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Novel Discrete Chris–Jerry Distribution: Properties, Integer Autoregressive Process, and Applications.

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Title: Novel Discrete Chris–Jerry Distribution: Properties, Integer Autoregressive Process, and Applications.
Authors: Amidu, Abdul Hamid1,2 (AUTHOR), Abubakari, Abdul Ghaniyyu3 (AUTHOR) agabubakari@ubids.edu.gh, Nasiru, Suleman1 (AUTHOR), Sen, Smritijit (AUTHOR) smsen@wiley.com
Source: Journal of Probability & Statistics. 6/16/2026, Vol. 2026, p1-19. 19p.
Subjects: Distribution (Probability theory), Autoregressive models, Maximum likelihood statistics, Simulation methods & models, Statistical measurement, Discrete systems
Abstract: A unique one‐parameter discrete distribution, known as the Poisson Two‐Sum Chris–Jerry distribution, is proposed in this study. The structural properties of the contemporary distribution, such as index of dispersion, moments, and probability‐generating function, are determined. To obtain the estimates of the parameter, the maximum likelihood estimation procedure is used. The performance of the estimation technique on finite samples is assessed through a comprehensive simulation study. The formulated distribution is further used to develop an integer autoregressive process for modeling autocorrelated count data. The usefulness of the new distribution and its autoregressive process are demonstrated by modeling some count data and their performances compared with other existing competing discrete distributions. The results show that both the distribution and its autoregressive process can serve as alternative models for count data modeling. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Probability & Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Novel Discrete Chris–Jerry Distribution: Properties, Integer Autoregressive Process, and Applications.
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  Data: <searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Autoregressive+models%22">Autoregressive models</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+measurement%22">Statistical measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Discrete+systems%22">Discrete systems</searchLink>
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  Data: A unique one‐parameter discrete distribution, known as the Poisson Two‐Sum Chris–Jerry distribution, is proposed in this study. The structural properties of the contemporary distribution, such as index of dispersion, moments, and probability‐generating function, are determined. To obtain the estimates of the parameter, the maximum likelihood estimation procedure is used. The performance of the estimation technique on finite samples is assessed through a comprehensive simulation study. The formulated distribution is further used to develop an integer autoregressive process for modeling autocorrelated count data. The usefulness of the new distribution and its autoregressive process are demonstrated by modeling some count data and their performances compared with other existing competing discrete distributions. The results show that both the distribution and its autoregressive process can serve as alternative models for count data modeling. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Journal of Probability & Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1155/jpas/2228572
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      – Code: eng
        Text: English
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        PageCount: 19
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        Type: general
      – SubjectFull: Autoregressive models
        Type: general
      – SubjectFull: Maximum likelihood statistics
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      – SubjectFull: Simulation methods & models
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      – SubjectFull: Statistical measurement
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      – SubjectFull: Discrete systems
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      – TitleFull: Novel Discrete Chris–Jerry Distribution: Properties, Integer Autoregressive Process, and Applications.
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            NameFull: Nasiru, Suleman
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            – D: 16
              M: 06
              Text: 6/16/2026
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              Y: 2026
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