ci_lower_bound.py

import sys
from math import log, sqrt

def pnormaldist(qn):
    b = [1.570796288, 0.03706987906, -0.8364353589e-3,
         -0.2250947176e-3, 0.6841218299e-5, 0.5824238515e-5,
         -0.104527497e-5, 0.8360937017e-7, -0.3231081277e-8,
         0.3657763036e-10, 0.6936233982e-12]

    if qn < 0.0 or 1.0 < qn:
        sys.stderr.write("Error : qn <= 0 or qn >= 1  in pnorm()!\n")
        return 0.0

    if qn == 0.5:
        return 0.0

    w1 = qn

    if qn > 0.5:
        w1 = 1.0 - w1

    w3 = -log(4.0 * w1 * (1.0 - w1))
    w1 = b[0]

    for i in range(1, 10):
        w1 += b[i] * w3**i

    if qn > 0.5:
        return sqrt(w1 * w3)

    return -sqrt(w1 * w3)

def ci_lower_bound(pos, n, power):
    """Calculate the lower bound of Wilson score confidence interval 
    for a Bernoulli parameter, whatever that means!

    """
    if n == 0:
        return 0
    z = pnormaldist(1-power/2)
    phat = 1.0*pos/n
    return (phat + z*z/(2*n) - z * sqrt((phat*(1-phat)+z*z/(4*n))/n))/(1+z*z/n)

Isn't the for loop supposed to be over range(1, 11)?

Reasons:

• b has 11 elements. If we're not accessing b[10] ever, then why is it there.
• the original Ruby code does "1.upto 10 do |i|", which includes the 10.