A New Bounded Distribution: Covid-19 Application

The modeling of proportional or percentage data through continuous distributions specified on the unit interval has become progressively relevant in various fields. This paper presents the unit inverse power Lomax distribution as a strong framework for such applications. The proposed model is thoroughly investigated, detailing its quantile function, moments, incomplete moments, probability-weighted moments, order statistics, stress-strength reliability function, and entropy measures. Ten distinct methods for estimation of the involved parameters, such as maximum likelihood, maximum product of spacings, minimum spacing absolute-log distance, least square, weighted least square, percentile, Anderson-Darling, left-tail Anderson-Darling estimation, left-tail Anderson-Darling second-order, and Cramer-von Mises, are studied. The significance of the presented model is demonstrated through comparative analysis with several existing statistical models via two applications using real datasets. This research underlines the potential advantages of the new distribution in accurately modeling proportional data, paving the way for further studies and practical applications.