Tests for properties of the percentile residual life function

Abstract

The lOOα -percentile (0 < α < 1) residual life function at time× x is defined to be the 100α -percentile of the remaining life given survival up to time x. Tests are developed for testing the null hypothesis of exponentiality against alternatives repre-senting decreasing 100α -percentile residual life and the property new better than used with respect to the lOOa-percentile. These tests are also extended to accommodate randomly censored data. Consistency and asymptotic relative efficiency results are obtained for the proposed tests. Exact critical values are obtained for the test statistics in the complete data case.

Keywords:

• 100α-perdentile residual life function
• mean residual life function
• inference for life distributions
• exponential distribution
• L-statistic
• randomly censored data
• Kaplan-Meier product-limit estimator
• asymptotic relative efficiency