bdtr

Binomial distribution.

SYNOPSIS:

int k, n;
double p, y, bdtr();
y = bdtr(k, n, p);

DESCRIPTION:

Returns the sum of the terms 0 through k of the Binomial probability density:

   k
   -- ( n )   j      n-j
   >   (   ) p (1-p)
   -- ( j )
j=0

The terms are not summed directly; instead the incomplete beta integral is employed, according to the formula:

y = bdtr(k, n, p) = incbet(n-k, k+1, 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
For p between 0.001 and 1:
    IEEE     0,100       100000      4.3e-15     2.6e-16

ERROR MESSAGES:

message      condition       value returned
domain         k < 0             0.0
                 n < k
                 x < 0, x > 1