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/* nbdtrl.c
*
* Negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* long double p, y, nbdtrl();
*
* y = nbdtrl( 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:
*
* Tested at random points (k,n,p) with k and n between 1 and 10,000
* and p between 0 and 1.
*
* arithmetic domain # trials peak rms
* Absolute error:
* IEEE 0,10000 10000 9.8e-15 2.1e-16
*
*/
/* nbdtrcl.c
*
* Complemented negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* long double p, y, nbdtrcl();
*
* y = nbdtrcl( 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:
*
* See incbetl.c.
*
*/
/* nbdtril
*
* Functional inverse of negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* long double p, y, nbdtril();
*
* p = nbdtril( k, n, y );
*
*
*
* DESCRIPTION:
*
* Finds the argument p such that nbdtr(k,n,p) is equal to y.
*
* ACCURACY:
*
* Tested at random points (a,b,y), with y between 0 and 1.
*
* a,b Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100
* See also incbil.c.
*/
/*
Cephes Math Library Release 2.3: January,1995
Copyright 1984, 1995 by Stephen L. Moshier
*/
#include <math.h>
#ifdef ANSIPROT
extern long double incbetl ( long double, long double, long double );
extern long double powl ( long double, long double );
extern long double incbil ( long double, long double, long double );
#else
long double incbetl(), powl(), incbil();
#endif
long double nbdtrcl( k, n, p )
int k, n;
long double p;
{
long double dk, dn;
if( (p < 0.0L) || (p > 1.0L) )
goto domerr;
if( k < 0 )
{
domerr:
mtherr( "nbdtrl", DOMAIN );
return( 0.0L );
}
dn = n;
if( k == 0 )
return( 1.0L - powl( p, dn ) );
dk = k+1;
return( incbetl( dk, dn, 1.0L - p ) );
}
long double nbdtrl( k, n, p )
int k, n;
long double p;
{
long double dk, dn;
if( (p < 0.0L) || (p > 1.0L) )
goto domerr;
if( k < 0 )
{
domerr:
mtherr( "nbdtrl", DOMAIN );
return( 0.0L );
}
dn = n;
if( k == 0 )
return( powl( p, dn ) );
dk = k+1;
return( incbetl( dn, dk, p ) );
}
long double nbdtril( k, n, p )
int k, n;
long double p;
{
long double dk, dn, w;
if( (p < 0.0L) || (p > 1.0L) )
goto domerr;
if( k < 0 )
{
domerr:
mtherr( "nbdtrl", DOMAIN );
return( 0.0L );
}
dk = k+1;
dn = n;
w = incbil( dn, dk, p );
return( w );
}
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