Modelling Zero-Truncated Count Data Using the Poisson-Prakaamy Distribution.

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Bibliographic Details
Title:	Modelling Zero-Truncated Count Data Using the Poisson-Prakaamy Distribution.
Authors:	Wongprachan, Ratchaneewan¹ ratchaneewan@mju.ac.th
Source:	IAENG International Journal of Applied Mathematics. Jul2026, Vol. 56 Issue 7, p2644-2656. 13p.
Subjects:	Distribution (Probability theory), Statistical models, Parameter estimation, Maximum likelihood statistics, Monte Carlo method
Abstract:	This study introduces the zerotruncated Poisson-Prakaamy (ZTPP) distribution, a new one-parameter probability model for zerotruncated count data. The ZTPP is formulated as a zero-truncated extension of the Poisson-Prakaamy distribution and provides a unified framework capable of modelling underdispersion, equidispersion, and overdispersion. Closed-form expressions for the first four moments are derived, and maximum likelihood estimation procedures are developed for parameter inference. A Monte Carlo simulation study across a range of sample sizes and parameter settings confirms the consistency of the estimator and demonstrates improved estimation accuracy as the sample size increases. Applications to real datasets from healthcare, cytogenetics, ecology, and insurance illustrate the practical applicability of the proposed model. Comparative analyses with existing zero-truncated models, based on chi-square goodness-of-fit tests, information criteria (AIC and BIC), and root mean square error, indicate that the ZTPP model provides a competitive or improved fit across several datasets. Overall, these results suggest that the ZTPP distribution offers a flexible and useful framework for modelling heterogeneous zero-truncated count data for a variety of scientific applications. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	This study introduces the zerotruncated Poisson-Prakaamy (ZTPP) distribution, a new one-parameter probability model for zerotruncated count data. The ZTPP is formulated as a zero-truncated extension of the Poisson-Prakaamy distribution and provides a unified framework capable of modelling underdispersion, equidispersion, and overdispersion. Closed-form expressions for the first four moments are derived, and maximum likelihood estimation procedures are developed for parameter inference. A Monte Carlo simulation study across a range of sample sizes and parameter settings confirms the consistency of the estimator and demonstrates improved estimation accuracy as the sample size increases. Applications to real datasets from healthcare, cytogenetics, ecology, and insurance illustrate the practical applicability of the proposed model. Comparative analyses with existing zero-truncated models, based on chi-square goodness-of-fit tests, information criteria (AIC and BIC), and root mean square error, indicate that the ZTPP model provides a competitive or improved fit across several datasets. Overall, these results suggest that the ZTPP distribution offers a flexible and useful framework for modelling heterogeneous zero-truncated count data for a variety of scientific applications. [ABSTRACT FROM AUTHOR]
ISSN:	19929978