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:

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 the incbet Help topic.