Generalized inferential procedures for generalized Lorenz curves under the Pareto distribution

ABSTRACT

This paper considers problems of interval estimation and hypotheses testing for the generalized Lorenz curve under the Pareto distribution. Our approach is based on the concepts of generalized test variables and generalized pivotal quantities. The merits of the proposed procedures are numerically carried out and compared with asymptotic and bootstrap methods. Empirical evidence shows that the coverage accuracy of the proposed confidence intervals and the type I error control of the proposed exact tests are satisfactory. For illustration purposes, a real data set on median income of the 20 occupations in the United States Census of Population is analysed.

KEYWORDS:

• Coverage probability
• generalized pivotal quantity
• generalized test variable
• Mont Carlo estimate
• type I error control

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 62F25
• Secondary: 62P20

Acknowledgments

The authors are grateful to the editor and three anonymous referees for their many helpful comments and suggestions on an earlier version of this paper which led to this improved version.

Additional information

Funding

The authors advise no direct funding is associated with the research reported on this article.