  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.
