Python implementation - Lower bound of Wilson score confidence interval for a Bernoulli parameter

wilson.py

"""
Python implementation - Lower bound of Wilson score confidence interval for a Bernoulli parameter

- http://www.evanmiller.org/how-not-to-sort-by-average-rating.html
- https://news.ycombinator.com/item?id=15131611
- https://stackoverflow.com/questions/10029588/python-implementation-of-the-wilson-score-interval/45965534
- https://stackoverflow.com/questions/10029588/python-implementation-of-the-wilson-score-interval/45965534#45965534
"""

import math

import scipy.stats as st


def get_z(confidence):
    return st.norm.ppf(1 - (1 - confidence) / 2)


def ci_lower_bound(pos, n, confidence=None, z=None):
    if n == 0:
        return 0
    if z is None:
        z = get_z(confidence)
    phat = 1.0 * pos / n
    return (phat + z * z / (2 * n) - z * math.sqrt((phat * (1 - phat) + z * z / (4 * n)) / n)) / (1 + z * z / n)

Doh!!! Thanks @pierre-vr