Entropy-Based Trivariate q-Gaussian Model (TVq-GD): An Application to Financial Data

Abstract

Understanding the characteristics of the random variables through their distributions is a really important way to understand the model. In this article, we employ the entropy maximazation method to construct a trivariate q-Gaussian distribution (TVq-GD). Maximum likelihood estimation (MLE) is used to estimate the parameters of the TVq-GD. We demonstrate the practical relevance of this distribution by applying it to a real-world financial dataset, specifically the NIFTY50 Index data, using metrics such as volatility, trading volume, and returns, as well as the soyabean complex and gold commodity markets. This application highlights the effectiveness of the trivariate q-Gaussian distribution in capturing complex dependencies and variations of financial data. A comparison is made with the trivariate Gaussian distribution and the Cauchy distribution to demonstrate the effectiveness of the proposed TVq-GD distribution.