A bivariate unit power–Weibull distribution via copula construction: analytical properties and asymptotic inference

A copula-based bivariate unit power-Weibull distribution is proposed using the Farlie–Gumbel–Morgenstern copula. The construction preserves the marginal distributions and leads to an explicit expression for the joint density on (0,1)2. We study dependence properties and derive closed-form expressions for mixed moments, which are represented by absolutely convergent Meijer G-function series. An entropy decomposition involving the copula entropy is obtained, together with a convergent series representation for the latter. Identifiability and asymptotic properties of the maximum likelihood estimator are established. The analysis provides a mathematically explicit bivariate extension of the UPWD distribution and complements existing univariate results through tractable dependence modeling, moment representations, entropy analysis, and likelihood-based inference.