ratio_of_proportions_with_uncertainty.py

def ratio_lossed_gained_uncertainty(num_lossed:int, 
                                    num_gained:int, 
                                    alpha:float = 0.01, 
                                    verbose:bool = False) -> tuple[float, float]:
    """Estimate ratio lossed / gained with statistical uncertainty

    Using confidence interval (CI) estimation for binomal estimation (loss, gain).
    NOTE> In this case lossed is win and gained is loss, that is, ratio = lossed / gained.

    Arguments:
        num_lossed {int} -- Number of lossed.
        num_gained {int} -- Number of gained.

    Keyword Arguments:
        alpha {float} -- Confidence (default: {0.01})
        verbose {bool} -- Display or not (default, False)

    Returns:
        tuple[float, float] -- (ratio, relative uncertainty)
    """
    # estimate total
    total = num_gained + num_lossed
    # validation
    if total == 0 or num_gained == 0:
        return (float('inf'), 0.)
    # proportions
    p = num_lossed / total
    R = num_lossed / num_gained
    # confidence interval for binomial distribution
    ci_low, ci_high = proportion_confint(num_lossed, total, alpha=alpha, method='wilson')
    # confidence interval to ratios interval
    R_low = ci_low / (1 - ci_low)
    R_high = ci_high / (1 - ci_high)
    # relative uncertainty
    uncertainty = (R_high - R_low) / R
    # build results container
    d_results = {
        'ratio': R,
        'probability lossed': p,
        'CI ratio': (R_low, R_high),
        'relative uncertainty': uncertainty
    }
    # display
    if verbose:
        print(d_results)
    # return
    return (d_results["ratio"], d_results['relative uncertainty'])