Kullback-Leibler 散度分布及其应用。

Distributions of the Kullback-Leibler divergence with applications.

机构信息

Law School Admission Council, Newtown, PA, USA.

出版信息

Br J Math Stat Psychol. 2011 May;64(Pt 2):291-309. doi: 10.1348/000711010X522227.

Abstract

The Kullback-Leibler divergence (KLD) is a widely used method for measuring the fit of two distributions. In general, the distribution of the KLD is unknown. Under reasonable assumptions, common in psychometrics, the distribution of the KLD is shown to be asymptotically distributed as a scaled (non-central) chi-square with one degree of freedom or a scaled (doubly non-central) F. Applications of the KLD for detecting heterogeneous response data are discussed with particular emphasis on test security.

摘要

克劳福德-莱布勒散度（KLD）是一种广泛用于衡量两个分布拟合程度的方法。通常，KLD 的分布是未知的。在心理测量学中常见的合理假设下，KLD 的分布被证明渐近分布为一个缩放（非中心）卡方分布，自由度为 1，或者是一个缩放（双重非中心）F 分布。讨论了 KLD 用于检测异构响应数据的应用，特别强调了测试安全性。