Preprint
Properties and maximum likelihood estimation of the gamma-normal and related probability distributions
arXiv.org
Cornell University
02/16/2024
DOI: 10.48550/arxiv.2402.11088
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.
Details
- Title: Subtitle
- Properties and maximum likelihood estimation of the gamma-normal and related probability distributions
- Creators
- Massimiliano BonamenteDale Zimmerman
- Resource Type
- Preprint
- Publication Details
- arXiv.org
- DOI
- 10.48550/arxiv.2402.11088
- eISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 02/16/2024
- Academic Unit
- Statistics and Actuarial Science; Biostatistics
- Record Identifier
- 9984560490602771
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