#include "mconf.h"

double
pdtrc (int k, double m)
{
  double v;

  if ((k < 0) || (m <= 0.0)) {
    mtherr ("pdtrc", MATHERR_DOMAIN);
    return (0.0);
  }
  v = k + 1;
  return (igam (v, m));
}



double
pdtr (int k, double m)
{
  double v;

  if ((k < 0) || (m <= 0.0)) {
    mtherr ("pdtr", MATHERR_DOMAIN);
    return (0.0);
  }
  v = k + 1;
  return (igamc (v, m));
}


double
pdtri (int k, double y)
{
  double v;

  if ((k < 0) || (y < 0.0) || (y >= 1.0)) {
    mtherr ("pdtri", MATHERR_DOMAIN);
    return (0.0);
  }
  v = k + 1;
  v = igami (v, y);
  return (v);
}