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/* nbdtr.c
*
* Negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, nbdtr();
*
* y = nbdtr( 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 (a,b,p), with p between 0 and 1.
*
* a,b Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 100000 1.7e-13 8.8e-15
* See also incbet.c.
*
*/
/* nbdtrc.c
*
* Complemented negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, nbdtrc();
*
* y = nbdtrc( 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:
*
* Tested at random points (a,b,p), with p between 0 and 1.
*
* a,b Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 100000 1.7e-13 8.8e-15
* See also incbet.c.
*/
/* nbdtrc
*
* Complemented negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, nbdtrc();
*
* y = nbdtrc( 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 incbet.c.
*/
/* nbdtri
*
* Functional inverse of negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, nbdtri();
*
* p = nbdtri( 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 100000 1.5e-14 8.5e-16
* See also incbi.c.
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*/
#include <math.h>
#ifdef ANSIPROT
extern double incbet ( double, double, double );
extern double incbi ( double, double, double );
#else
double incbet(), incbi();
#endif
double nbdtrc( k, n, p )
int k, n;
double p;
{
double dk, dn;
if( (p < 0.0) || (p > 1.0) )
goto domerr;
if( k < 0 )
{
domerr:
mtherr( "nbdtr", DOMAIN );
return( 0.0 );
}
dk = k+1;
dn = n;
return( incbet( dk, dn, 1.0 - p ) );
}
double nbdtr( k, n, p )
int k, n;
double p;
{
double dk, dn;
if( (p < 0.0) || (p > 1.0) )
goto domerr;
if( k < 0 )
{
domerr:
mtherr( "nbdtr", DOMAIN );
return( 0.0 );
}
dk = k+1;
dn = n;
return( incbet( dn, dk, p ) );
}
double nbdtri( k, n, p )
int k, n;
double p;
{
double dk, dn, w;
if( (p < 0.0) || (p > 1.0) )
goto domerr;
if( k < 0 )
{
domerr:
mtherr( "nbdtri", DOMAIN );
return( 0.0 );
}
dk = k+1;
dn = n;
w = incbi( dn, dk, p );
return( w );
}
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