An extension of the Inverse Gaussian distribution

• Grant number: 19/05077-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2019
• End date: April 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Filidor Edilfonso Vilca Labra
• Grantee: Letícia Bettine Infante
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The goal of this project is to present an extension of the well-known Inverse Gaussian (IG) distribution), which is the distribution of a random variable that can be defined as the time that a Brownian movement takes to reach a certain level by first time. This extension is obtained as the quotient of two independent random variables, one is the IG distribution, and the other is the power of a random variable following IG distribution. For this resulting distribution, we will reproduce and discuss its properties inspired by the properties of the usual GI distribution. In addition, we will present a study of model parameter estimation based on the methods of moments and the maximum likelihood method. Applications to real data will be developed towards where the GI distributions have been applied.