Asymptotic Efficiency of New Exponentiality Tests Based on a Characterization

TL;DR

This paper introduces two new exponentiality tests based on a recent characterization, analyzes their asymptotic properties, efficiency, and compares their performance with existing tests for small samples.

Contribution

It presents novel exponentiality tests derived from a recent characterization, with detailed asymptotic analysis and efficiency evaluation.

Findings

Tests have high local Bahadur efficiency against common alternatives.

New tests outperform some existing methods in small sample power.

Identified classes of locally optimal alternatives for each test.

Abstract

Two new tests for exponentiality, of integral and Kolmogorov type, are proposed. They are based on a recent characterization and formed using appropriate V-statistics. Their asymptotic properties are examined and their local Bahadur efficiencies against some common alternatives are found. A class of locally optimal alternatives for each test is obtained. The powers of these tests, for some small sample sizes, are compared with different exponentiality tests.