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<p>Positive-valued measurements such as failure times, waiting durations, and event intervals frequently arise in reliability engineering, environmental monitoring, and survival analysis. These data often exhibit skewness and non–monotonic hazard behaviour that classical lifetime models, including the exponential and Weibull distributions, fail to capture adequately. This paper proposes a flexible modeling framework for analyzing both independent lifetime observations and dependent positive time-series data. The approach is based on a modified Fréchet transformation applied to a positive baseline distribution, producing a tractable model with a closed-form quantile representation that facilitates simulation and statistical inference. Several statistical properties are derived, and parameter estimation procedures are investigated through Monte Carlo experiments. To account for temporal dependence commonly observed in duration data, a positive-valued first-order autoregressive process is also developed. Applications to real datasets demonstrate improved fitting accuracy and predictive performance compared with commonly used lifetime models. The proposed framework provides a practical and interpretable tool for modeling reliability data, event durations, and asymmetric time-dependent measurements encountered in applied statistical analysis.</p>

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Modeling real life data through an extension of the power Ailamujia distribution and its AR(1) process

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月22日

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  • Rabab S. Gomaa,
  • Mohamed A. Abd Elgawad,
  • Ibtehal Alazman,
  • Fatma M. Mowafy,
  • Beih S. El-Desouky,
  • Shimaa M. El-Hadidy

摘要

Positive-valued measurements such as failure times, waiting durations, and event intervals frequently arise in reliability engineering, environmental monitoring, and survival analysis. These data often exhibit skewness and non–monotonic hazard behaviour that classical lifetime models, including the exponential and Weibull distributions, fail to capture adequately. This paper proposes a flexible modeling framework for analyzing both independent lifetime observations and dependent positive time-series data. The approach is based on a modified Fréchet transformation applied to a positive baseline distribution, producing a tractable model with a closed-form quantile representation that facilitates simulation and statistical inference. Several statistical properties are derived, and parameter estimation procedures are investigated through Monte Carlo experiments. To account for temporal dependence commonly observed in duration data, a positive-valued first-order autoregressive process is also developed. Applications to real datasets demonstrate improved fitting accuracy and predictive performance compared with commonly used lifetime models. The proposed framework provides a practical and interpretable tool for modeling reliability data, event durations, and asymmetric time-dependent measurements encountered in applied statistical analysis.