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

Abstract 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.