On the convoluted gamma to length-biased inverse Gaussian distribution and application in financial modeling

Abstract

This paper studies a convoluted form of length-biased inverse Gaussian and gamma distributions due to its structural relationship with the Wright distribution [Naik and Abraham 2013]. The convoluted form of the derived distribution is named as Inverse Gaussian-gamma abbreviated as IGG distribution which shows heavy-tailedness properties and unimodality. The study also examines some interesting statistical properties of the distribution and compares them with inverse Gaussian and gamma distributions. Results show that the IGG model outperformed inverse Gaussian and gamma distributions through its model characteristics. A theoretical application of the IGG distribution is established to illustrate the model applicability in the financial industry that explains the versatility of the distribution in data analysis. Despite these applications, an autoregressive model of order one is derived to establish utilization of the distribution in time series modeling.