<p>This paper introduces a novel transformation technique based on the cumulative distribution function and inverse trigonometric function, aimed to generate a new family of lifetime distributions. The proposed transformation technique is applied using the exponential distribution as a baseline, and its various statistical properties such as ordinary moments, quantile function, complete and incomplete moments, hazard rate, retro-hazard rate, moment generating function, entropy, and mixture representation are thoroughly examined. Further, the analytical, graphical, and numerical approaches are employed to study the characteristics of the resulting distribution, which is found to be positively skewed with a heavy tail. The hazard function displays increasing, decreasing, and constant patterns, making the model suitable for data exhibiting these behaviors. Different classical estimation methods are used to estimate the model parameters, and their performance is evaluated through a detailed Monte Carlo simulation study. The flexibility and practical utility of the proposed Arcsin Topp-Leone exponential (ASTLE) distribution are thoroughly demonstrated through the analysis of four real-world datasets. By comparing its performance against a range of existing lifetime distribution models, the study evaluates the effectiveness of the ASTLE model using various goodness-of-fit measures. These comparisons suggest that the ASTLE model may be a better choice among models with similar hazard rate structures, particularly for datasets exhibiting complex behaviors such as increasing, decreasing, or constant hazard rates. Its superior performance underscores the model’s enhanced flexibility in fitting diverse real-world data, making it a valuable tool for practical applications in reliability analysis and survival studies.</p>

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A new class of ArcSin Topp-Leone probability distribution: classical estimation and its application to real data

  • Aashutosh Kumar,
  • Abhimanyu Singh Yadav

摘要

This paper introduces a novel transformation technique based on the cumulative distribution function and inverse trigonometric function, aimed to generate a new family of lifetime distributions. The proposed transformation technique is applied using the exponential distribution as a baseline, and its various statistical properties such as ordinary moments, quantile function, complete and incomplete moments, hazard rate, retro-hazard rate, moment generating function, entropy, and mixture representation are thoroughly examined. Further, the analytical, graphical, and numerical approaches are employed to study the characteristics of the resulting distribution, which is found to be positively skewed with a heavy tail. The hazard function displays increasing, decreasing, and constant patterns, making the model suitable for data exhibiting these behaviors. Different classical estimation methods are used to estimate the model parameters, and their performance is evaluated through a detailed Monte Carlo simulation study. The flexibility and practical utility of the proposed Arcsin Topp-Leone exponential (ASTLE) distribution are thoroughly demonstrated through the analysis of four real-world datasets. By comparing its performance against a range of existing lifetime distribution models, the study evaluates the effectiveness of the ASTLE model using various goodness-of-fit measures. These comparisons suggest that the ASTLE model may be a better choice among models with similar hazard rate structures, particularly for datasets exhibiting complex behaviors such as increasing, decreasing, or constant hazard rates. Its superior performance underscores the model’s enhanced flexibility in fitting diverse real-world data, making it a valuable tool for practical applications in reliability analysis and survival studies.