A Bi-variate Gamma Generalized Laplace Distribution
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Authors
Spiker, James Anthony
Issue Date
2024
Type
Thesis
Language
en_US
Keywords
Laplace Distribution , Mixture Models
Alternative Title
Abstract
This thesis introduces the Bivariate Gamma Generalized Laplace (BGGL) distribution, a novel member of the Bivariate Conditionally Normal (BCN) family. The BGGL combines a gamma-distributed variable with a conditionally normal variable, offering a flexible model for asymmetric, heavy-tailed bivariate data. We derive the distribution's properties, including its probability density function, marginal and conditional distributions, and moments.A major contribution is the development of maximum likelihood estimators (MLEs) for BGGL parameters, with explicit forms for most estimators and numerical methods for others. Simulation studies validate these estimators across various scenarios. The thesis also explores generalizations of the BCN family using different mixing distributions, demonstrating the model's adaptability.
To illustrate practical applications, we apply the BGGL to financial market data, modeling the joint behavior of log returns and volatility for major stock indices. These empirical examples showcase the distribution's ability to capture complex relationships in financial data.
This research expands the toolkit of bivariate distributions, with potential applications in finance, risk management, and other fields requiring flexible modeling of asymmetric, correlated data. The thesis provides a foundation for future exploration of BGGL properties and applications in various domains.