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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年10月14日

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  • Mohammad Sepehrifar

摘要

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.