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/* nbdtrf.c
*
* Negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* float p, y, nbdtrf();
*
* y = nbdtrf( k, n, p );
*
*
*
* DESCRIPTION:
*
* Returns the sum of the terms 0 through k of the negative
* binomial distribution:
*
* k
* -- ( n+j-1 ) n j
* > ( ) p (1-p)
* -- ( j )
* j=0
*
* In a sequence of Bernoulli trials, this is the probability
* that k or fewer failures precede the nth success.
*
* The terms are not computed individually; instead the incomplete
* beta integral is employed, according to the formula
*
* y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
*
* The arguments must be positive, with p ranging from 0 to 1.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 1.5e-4 1.9e-5
*
*/
/* nbdtrcf.c
*
* Complemented negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* float p, y, nbdtrcf();
*
* y = nbdtrcf( k, n, p );
*
*
*
* DESCRIPTION:
*
* Returns the sum of the terms k+1 to infinity of the negative
* binomial distribution:
*
* inf
* -- ( n+j-1 ) n j
* > ( ) p (1-p)
* -- ( j )
* j=k+1
*
* The terms are not computed individually; instead the incomplete
* beta integral is employed, according to the formula
*
* y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
*
* The arguments must be positive, with p ranging from 0 to 1.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 1.4e-4 2.0e-5
*
*/
/*
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
#ifdef ANSIC
float incbetf(float, float, float);
#else
float incbetf();
#endif
float nbdtrcf( int k, int n, float pp )
{
float dk, dn, p;
p = pp;
if( (p < 0.0) || (p > 1.0) )
goto domerr;
if( k < 0 )
{
domerr:
mtherr( "nbdtrf", DOMAIN );
return( 0.0 );
}
dk = k+1;
dn = n;
return( incbetf( dk, dn, 1.0 - p ) );
}
float nbdtrf( int k, int n, float pp )
{
float dk, dn, p;
p = pp;
if( (p < 0.0) || (p > 1.0) )
goto domerr;
if( k < 0 )
{
domerr:
mtherr( "nbdtrf", DOMAIN );
return( 0.0 );
}
dk = k+1;
dn = n;
return( incbetf( dn, dk, p ) );
}
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