Testing exponentiality based on Gini-index characterization

Abstract

The exponential distribution possesses several important properties that make it valuable in statistical inference and applications, such as reliability analysis, queueing theory, and survival analysis. Based on a Gini-index characterization for the exponential distribution, we propose different statistics for testing exponentiality under both complete data and right-censored data. Asymptotic results of the proposed test statistics are studied and a large Monte-Carlo simulation study is designed and performed to evaluate the performance of these statistics and to compare them against the best existing tests. Simulation studies indicate that the proposed tests are comparable to the best existing methods for complete data, while offering simple implementation and robust performance across various alternatives–including IFR, DFR, and UFR–and showing particular effectiveness for small sample sizes and under IFR and UFR alternatives in right-censored data. Finally, three real data sets are used to demonstrate the applicability of the proposed tests.