An extension of Azzalini's method

The aim of this paper is to extend Azzalini’s method. This extension is done in two stages: consider two dependent and non-identically distributed random variables say $X_1$ and $X_2$; model the dependence between $X_1$ and $X_2$ by a copula. To illustrate the new method, we assume $X_1$ and $X_2$ are exponential random variables. This assumption leads to a new distribution called the Generalized Weighted Exponential Distribution (GWED), a generalization of Gupta and Kundu (2009)'s Weighted Exponential Distribution (WED). Some mathematical properties of the GWED are derived, and its parameters estimated by maximum likelihood. The GWED is applied to biochemical data sets showing its good performance compared to the WED.