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<p>This study introduces a novel three-parameter probability distribution, termed the Modi Rayleigh distribution (MRD), which incorporates two shape parameters and one scale parameter. The mathematical and statistical properties of the proposed distribution, including moments, quantiles, and reliability characteristics, are systematically derived and analyzed. The model’s parameters are determined through maximum likelihood estimation (MLE), with their accuracy assessed via a detailed Monte Carlo simulation that measures estimator performance using mean square error (MSE) criteria. The practical utility and flexibility of the MRD are demonstrated by fitting it to two real-world datasets, where its performance is compared with several existing distributions. Empirical results reveal that the proposed model outperforms its competitors, exhibiting superior goodness of fit. The study highlights the MRD adaptability in modeling diverse data types, making it a valuable addition to the family of lifetime distributions for applications in reliability, survival analysis, and related fields.</p>

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Modi rayleigh distribution and its application to survival time data sets

  • 期刊论文

  • 发表日期：

    2025年7月12日

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  • Surinder Kumar,
  • Bhupendra Meena,
  • Rahul Shukla,
  • Shivendra Pratap Singh

摘要

This study introduces a novel three-parameter probability distribution, termed the Modi Rayleigh distribution (MRD), which incorporates two shape parameters and one scale parameter. The mathematical and statistical properties of the proposed distribution, including moments, quantiles, and reliability characteristics, are systematically derived and analyzed. The model’s parameters are determined through maximum likelihood estimation (MLE), with their accuracy assessed via a detailed Monte Carlo simulation that measures estimator performance using mean square error (MSE) criteria. The practical utility and flexibility of the MRD are demonstrated by fitting it to two real-world datasets, where its performance is compared with several existing distributions. Empirical results reveal that the proposed model outperforms its competitors, exhibiting superior goodness of fit. The study highlights the MRD adaptability in modeling diverse data types, making it a valuable addition to the family of lifetime distributions for applications in reliability, survival analysis, and related fields.