Properties and maximum likelihood estimation of the gamma-normal and related probability distributions
Abstract
This paper presents likelihood-based inference methods for the family of univariate gamma-normal distributions GN({\alpha}, r, {\mu}, {\sigma}^2 ) that result from summing independent gamma({\alpha}, r) and N({\mu}, {\sigma}^2 ) random variables. First, the probability density function of a gamma-normal variable is provided in compact form with the use of parabolic cylinder functions, along with key properties. We then provide analytic expressions for the maximum-likelihood score equations and the Fisher information matrix, and discuss inferential methods for the gamma-normal distribution. Given the widespread use of the two constituting distributions, the gamma-normal distribution is a general purpose tool for a variety of applications. In particular, we discuss two distributions that are obtained as special cases and that are featured in a variety of statistical applications: the exponential-normal distribution and the chi-squared-normal (or overdispersed chi-squared) distribution.
Keywords
Cite
@article{arxiv.2402.11088,
title = {Properties and maximum likelihood estimation of the gamma-normal and related probability distributions},
author = {Massimiliano Bonamente and Dale Zimmerman},
journal= {arXiv preprint arXiv:2402.11088},
year = {2024}
}
Comments
Accepted for the Journal of the Indian Society for Probability and Statistics (JISP-D-24-00067R2). Typos corrected