Some extended Pareto Type I distributions

Abstract

Probability distributions are essential in data modeling. Introduction of parameter(s) into existing probability distributions is a method of extending or generalizing distributions to produce more flexible distributions and for better fit to data. The Pareto type 1 distribution (PT1) is a right skewed continuous distribution originally used in description of wealth and income but also used for modeling other right skewed data. To add flexibility, Pareto type 1 distribution was extended by introducing parameter(s) into its probability distribution to accommodate more types of data. Some functions of the extended Pareto type 1 distributions were derived using five parameter induction methods. Flexibility of extended distributions was demonstrated through comparisons of density and hazard function shapes of some of the extended distributions with those of the PT1. Further study on properties of non-existing extended Pareto Type I distributions and real-life applications are recommended.