An extension of Azzalini's method

TL;DR

This paper extends Azzalini's method by modeling dependence between two non-identical variables with copulas, leading to the Generalized Weighted Exponential Distribution, which shows improved data fitting over previous models.

Contribution

It introduces the GWED, a new distribution derived from dependent exponential variables modeled via copulas, expanding Azzalini's method.

Findings

GWED effectively models biochemical data.

Parameters estimated by maximum likelihood.

GWED outperforms the WED in data fitting.

Abstract

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.