Some properties of the bivariate Burr type III distribution

Abstract

In this paper, we extend some results related to the dependence structure of the bivariate Burr type III distribution, proposed by Rodriguez [Multivariate Burr III distributions, Part I. Theoretical Properties, Research Publication GMR-3232, General Motors Research Laboratories, Warren, Michigan, 1980; Frequency surfaces, system of, in Encyclopedia of Statistical Sciences, Vol. 3, 1983, Wiley, New York, pp. 232–247]. Using copula representations of bivariate distributions, in the first part of the work, we study some dependence properties and ordering, and we prove that this model can also describe situations of negative dependence. In the second part, we study some dependence measures such as the Kendall's tau, medial correlation and tail dependence. Finally, we show that the correlation coefficient exists and can also be negative.

Keywords:

• bivariate Burr III distribution
• copula
• dependence ordering
• tau index
• correlation