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Distributions of the Kullback–Leibler divergence with applications
Article first published online: 15 APR 2011
DOI: 10.1348/000711010X522227
©Law School Admission Council. British Journal of Mathematical and Statistical Psychology. © The British Psychological Society.
Issue
British Journal of Mathematical and Statistical Psychology
Volume 64, Issue 2, pages 291–309, May 2011
Additional Information
How to Cite
Belov, D. I. and Armstrong, R. D. (2011), Distributions of the Kullback–Leibler divergence with applications. British Journal of Mathematical and Statistical Psychology, 64: 291–309. doi: 10.1348/000711010X522227
Publication History
- Issue published online: 15 APR 2011
- Article first published online: 15 APR 2011
- Received 6 November 2009; revised version received 28 April 2010
- Abstract
- Article
- References
- Cited By
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.