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

Ahmadini, Abdullah Ali H.; Ahsan-ul-Haq, Muhammad; Hussain, Muhammad Nasir Saddam

doi:10.1016/j.heliyon.2024.e36764

Heliyon

2024

DOI: 10.1016/j.heliyon.2024.e36764

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

Abdullah Ali H. Ahmadini,

Muhammad Ahsan-ul-Haq,

Muhammad Nasir Saddam Hussain

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2024

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

Alrumayh

2024

International Journal of Mathematics and Mathematical Sciences

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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.

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

Alrumayh

2024

International Journal of Mathematics and Mathematical Sciences

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

Cited by 1 publication

References 19 publications

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

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

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