gistfile1.py

def combination( a, b ):
    """
        >>> combination( 3, 1 )
        3
        >>> combination( 3, 2 )
        3
        >>> combination( 4, 2 )
        6 
    """    
    # a! / b!(a-b)!
    return float(factorial(a)) / float(factorial(b)) / float(factorial(a-b))
    
def factorial( n ):
    """
        >>> factorial( 1 )
        1
        >>> factorial( 3 )
        6
        >>> factorial( 5 )
        120
    """    
    if n > 1: return n * factorial(n-1)
    else:      return 1

def negative_hypergeometric_distribution( N, p, r, x):
    fx = combination( x-1, r-1 ) * combination( N-x, N*p - r ) / combination( N,
    N * p)
    return fx

if __name__ == "__main__":
    import doctest
    doctest.testmod(verbose = True)
    N = 8.0
    p = 0.125
    r = 1 
    E = 0
    for x in range( 1, N+1 ): 
        fx = negative_hypergeometric_distribution( N, p, r, x ) 
        print "f(x) %s" % fx 
        E += fx * x
    print E