Nonparametric Tests for Exponentiality Against IFRA Alternatives Based on Cumulative Extropy Measures

TL;DR

This paper introduces new nonparametric tests to check if data follows an exponential distribution against IFRA alternatives using information-theoretic measures.

Contribution

The novelty lies in using cumulative extropy measures to construct tests with strong power and asymptotic normality for IFRA alternatives.

Findings

The proposed tests outperform existing methods for moderate to large sample sizes.

Scale-invariant versions ensure limiting distributions are free of unknown parameters.

Real data analyses confirm the tests' effectiveness in reliability studies.

Abstract

This paper develops two nonparametric test statistics for testing exponentiality against alternatives in the increasing failure rate average (IFRA) class. The proposed procedures are constructed using information-theoretic functionals, namely the cumulative residual extropy and the cumulative past extropy of the first-order statistic. Exploiting fundamental properties of IFRA distributions, we derive explicit inequality relations that motivate the test statistics and establish their asymptotic normality under mild regularity conditions. To facilitate practical implementation, scale-invariant versions of the proposed tests are introduced, ensuring that their limiting distributions do not depend on unknown scale parameters. A comprehensive Monte Carlo simulation study demonstrates that the proposed tests possess strong power properties and frequently outperform several established competitors, particularly for moderate to large sample sizes. The applicability and effectiveness of the methodology are further illustrated through analyses of real lifetime datasets arising in reliability studies. The proposed tests are shown to be particularly effective for moderate sample sizes and provide a competitive alternative to existing IFRA-based procedures.

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