Beta Distribution Ranking

beta_distribution_ranking.py

import numpy as np
from scipy import stats
import pandas as pd

def score_for_confidence(alpha, beta, confidence=.95):
    """
    alpha: 1 + num_positive
    beta: 1 + num_negative
    confidence: confidence you can have that positive fraction is greater than this
    """
    quantile = 1 - confidence
    return stats.distributions.beta(a=alpha, b=beta).ppf(quantile)

def example():
    N = 10
    wins = np.random.poisson(2, size=N)
    totals =  wins + np.random.poisson(3, size=N)
    losses = totals - wins
    alpha = wins + 1
    beta = losses + 1
    confidence = .9
    df = pd.DataFrame({'wins': np.random.poisson(2, size=N),'losses': np.random.poisson(3, size=N)})
    df['alpha'] = df.wins + 1
    df['beta'] = df.losses + 1
    df['score'] = score_for_confidence(df.alpha, df.beta, confidence)
    return df
example()