A class of tests for exponentiality against decreasing mean residual life alternatives

Abstract

A class of tests is proposed for testing Exponentiality against the Decreasing Mean Residual Life (DMRL) class of non-exponential probability distributions. These tests are consistent and asymptotically unbiased against all continuous DMRL alternatives. They are U - statistics and hence asymptotically normally distributed. The asymptotic relative efficiency (ARE) with respect to other tests for DMRL are quite high. Small sample powers are also comparable with small sample powers of the competitors.

Keywords:

• asymptotic relative efficiency
• exponential distribution
• DMRL distributions
• nonparametric test
• tests for exponentiality
• reliability
• unbiasedness
• U - statistics