A Bivariate Generalized Inverse Weibull Distribution for Advanced Modeling in Economics and Environmental Science

Source abstract

Introduction: Modeling economic and environmental phenomena is a great importance due to the complex, uncertain and independent nature of real-world data arising in these fields. This paper introduces a new bivariate distribution known as FGM bivariate Generalized Inverse Weibull distribution. The proposed model is constructed by combining Generalized Inverse Weibull marginals through FGM copula framework, allowing for flexible modelling of dependence in economic and environmental data. Methodology: Some of the important statistical properties of the proposed distribution are discussed which include the following: conditional distributions, conditional expectations, product moment, moment generating functions, and reliability functions. The estimation of the distribution parameters is carried out using maximum likelihood estimation method, inference functions for margins and Bayesian estimation method. Interval estimation is provided through confidence intervals for MLE and IFM and higher posterior density intervals for Bayesian estimates. To asses, the performance of the estimator in terms of bias, mean square error and interval length a simulation study is conducted. Results: The results of the simulation show that all methods with improved accuracy for larger sample sizes. The utility of the developed distribution is discussed using empirical data from both economic and environmental science, showing greater flexibility and fit than the existing models. Conclusion: The developed distribution offers a better model for modeling complicated bivariate relationships in economics and environmental science.