Properties and maximum likelihood estimation of the gamma-normal and related probability distributions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916500067057664 |
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| author | Bonamente, Massimiliano Zimmerman, Dale |
| author_facet | Bonamente, Massimiliano Zimmerman, Dale |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties and maximum likelihood estimation of the gamma-normal and related probability distributions Bonamente, Massimiliano Zimmerman, Dale Applications 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. |
| title | Properties and maximum likelihood estimation of the gamma-normal and related probability distributions |
| topic | Applications |
| url | https://arxiv.org/abs/2402.11088 |