Power Unit Garima Distribution: Properties, Comparison of Estimation Procedures and Diverse Applications

This paper derives the power unit Garima distribution (PUGD), which is an extension of the unit Garima distribution (UGD) obtained through a power transformation. Properties of this new model, among which are mode, moments, moment generating function, entropies, extropy, and Bonferroni and Lorenz curves, are studied in detail. The relationship between the PUGD and the Garima distribution is established mathematically. Additionally, several estimation techniques for the parameters of the PUGD are examined through a Monte Carlo simulation procedure, including maximum likelihood, ordinary least squares, weighted least squares, and the Anderson–Darling and Cramer–von Mises methods. The simulation results obtained are favorable to the maximum likelihood approach. Both the observed and expected information matrices are discussed. The goodness of fit of the distribution to three data sets relating to various fields is determined relative to that of the unit power Lindley, UGD, Kumaraswamy and beta distributions. Among the distributions considered, the PUGD proved to be the best in modeling the data.