nbdtr

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.