Ordering properties of largest order statistics from independent and heterogeneous Dagum populations

Abstract

The Dagum distribution has been extensively used to model income data, and its features have been appreciated in economics and financial studies. In this article, we discuss ordering properties of largest order statistics from independent and heterogeneous Dagum populations. We present some sufficient conditions for stochastic comparisons between largest order statistics in terms of the reversed hazard rate order, the usual stochastic order, the convex order, the likelihood ratio order and the dispersive order. Several numerical examples are presented to illustrate the results established here.

Keywords:

• Dagum distribution
• reversed hazard rate order
• usual stochastic order
• convex order
• likelihood ratio order
• dispersive order

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 60E15
• 62G30
• 62D05; 62N05

Additional information

Funding

This research is supported by the Provincial Natural Science Research Project of Anhui Colleges (No. KJ2016A263, KJ2017ZD27), Anhui Provincial Natural Science Foundation (No. 1808085MA03), Anhui science and technology innovation strategy and soft science research project (No. 1706a02020010), the PhD research startup foundation of Anhui Normal University (No. 2014bsqdjj34). Zhejiang Provincial Natural Science Foundation (No. LQ16A010008) and National Natural Science Foundation of China (No. 11601483).