Exponentiated Pareto Distribution with Application in Financial Data

The Pareto distribution is a skewed, heavy-tailed distribution that is usually used to model the distribution of incomes and other financial variables. Moreover, adding one or more parameters to a distribution makes it richer and more flexible for modeling data. In this paper, we consider the problem of estimation of the parameters of the exponentiated Pareto distribution. A graphical method is developed to obtain maximum likelihood estimates of the unknown parameters. Applying the Bayesian approach, the estimators of the unknown parameters are derived under squared error loss function. Since closed-form expressions for the Bayesian estimators cannot be obtained, we use the approximation procedure for computing them. A real data set represents the annual wages of the production-line workers is used to illustrate the proposed results. An important implication of the present study is that the exponentiated Pareto distribution, in contrast to other distributions, fits more appropriately in the financial data.