Category : C Source Code
Archive   : CEPHES22.ZIP
Filename : BDTR.C

/* bdtr.c
*
* Binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, bdtr();
*
* y = bdtr( k, n, p );
*
*
*
* DESCRIPTION:
*
* Returns the sum of the terms 0 through k of the Binomial
* probability density:
*
* k
* -- ( n ) j n-j
* > ( ) p (1-p)
* -- ( j )
* j=0
*
* The terms are not summed directly; instead the incomplete
* beta integral is employed, according to the formula
*
* y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
*
* The arguments must be positive, with p ranging from 0 to 1.
*
*
*
* ACCURACY:
*
* See incbet.c
*
* ERROR MESSAGES:
*
* message condition value returned
* bdtr domain k < 0 0.0
* n < k
* x < 0, x > 1
*
*/
/* bdtrc()
*
* Complemented binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, bdtrc();
*
* y = bdtrc( k, n, p );
*
*
*
* DESCRIPTION:
*
* Returns the sum of the terms k+1 through n of the Binomial
* probability density:
*
* n
* -- ( n ) j n-j
* > ( ) p (1-p)
* -- ( j )
* j=k+1
*
* The terms are not summed directly; instead the incomplete
* beta integral is employed, according to the formula
*
* y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
*
* The arguments must be positive, with p ranging from 0 to 1.
*
*
*
* ACCURACY:
*
* See incbet.c.
*
* ERROR MESSAGES:
*
* message condition value returned
* bdtrc domain x<0, x>1, n */
/* bdtri()
*
* Inverse binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, bdtri();
*
* p = bdtr( k, n, y );
*
*
*
* DESCRIPTION:
*
* Finds the event probability p such that the sum of the
* terms 0 through k of the Binomial probability density
* is equal to the given cumulative probability y.
*
* This is accomplished using the inverse beta integral
* function and the relation
*
* 1 - p = incbi( n-k, k+1, y ).
*
*
*
*
* ACCURACY:
*
* See incbi.c.
*
* ERROR MESSAGES:
*
* message condition value returned
* bdtri domain k < 0, n <= k 0.0
* x < 0, x > 1
*
*/

/* bdtr() */


/*
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 bdtrc( k, n, p )
int k, n;
double p;
{
double dk, dn;
double incbet(), pow();

if( (p < 0.0) || (p > 1.0) )
goto domerr;
if( k < 0 )
return( 1.0 );

if( n < k )
{
domerr:
mtherr( "bdtrc", DOMAIN );
return( 0.0 );
}

if( k == n )
return( 0.0 );
dn = n - k;
if( k == 0 )
{
dk = 1.0 - pow( 1.0-p, dn );
}
else
{
dk = k + 1;
dk = incbet( dk, dn, p );
}
return( dk );
}



double bdtr( k, n, p )
int k, n;
double p;
{
double dk, dn;
double incbet(), pow();

if( (p < 0.0) || (p > 1.0) )
goto domerr;
if( (k < 0) || (n < k) )
{
domerr:
mtherr( "bdtr", DOMAIN );
return( 0.0 );
}

if( k == n )
return( 1.0 );

dn = n - k;
if( k == 0 )
{
dk = pow( 1.0-p, dn );
}
else
{
dk = k + 1;
dk = incbet( dn, dk, 1.0 - p );
}
return( dk );
}


double bdtri( k, n, y )
int k, n;
double y;
{
double dk, dn, p;
double incbi(), pow();

if( (y < 0.0) || (y > 1.0) )
goto domerr;
if( (k < 0) || (n <= k) )
{
domerr:
mtherr( "bdtri", DOMAIN );
return( 0.0 );
}

dn = n - k;
if( k == 0 )
{
p = 1.0 - pow( y, 1.0/dn );
}
else
{
dk = k + 1;
p = 1.0 - incbi( dn, dk, y );
}
return( p );
}