双截断随机变量的Cox-Czanner散度

Cox-Czanner Divergence of a Doubly Truncated Random Variable

摘要: Cox和Czanner (2016)提出了生存散度的概念并研究了一些分布的生存散度。作为KL散度的推广，生存散度在统计学、生态学等领域获得了广泛应用。本文提出了Cox-Czanner散度在双截断随机变量下的分布差异，通过广义失效率的方法研究了双截断随机变量生存散度的有界性和单调性，并讨论了单调变换对生存散度的影响，最后通过分布的变换将双截断随机变量的生存散度应用到比例优势模型进行实例检验。

Abstract: Cox and Czanner (2016) put forward the concept of survival divergence and studied the survival divergence of some distributions. As a generalization of KL divergence, survival divergence has been widely used in statistics, ecology and other fields. This paper proposes the distribution difference of Cox-Czanner divergence under double-truncated random variables, studies the boundedness and monotonicity of the survival divergence of double-truncated random variables by means of generalized failure rate method, and discusses the influence of monotonic transformation on the survival divergence. Finally, the survival divergence of double truncated random variables is applied to the proportional dominance model by the transformation of distribution.