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Bibliographic Details
Main Authors: Bonamente, Massimiliano, Zimmerman, Dale
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.11088
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Table of Contents:
  • This paper presents likelihood-based inference methods for the family of univariate gamma-normal distributions GN(α, r, μ, σ^2 ) that result from summing independent gamma(α, r) and N(μ, σ^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.