On the goodness-of-fit test based on the ratio of cumulative hazard functions with the Type II censored data

ABSTRACT

For comparing two cumulative hazard functions, we consider an extension of the Kullback–Leibler information to the cumulative hazard function, which is concerning the ratio of cumulative hazard functions. Then we consider its estimate as a goodness-of-fit test with the Type II censored data. For an exponential null distribution, the proposed test statistic is shown to outperform other test statistics based on the empirical distribution function in the heavy censoring case against the increasing hazard alternatives.

KEYWORDS:

• Exponential distribution
• Kaplan–Meier estimator
• Kullback–Leibler information
• Nelson–Aalen estimator
• Survival function

MATHEMATICS SUBJECT CLASSIFICATION:

• 62B10
• 62N86

Acknowledgments

The author is grateful to an anonymous referee and an associate editor for making some useful comments on an earlier version of this manuscript.

Funding

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MOE) (NO. 2015R1D1A1A01056578) and by the Korea government (MSIP (NRF-2015R1A2A1A15051493)).