Journal article
Properties and Maximum Likelihood Estimation of the Gamma-Normal and Related Probability Distributions
Journal of the Indian Society for Probability and Statistics, Vol.26(1), pp.113-144
06/2025
DOI: 10.1007/s41096-024-00218-4
Abstract
This paper presents likelihood-based inference methods for the family of univariate gamma-normal distributions GN(a , r, u, a2) that result from summing independent y(a, r) and N (u, a2) 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.
Details
- Title: Subtitle
- Properties and Maximum Likelihood Estimation of the Gamma-Normal and Related Probability Distributions
- Creators
- Massimiliano Bonamente - University of Alabama in HuntsvilleDale Zimmerman - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of the Indian Society for Probability and Statistics, Vol.26(1), pp.113-144
- DOI
- 10.1007/s41096-024-00218-4
- eISSN
- 2364-9569
- Publisher
- Springer Nature
- Number of pages
- 32
- Language
- English
- Electronic publication date
- 12/07/2024
- Date published
- 06/2025
- Academic Unit
- Statistics and Actuarial Science; Biostatistics
- Record Identifier
- 9984758188702771
Metrics
7 Record Views