TITLE:
Pareto Distribution: A Probability Model in Social Research
AUTHORS:
José Moral de la Rubia
KEYWORDS:
Continuous Probability Distribution, Parameter Estimation, Descriptive Measures, Pareto Tail Index, Gini Concentration Index
JOURNAL NAME:
Open Journal of Social Sciences,
Vol.13 No.1,
January
14,
2025
ABSTRACT: This methodological article aims to present the type I Pareto distribution in a clear and illustrative manner for better understanding among social researchers. It also provides R scripts for practical application. This continuous distribution, with its inverted J shape, skewness towards the right side, and heavy right tail, serves as an effective probability model for various social variables, such as wealth and income, as well as behaviors that are highly frequent in a few individuals and infrequent in the majority. The type I distribution, which has a scale parameter xm and a shape parameter α, is introduced, beginning with a brief historical overview. The density, cumulative distribution, tail, moment, and characteristic functions are presented. The article proceeds with descriptive measures, estimators based on the method of moments and maximum likelihood, its relationship with other distributions, and goodness-of-fit tests. This material is applied through two examples: one involving probability and descriptive measure calculations, and the other focused on parameter estimation and fit testing using the Kolmogorov-Smirnov and Anderson-Darling tests. Additionally, scripts were developed to perform the corresponding calculations in R, a freely available software. Simulated data were used in two examples illustrating the application of the distribution. Finally, suggestions for its use are provided.