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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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/5687958 |
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| _version_ | 1832557304549998592 |
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| author | Amani Alrumayh |
| author_facet | Amani Alrumayh |
| author_sort | Amani Alrumayh |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5f63f53082ed43e39487a945c5e1acd8 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5f63f53082ed43e39487a945c5e1acd82025-02-03T05:29:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252024-01-01202410.1155/2024/5687958Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and ApplicationsAmani Alrumayh0Department of MathematicsWe 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.http://dx.doi.org/10.1155/2024/5687958 |
| spellingShingle | Amani Alrumayh Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and Applications International Journal of Mathematics and Mathematical Sciences |
| title | Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and Applications |
| title_full | Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and Applications |
| title_fullStr | Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and Applications |
| title_full_unstemmed | Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and Applications |
| title_short | Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and Applications |
| title_sort | bernoulli poisson moment exponential distribution mathematical properties regression model and applications |
| url | http://dx.doi.org/10.1155/2024/5687958 |
| work_keys_str_mv | AT amanialrumayh bernoullipoissonmomentexponentialdistributionmathematicalpropertiesregressionmodelandapplications |