Pareto exponentiated log-logistic distribution (PELL) with an application to Covid-19 data

Recently, the Covid-19 pandemic has caused tremendous trauma over the world, leading to psychological and behavioral harm in addition to social and economic instabilities. Even though the pandemic’s statistical analysis is still in progress, it is essential to fit Covid-19 data using statistical models to prevent further harm. In order to model Covid-19 data, the study suggests a novel family of distributions called the exponentiated log-logistic family. The basic Pareto distribution is transformed as a special case, and certain properties of the proposed distribution are discussed. To estimate the model parameters, the maximum likelihood estimation approach is used. Moreover, a simulation study is conducted to ensure the consistency of parameter estimates. Three real-world datasets relevant to the Covid-19 pandemic are examined to demonstrate the applicability of the suggested approach. The proposed model is shown to be more flexible and provides an improved fit to describe the Covid-19 data when compared to various alternative forms of Pareto distribution.