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<p>In this article, we introduce a new family of probability distributions, the Exponentiated Odd Lindley-X Power Series (EOL-XPS) class, which is derived by integrating the power series distribution with the exponentiated odd Lindley-X family. We establish several statistical properties of this new class, including moments, the moment-generating function, the quantile function, mean deviations, order statistics, and Rényi entropy. As a special case, we derive the probability density function and cumulative distribution function of the Exponentiated Odd Lindley-Weibull Poisson (EOL-WP) distribution, using the Weibull-Poisson distribution as the baseline. To assess the robustness of the proposed model, we conduct a Monte Carlo simulation study to evaluate the performance of maximum likelihood estimation for parameter estimation. Furthermore, we apply the EOL-WP model to COVID-19 and Kevlar datasets, demonstrating its flexibility and practical relevance in modeling complex data.</p>

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Exponentiated Odd Lindley-X Power Series Class of Distributions: Properties and Applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月30日

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  • Fastel Chipepa,
  • Nonhle Mdziniso,
  • Shahid Mohammad,
  • Sher Chhetri

摘要

In this article, we introduce a new family of probability distributions, the Exponentiated Odd Lindley-X Power Series (EOL-XPS) class, which is derived by integrating the power series distribution with the exponentiated odd Lindley-X family. We establish several statistical properties of this new class, including moments, the moment-generating function, the quantile function, mean deviations, order statistics, and Rényi entropy. As a special case, we derive the probability density function and cumulative distribution function of the Exponentiated Odd Lindley-Weibull Poisson (EOL-WP) distribution, using the Weibull-Poisson distribution as the baseline. To assess the robustness of the proposed model, we conduct a Monte Carlo simulation study to evaluate the performance of maximum likelihood estimation for parameter estimation. Furthermore, we apply the EOL-WP model to COVID-19 and Kevlar datasets, demonstrating its flexibility and practical relevance in modeling complex data.