A new discrete model generated from mixed Poisson transmuted record type exponential distribution

Erbayram, Tenzile; Akdoğan, Yunus

doi:10.1007/s11587-022-00755-9

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…These new distributions share the overdispersion characteristic common to mixed Poisson distributions [20]. Other notable mixed Poisson models include the Poisson Inverse Pareto distribution [21] and the Poisson-transmuted record-type exponential distribution [22], among others.…”

Section: Introductionmentioning

confidence: 99%

A Statistical Model for Count Data Analysis and Population Size Estimation: Introducing a Mixed Poisson–Lindley Distribution and Its Zero Truncation

Alomair,

Tajuddin,

Bakouch

et al. 2024

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Count data consists of both observed and unobserved events. The analysis of count data often encounters overdispersion, where traditional Poisson models may not be adequate. In this paper, we introduce a tractable one-parameter mixed Poisson distribution, which combines the Poisson distribution with the improved second-degree Lindley distribution. This distribution, called the Poisson-improved second-degree Lindley distribution, is capable of effectively modeling standard count data with overdispersion. However, if the frequency of the unobserved events is unknown, the proposed distribution cannot be directly used to describe the events. To address this limitation, we propose a modification by truncating the distribution to zero. This results in a tractable zero-truncated distribution that encompasses all types of dispersions. Due to the unknown frequency of unobserved events, the population size as a whole becomes unknown and requires estimation. To estimate the population size, we develop a Horvitz–Thompson-like estimator utilizing truncated distribution. Both the untruncated and truncated distributions exhibit desirable statistical properties. The estimators for both distributions, as well as the population size, are asymptotically unbiased and consistent. The current study demonstrates that both the truncated and untruncated distributions adequately explain the considered medical datasets, which are the number of dicentric chromosomes after being exposed to different doses of radiation and the number of positive Salmonella. Moreover, the proposed population size estimator yields reliable estimates.

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Section: Introductionmentioning

confidence: 99%

A Statistical Model for Count Data Analysis and Population Size Estimation: Introducing a Mixed Poisson–Lindley Distribution and Its Zero Truncation

Alomair,

Tajuddin,

Bakouch

et al. 2024

Axioms

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A new two-parameter over-dispersed discrete distribution with mathematical properties, estimation, regression model and applications

Ahmadini,

Ahsan-ul-Haq,

Hussain

2024

Heliyon

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A New Two-Parameter Discrete Distribution for Overdispersed and Asymmetric Data: Its Properties, Estimation, Regression Model, and Applications

Alrumayh

Khogeer

2023

Symmetry

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A novel discrete Poisson mixing probability distribution with two parameters has been developed by combining the Poisson distribution with the transmuted moment exponential distribution. It is possible to deduce several mathematical properties, such as the moment-generating function, ordinary moments, moments about the mean, skewness, kurtosis, and the dispersion index. The maximum likelihood estimation method is utilized to estimate the model’s parameters. A thorough simulation study is utilized to determine the behavior of the generated estimators. Estimating model parameters using a Bayesian methodology is another primary topic of this research. The behavior of Bayesian estimates is evaluated by first charting the trace, then generating 1,005,000 iterations of the Markov chain Monte Carlo method. In addition to this, we suggest a new count regression model that uses Poisson and negative binomial models in an alternating fashion. In conclusion, asymmetric datasets derived from various research areas are utilized for practical applications.

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A new discrete model generated from mixed Poisson transmuted record type exponential distribution

Cited by 3 publications

References 22 publications

A Statistical Model for Count Data Analysis and Population Size Estimation: Introducing a Mixed Poisson–Lindley Distribution and Its Zero Truncation

A Statistical Model for Count Data Analysis and Population Size Estimation: Introducing a Mixed Poisson–Lindley Distribution and Its Zero Truncation

A new two-parameter over-dispersed discrete distribution with mathematical properties, estimation, regression model and applications

A New Two-Parameter Discrete Distribution for Overdispersed and Asymmetric Data: Its Properties, Estimation, Regression Model, and Applications

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