Censored Kullback-Leibler Information and Goodness-of-Fit Test with Type II Censored Data

Abstract

The Kulback-Leibler information has been considered for establishing goodness-of-fit test statistics, which have been shown to perform very well (Arizono & Ohta, 1989; Ebrahimi et al., 1992, etc). In this paper, we propose censored Kullback-Leibler information to generalize the discussion of the Kullback-Leibler information to the censored case. Then we establish a goodness-of-fit test statistic based on the censored Kullback-Leibler information with the type 2 censored data, and compare the test statistics with some existing test statistics for the exponential and normal distributions.

Keywords:

• Entropy difference
• maximum entropy distribution
• minimum discrimination information loss estimation
• order statistics
• sample entropy

Acknowledgements

The authors wish to express their sincere thanks to an anonymous referee for very helpful comments and suggestions, particularly Remark 1, which are incorporated in the paper. This work of the second author was supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD) (KRF-2006-312-C00068).