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/* pdtrf.c
*
* Poisson distribution
*
*
*
* SYNOPSIS:
*
* int k;
* float m, y, pdtrf();
*
* y = pdtrf( 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:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 6.9e-5 8.0e-6
*
*/
/* pdtrcf()
*
* Complemented poisson distribution
*
*
*
* SYNOPSIS:
*
* int k;
* float m, y, pdtrcf();
*
* y = pdtrcf( 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:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 8.4e-5 1.2e-5
*
*/
/* pdtrif()
*
* Inverse Poisson distribution
*
*
*
* SYNOPSIS:
*
* int k;
* float m, y, pdtrf();
*
* m = pdtrif( 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:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 8.7e-6 1.4e-6
*
* ERROR MESSAGES:
*
* message condition value returned
* pdtri domain y < 0 or y >= 1 0.0
* k < 0
*
*/
/*
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
#ifdef ANSIC
float igamf(float, float), igamcf(float, float), igamif(float, float);
#else
float igamf(), igamcf(), igamif();
#endif
float pdtrcf( int k, float mm )
{
float v, m;
m = mm;
if( (k < 0) || (m <= 0.0) )
{
mtherr( "pdtrcf", DOMAIN );
return( 0.0 );
}
v = k+1;
return( igamf( v, m ) );
}
float pdtrf( int k, float mm )
{
float v, m;
m = mm;
if( (k < 0) || (m <= 0.0) )
{
mtherr( "pdtr", DOMAIN );
return( 0.0 );
}
v = k+1;
return( igamcf( v, m ) );
}
float pdtrif( int k, float yy )
{
float v, y;
y = yy;
if( (k < 0) || (y < 0.0) || (y >= 1.0) )
{
mtherr( "pdtrif", DOMAIN );
return( 0.0 );
}
v = k+1;
v = igamif( v, y );
return( v );
}
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