Testing exponentiality based on Kullback—Leibler information for progressively Type II censored data

ABSTRACT

In many life-testing and reliability experiments, data are often censored in order to reduce the cost and time associated with testing and since the conventional Type-I and Type-II censoring schemes are not flexible enough, progressive censoring is developed by researchers. In this article, we develop a general goodness of fit test by using a new estimate of Kullback–Leibler information based on progressively Type-II censored data. Consistency and other properties of the proposed test are shown. Then, we use the proposed test statistic to test for exponentiality based on progressively Type-II censored data. The power values of the proposed test under different progressively Type-II censoring schemes are computed, through Monte Carlo simulations. It is observed that the proposed test is quite powerful in compared with the test proposed by Balakrishnan et al. (2007). Two real datasets from progressive censoring literature are finally presented for illustrative purpose.

KEYWORDS:

• Entropy
• Kullback–Leibler information
• Monte Carlo simulation
• Power study
• Progressively Type-II censoring
• Test for exponentiality

Mathematics Subject Classification:

• 62N01
• 62N03

Acknowledgment

The author thanks the Associate Editor and anonymous referees for making some valuable suggestions which led to a considerable improvement in the presentation of this manuscript.