On a Class of Tests of Exponentiality

Abstract

The class of statistics T, = (Σ^α _i=1, X ^α _i /n)/ ^x , where α > 0 and ≠ 1, have been considered in the literature for testing exponentiality versus omnibus alternatives. These tests have a twosided rejection region. It is shown here that tests based on these statistics are not consistent for certain alternatives. However, it is shown that one-sided tests based on these statistics are consistent for IFRA (DFRA) distributions. A Monte Carlo power study suggests that lower tail tests based on T _½ and T ₂ are very competitive for DFRA and IFRA alternatives, respectively. The null distributions of T _½ and T ₂ are approximated by members of the Johnson families of distributions.

KEY WORDS:

• Consistent test
• Monotone failure rate average
• Omnibus test
• Sample moments