Bivariate and Multivariate Weighted Kumaraswamy Distributions: Theory and Applications

Abstract

Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this paper, we derive the bivariate and multivariate weighted Kumaraswamy distributions via the construction method as discussed in B.C. Arnold, I. Ghosh, A. Alzaatreh, Commun. Stat. Theory Methods. 46 (2017), 8897–8912. Several structural properties of the bivariate weighted distributions including marginals, distributions of the minimum and maximum, reliability parameter, and total positivity of order two are discussed. We provide some multivariate extensions of the proposed bivariate weighted Kumaraswamy model. Two real-life data sets are used to show the applicability of the bivariate weighted Kumaraswamy distributions and is compared with other rival bivariate Kumaraswamy models.

Keywords

• Weighted distributions
• Bivariate weighted Kumaraswamy distribution
• Renyi entropy
• Multivariate weighted Kumaraswamy distribution