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On Poisson Moment Exponential Distribution with Associated Regression and INAR(1) Process

On Poisson Moment Exponential Distribution with Associated Regression and INAR(1) Process Numerous studies have emphasised the significance of count data modeling and its applications to phenomena that occur in the real world. From this perspective, this article examines the traits and applications of the Poisson-moment exponential (PME) distribution in the contexts of time series analysis and regression analysis for real-world phenomena. The PME distribution is a novel one-parameter discrete distribution that can be used as a powerful alternative for the existing distributions for modeling over-dispersed count datasets. The advantages of the PME distribution, including the simplicity of the probability mass function and the explicit expressions of the functions of all the statistical properties, drove us to develop the inferential aspects and learn more about its practical applications. The unknown parameter is estimated using both maximum likelihood and moment estimation methods. Also, we present a parametric regression model based on the PME distribution for the count datasets. To strengthen the utility of the suggested distribution, we propose a new first-order integer-valued autoregressive (INAR(1)) process with PME innovations based on binomial thinning for modeling integer-valued time series with over-dispersion. Application to four real datasets confirms the empirical significance of the proposed model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Data Science Springer Journals

On Poisson Moment Exponential Distribution with Associated Regression and INAR(1) Process

Maya, R.; Huang, Jie; Irshad, M. R.; Zhu, Fukang
Annals of Data Science , Volume OnlineFirst – Jun 8, 2023
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References (22)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
2198-5804
eISSN
2198-5812
DOI
10.1007/s40745-023-00476-2
Publisher site
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Abstract

Numerous studies have emphasised the significance of count data modeling and its applications to phenomena that occur in the real world. From this perspective, this article examines the traits and applications of the Poisson-moment exponential (PME) distribution in the contexts of time series analysis and regression analysis for real-world phenomena. The PME distribution is a novel one-parameter discrete distribution that can be used as a powerful alternative for the existing distributions for modeling over-dispersed count datasets. The advantages of the PME distribution, including the simplicity of the probability mass function and the explicit expressions of the functions of all the statistical properties, drove us to develop the inferential aspects and learn more about its practical applications. The unknown parameter is estimated using both maximum likelihood and moment estimation methods. Also, we present a parametric regression model based on the PME distribution for the count datasets. To strengthen the utility of the suggested distribution, we propose a new first-order integer-valued autoregressive (INAR(1)) process with PME innovations based on binomial thinning for modeling integer-valued time series with over-dispersion. Application to four real datasets confirms the empirical significance of the proposed model.

Journal

Annals of Data Science – Springer Journals

Published: Jun 8, 2023

Keywords: Modeling integer-valued time series; Count data; Discrete distribution; Moment exponential distribution; Poisson distribution; Regression; INAR(1) process

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