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Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and Applications

We introduce a new flexible count distribution by combining Bernoulli and Poisson moment exponential (PMEx) distributions. The new model named the Bernoulli PMEx distribution. Some mathematical properties are studied, including the hazard rate function, moments, moment generating function, probabili...

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Bibliographic Details
Published in:International journal of mathematics and mathematical sciences 2024-10, Vol.2024 (1)
Main Author: Alrumayh, Amani
Format: Article
Language:English
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Summary:We introduce a new flexible count distribution by combining Bernoulli and Poisson moment exponential (PMEx) distributions. The new model named the Bernoulli PMEx distribution. Some mathematical properties are studied, including the hazard rate function, moments, moment generating function, probability generating function, and dispersion index. A count regression model is also proposed based on this distribution. The maximum likelihood estimation method is used to estimate the model parameters. In the end, three datasets from different fields are utilized for application purposes. The findings show that the new model efficiently analyzed these datasets as compared to Poisson, discrete Pareto, discrete Rayleigh, discrete Burr‐Hatke, and discrete inverted Topp–Leone distributions.
ISSN:0161-1712
1687-0425
DOI:10.1155/2024/5687958