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/* bdtrf.c
*
* Binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* float p, y, bdtrf();
*
* y = bdtrf( 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:
*
* Relative error (p varies from 0 to 1):
* arithmetic domain # trials peak rms
* IEEE 0,100 2000 6.9e-5 1.1e-5
*
* ERROR MESSAGES:
*
* message condition value returned
* bdtrf domain k < 0 0.0
* n < k
* x < 0, x > 1
*
*/
/* bdtrcf()
*
* Complemented binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* float p, y, bdtrcf();
*
* y = bdtrcf( 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:
*
* Relative error (p varies from 0 to 1):
* arithmetic domain # trials peak rms
* IEEE 0,100 2000 6.0e-5 1.2e-5
*
* ERROR MESSAGES:
*
* message condition value returned
* bdtrcf domain x<0, x>1, n<k 0.0
*/
/* bdtrif()
*
* Inverse binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* float p, y, bdtrif();
*
* p = bdtrf( 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:
*
* Relative error (p varies from 0 to 1):
* arithmetic domain # trials peak rms
* IEEE 0,100 2000 3.5e-5 3.3e-6
*
* ERROR MESSAGES:
*
* message condition value returned
* bdtrif domain k < 0, n <= k 0.0
* x < 0, x > 1
*
*/
/* bdtr() */
/*
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 incbetf(float, float, float), powf(float, float);
float incbif( float, float, float );
#else
float incbetf(), powf(), incbif();
#endif
float bdtrcf( int k, int n, float pp )
{
float p, dk, dn;
p = pp;
if( (p < 0.0) || (p > 1.0) )
goto domerr;
if( k < 0 )
return( 1.0 );
if( n < k )
{
domerr:
mtherr( "bdtrcf", DOMAIN );
return( 0.0 );
}
if( k == n )
return( 0.0 );
dn = n - k;
if( k == 0 )
{
dk = 1.0 - powf( 1.0-p, dn );
}
else
{
dk = k + 1;
dk = incbetf( dk, dn, p );
}
return( dk );
}
float bdtrf( int k, int n, float pp )
{
float p, dk, dn;
p = pp;
if( (p < 0.0) || (p > 1.0) )
goto domerr;
if( (k < 0) || (n < k) )
{
domerr:
mtherr( "bdtrf", DOMAIN );
return( 0.0 );
}
if( k == n )
return( 1.0 );
dn = n - k;
if( k == 0 )
{
dk = powf( 1.0-p, dn );
}
else
{
dk = k + 1;
dk = incbetf( dn, dk, 1.0 - p );
}
return( dk );
}
float bdtrif( int k, int n, float yy )
{
float y, dk, dn, p;
y = yy;
if( (y < 0.0) || (y > 1.0) )
goto domerr;
if( (k < 0) || (n <= k) )
{
domerr:
mtherr( "bdtrif", DOMAIN );
return( 0.0 );
}
dn = n - k;
if( k == 0 )
{
p = 1.0 - powf( y, 1.0/dn );
}
else
{
dk = k + 1;
p = 1.0 - incbif( dn, dk, y );
}
return( p );
}
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