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pdtr.c

/*                                        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 2.8:  June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*/

#include "mconf.h"

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

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

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