威尔逊置信区间
作者:互联网
由于正态区间对于小样本并不可靠,因而,1927年,美国数学家 Edwin Bidwell Wilson提出了一个修正公式,被称为“威尔逊区间”,很好地解决了小样本的准确性问题。
根据离散型随机变量的均值和方差定义:
μ=E(X)=0*(1-p)+1*p=p
σ=D(X)=(0-E(X))2(1-p)+(1-E(X))2p=p2(1-p)+(1-p)2p=p2-p3+p3-2p2+p=p-p2=p(1-p)
因此上面的威尔逊区间公式可以简写成:
代码:
def wilson_score(pos, total, p_z=2.): """ 威尔逊得分计算函数 参考:https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval :param pos: 正例数 :param total: 总数 :param p_z: 正太分布的分位数 :return: 威尔逊得分 """ pos_rat = pos * 1. / total * 1. # 正例比率 score = (pos_rat + (np.square(p_z) / (2. * total)) - ((p_z / (2. * total)) * np.sqrt(4. * total * (1. - pos_rat) * pos_rat + np.square(p_z)))) / \ (1. + np.square(p_z) / total) return score
SQL实现代码:
#wilson_score SELECT widget_id, ((positive + 1.9208) / (positive + negative) - 1.96 * SQRT((positive * negative) / (positive + negative) + 0.9604) / (positive + negative)) / (1 + 3.8416 / (positive + negative)) AS ci_lower_bound FROM widgets WHERE positive + negative > 0 ORDER BY ci_lower_bound DESC; # SELECT widget_id, (positive - negative) AS net_positive_ratings FROM widgets ORDER BY net_positive_ratings DESC; # SELECT widget_id, positive / (positive + negative) AS average_rating FROM widgets ORDER BY average_rating DESC;
excel实现代码:
=IFERROR((([@[Up Votes]] + 1.9208) / ([@[Up Votes]] + [@[Down Votes]]) - 1.96 * SQRT(([@[Up Votes]] * [@[Down Votes]]) / ([@[Up Votes]] + [@[Down Votes]]) + 0.9604) / ([@[Up Votes]] + [@[Down Votes]])) / (1 + 3.8416 / ([@[Up Votes]] + [@[Down Votes]])),0)
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参考资料:
标签:置信区间,Votes,positive,威尔逊,negative,pos,Up,total 来源: https://www.cnblogs.com/iupoint/p/13354631.html