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

Area of Science:

• Statistics
• Reliability Engineering
• Information Theory

Background:

• The exponential distribution is a fundamental model in reliability analysis.
• Testing for the increasing failure rate average (IFRA) class is crucial for accurate lifetime data modeling.
• Existing tests may lack power or applicability across various conditions.

Purpose of the Study:

• To develop novel nonparametric test statistics for assessing exponentiality against IFRA alternatives.
• To introduce tests based on information-theoretic functionals: cumulative residual extropy and cumulative past extropy.
• To provide robust statistical tools for reliability and lifetime data analysis.

Main Methods:

• Development of two nonparametric test statistics using cumulative residual extropy and cumulative past extropy.
• Derivation of inequality relations based on IFRA distribution properties.
• Establishment of asymptotic normality under mild regularity conditions.
• Introduction of scale-invariant test versions for practical application.

Main Results:

• The proposed tests demonstrate strong power properties in simulations.
• The new tests frequently outperform established competitors, especially for moderate to large sample sizes.
• Scale-invariant versions ensure consistent performance irrespective of unknown scale parameters.
• Analyses of real-world lifetime datasets confirm the methodology's effectiveness.

Conclusions:

• The developed nonparametric tests offer a competitive alternative for IFRA distribution analysis.
• The information-theoretic approach provides a powerful framework for reliability testing.
• The tests are particularly effective for moderate sample sizes in lifetime studies.