Analysis of Dependent Variables Following FGM Bivariate Generalized Burr Distribution Based on Economic Data

Document Type : Original Article

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1 Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt

2 Master's Researcher, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt.

Abstract

The generalized Burr (GB) distribution is a flexible distribution that is used to describe many types of data. This distribution has a flexible hazard function, which can take a decreasing, approximately constant, or unimodal shape over time. This makes the GB distribution one of the most applicable in many fields. This paper introduces a bivariate GB distribution that was created by using the Farlie-Gumbel-Morgenstern (FGM) copula and the univariate GB. Some mathematical properties of FGM bivariate GB (FGMBGB) are obtained, such as the reversed hazard function, product moment, and moment generating function. The maximum likelihood estimation method is used to estimate the unknown parameters, and a simulation study was conducted to assess the performance of the estimators under different sample sizes. The performance was evaluated using different measures. The simulation results show that all estimation criteria improve significantly with larger sample sizes. Moreover, dependence measures showed better convergence to true values as increased. The model was also applied to real economic data involving GDP growth and exports of goods and services, where the FGMBGB model showed a good fit according to the Anderson-Darling test and model selection criteria. These results confirm the flexibility and applicability of the FGMBGB model in modeling economic data and studying dependencies in various fields.

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