Function to calculate Jefferey's Interval for Binomial proportion confidence interval. See https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Jeffreys_interval

jeffreys_interval.py

def bin_prop_jeffreys_interval(trials, successes, α=0.05):
    """Binomial proportions confidence Jeffrey's interval.

    Parameters
    ----------
    trials : np.ndarray
        number of trials
    successes : int
        number of successes
    α : float, 0<α<1
        width of confidence interval

    Returns
    -------
    low, high : tuple of floats
        The lower and upper bounds of the proportions confidence interval

    See
    ---
    https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Jeffreys_interval
    """
    import scipy.stats
    n = int(trials)
    x = int(successes)
    assert 0 <= x <= n
    beta = scipy.stats.beta(x + 0.5, n - x + 0.5)
    if x == 0:
        low = 0
    else:
        low = beta.ppf(α / 2)
    if x == n:
        high = 1
    else:
        high = beta.ppf(1 - α / 2)
    return x / n - low, high - x / n