Various statistical methodologies embed a probability distribution in a more flexible family of distributions. The latter is called elaboration model, which is constructed by choice or a formal procedure and evaluated by asymmetric measures such as the likelihood ratio and Kullback–Leibler information. The use of asymmetric measures can be problematic for this purpose. This paper introduces two formal procedures, referred to as link functions, that embed any baseline distribution with a continuous density on the real line into model elaborations. Conditions are given for the link functions to render symmetric Kullback–Leibler divergence, Rényi divergence and phi-divergence family. The first link function elaborates quantiles of the baseline probability distribution. This approach produces continuous counterparts of the binary probability models. Examples include the Cauchy, probit, logit, Laplace and Student's $t$ links. The second link function elaborates the baseline survival function. Examples include the proportional odds and change point links. The logistic distribution is characterised as the one that satisfies the conditions for both links. An application demonstrates advantages of symmetric divergence measures for assessing the efficacy of covariates.

中文翻译：

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具有对称信息散度的精化模型


各种s $t$ 统计方法将概率分布嵌入到更灵活的分布族中。后者称为精化模型，它是通过选择或正式程序构建的，并通过似然比和 Kullback-Leibler 信息等不对称度量进行评估。为此目的使用不对称措施可能会出现问题。本文介绍了两个正式程序，称为链接函数，将实线上具有连续密度的任何基线分布嵌入到模型阐述中。给出了链接函数呈现对称 Kullback-Leibler 散度、Rényi 散度和 phi-散度族的条件。第一个链接函数详细说明了基线概率分布的分位数。这种方法产生二元概率模型的连续对应物。示例包括柯西、概率、logit、拉普拉斯和学生$t$链接。第二个链接函数详细阐述了基线生存函数。示例包括比例赔率和变化点链接。物流配送的特点是满足两个环节的条件。一个应用程序展示了对称散度度量在评估协变量功效方面的优势。