A novel extension of the power lindley distribution with statistical properties and application to COVID-19 data

In the recent years, there has been a notable shift in the landscape of statistical and data science research, with increasing attention directed toward the development of advanced probability distributions aimed at addressing the challenges posed by medical and health-related data. In response to this need, the present study introduces a novel probability distribution model termed as the Exponentiated Odd Lomax Power Lindley distribution constructed by embedding the Power Lindley distribution within the Lomax family framework through the T-X transformation technique. This article delves into the application of probability distributions in medical data analysis, with a special focus on their role in understanding and managing the COVID-19 data. A comprehensive theoretical investigation is conducted, deriving key statistical properties including the probability and cumulative distribution functions, reliability functions, moments, moment generating function, order statistics, and entropy measures. To ensure accurate parameter estimation, several estimation methods are employed and rigorously compared through simulation studies. The real-world applicability of the developed distribution is illustrated through the modelling of COVID-19 datasets, where its performance is evaluated against a range of well-established probability distribution models. Empirical findings demonstrate the superior adaptability and modelling accuracy of the distribution while analysing real-world datasets.