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<p>In this paper, we enhance a&#xa0;generator to produce new flexible lifetime distributions and consider the generalized Log-Exponential transformation method. Besides, the statistical properties and estimation topic with the parametric and non-parametric context has been studied thoroughly. The maximum empirical likelihood estimation is the serious competitor for the maximum likelihood method regarding the standard error measure. To corroborate the suitability of the proposed generator in practice, the Weibull and inverse Weibull distributions are taken as baseline distributions with the extensive discussion of statistical properties and estimation approaches. Both new lifetime distributions (generalized Log-Exponential Weibull and generalized Log-Exponential inverse Weibull) can be fitted to many types of data since they have different probability density and hazard functions. The moments, incomplete moments and moment generating function of both lifetime distributions have been obtained. The applicability of the new family is evaluated by the COVID-19 data set.</p>

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A novel generalized Log-Exponential family of lifetime distributions: Properties, comprehensive estimation approaches and applications

  • 期刊论文

  • 发表日期：

    2026年4月13日

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  • Mortaza Ghasemi Cherati,
  • Ezzatallah Baloui Jamkhaneh,
  • Einolah Deiri,
  • Masoumeh Shirozhan

摘要

In this paper, we enhance a generator to produce new flexible lifetime distributions and consider the generalized Log-Exponential transformation method. Besides, the statistical properties and estimation topic with the parametric and non-parametric context has been studied thoroughly. The maximum empirical likelihood estimation is the serious competitor for the maximum likelihood method regarding the standard error measure. To corroborate the suitability of the proposed generator in practice, the Weibull and inverse Weibull distributions are taken as baseline distributions with the extensive discussion of statistical properties and estimation approaches. Both new lifetime distributions (generalized Log-Exponential Weibull and generalized Log-Exponential inverse Weibull) can be fitted to many types of data since they have different probability density and hazard functions. The moments, incomplete moments and moment generating function of both lifetime distributions have been obtained. The applicability of the new family is evaluated by the COVID-19 data set.