Clopper-Pearson Lite

Problem

Return the exact Clopper-Pearson interval [low, high] for k successes in n trials at significance alpha. Solve the binomial tail equations by bisection over p in [0, 1] using the exact binomial CDF built from math.comb. Return [0.0, 0.0] when n <= 0 and [0.0, 1.0] when alpha lies outside (0, 1).

Hint

The lower bound solves P(X >= k; n, p) = alpha/2 and the upper bound solves P(X <= k; n, p) = alpha/2.

Test cases

case 1

in: [10,20,0.05]

expected: [0.2719578495607916,0.7280421504392083]

case 2

in: [0,10,0.05]

expected: [0,0.3084971078187607]

case 3

in: [10,10,0.05]

expected: [0.6915028921812392,1]

case 4

in: [3,10,0.1]

expected: [0.08726443391415034,0.6066242161054134]

Starter codePython

import math
def clopper_pearson(k, n, alpha):
    # Your code here
    pass

4 test cases · run your code against them in the editor