A U-statistic-based test for exponentiality using starshaped mean equilibrium class of life distributions

Mohammad Sepehrifar ()
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Mohammad Sepehrifar: Mississippi State University

Statistical Papers, 2025, vol. 66, issue 6, No 20, 19 pages

Abstract: Abstract Modeling aging in lifetime data is critical for reliability and survival analysis, yet existing models like the Decreasing-Then-Increasing Mean Residual Life (DIMRL) class often require restrictive assumptions about turning points. We propose the Starshaped Mean Equilibrium Life (SMEL) class, a nonparametric framework defined by a convex mean residual life (MRL) function, which flexibly captures diverse aging patterns without needing a known turning point. The convex shape enables SMEL to model both adverse and beneficial aging phases, generalizing beyond DIMRL. We develop a hypothesis test to distinguish exponential distributions (constant MRL) from SMEL distributions with non-constant MRL, addressing the need to detect complex aging behaviors. The test, robust to right-censored and randomly censored data prevalent in survival studies, uses U-statistics and requires only a finite first moment. Simulation studies demonstrate its empirical power, confirming its utility in practical applications.

Keywords: Starshaped function; Renewal process; U-statistics; Equilibrium distribution; Mean residual life distribution; Stochastic process (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01757-z

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