A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference
This study introduces a unique flexible family of discrete probability distributions for modeling extreme count and zero-inflated count data with different failure rates. Certain significant mathematical properties, such as the cumulant generating function, moment generating function, dispersion ind...
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MDPI AG
2023-02-01
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| Online Access: | https://www.mdpi.com/2227-7390/11/5/1125 |
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| author | Walid Emam Yusra Tashkandy G.G. Hamedani Mohamed Abdelhamed Shehab Mohamed Ibrahim Haitham M. Yousof |
| author_facet | Walid Emam Yusra Tashkandy G.G. Hamedani Mohamed Abdelhamed Shehab Mohamed Ibrahim Haitham M. Yousof |
| author_sort | Walid Emam |
| collection | DOAJ |
| description | This study introduces a unique flexible family of discrete probability distributions for modeling extreme count and zero-inflated count data with different failure rates. Certain significant mathematical properties, such as the cumulant generating function, moment generating function, dispersion index, L-moments, ordinary moments, and central moment are derived. The new failure rate function offers a wide range of flexibility, including “upside down”, “monotonically decreasing”, “bathtub”, “monotonically increasing” and “decreasing-constant failure rate” and “constant”. Moreover, the new probability mass function accommodates many useful shapes including the “right skewed function with no peak”, “symmetric”, “right skewed with one peak” and “left skewed with one peak”. To obtain significant characterization findings, the hazard function and the conditional expectation of certain function of the random variable are both employed. Both Bayesian and non-Bayesian estimate methodologies are considered when estimating, assessing, and comparing inferential efficacy. The Bayesian estimation approach for the squared error loss function is suggested, and it is explained. Markov chain Monte Carlo simulation studies are performed using the Metropolis Hastings algorithm and the Gibbs sampler to compare non-Bayesian vs. Bayesian results. Four real-world applications of count data sets are used to evaluate the Bayesian versus non-Bayesian techniques. Four more real count data applications are used to illustrate the significance and versatility of the new discrete class. |
| first_indexed | 2024-03-11T07:18:43Z |
| format | Article |
| id | doaj.art-96e7ed5df6514be1a810af1d7ae1c306 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T07:18:43Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-96e7ed5df6514be1a810af1d7ae1c3062023-11-17T08:08:34ZengMDPI AGMathematics2227-73902023-02-01115112510.3390/math11051125A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian InferenceWalid Emam0Yusra Tashkandy1G.G. Hamedani2Mohamed Abdelhamed Shehab3Mohamed Ibrahim4Haitham M. Yousof5Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematical and Statistical Sciences, Marquette University, 1313 W. Wisconsin Ave., Milwaukee, WI 53233, USADepartment of Economics, Faculty of Commerce, Damietta University, Damietta 34517, EgyptDepartment of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damiet 34517, EgyptDepartment of Statistics, Mathematics and Insurance, Benha University, Benha 13518, EgyptThis study introduces a unique flexible family of discrete probability distributions for modeling extreme count and zero-inflated count data with different failure rates. Certain significant mathematical properties, such as the cumulant generating function, moment generating function, dispersion index, L-moments, ordinary moments, and central moment are derived. The new failure rate function offers a wide range of flexibility, including “upside down”, “monotonically decreasing”, “bathtub”, “monotonically increasing” and “decreasing-constant failure rate” and “constant”. Moreover, the new probability mass function accommodates many useful shapes including the “right skewed function with no peak”, “symmetric”, “right skewed with one peak” and “left skewed with one peak”. To obtain significant characterization findings, the hazard function and the conditional expectation of certain function of the random variable are both employed. Both Bayesian and non-Bayesian estimate methodologies are considered when estimating, assessing, and comparing inferential efficacy. The Bayesian estimation approach for the squared error loss function is suggested, and it is explained. Markov chain Monte Carlo simulation studies are performed using the Metropolis Hastings algorithm and the Gibbs sampler to compare non-Bayesian vs. Bayesian results. Four real-world applications of count data sets are used to evaluate the Bayesian versus non-Bayesian techniques. Four more real count data applications are used to illustrate the significance and versatility of the new discrete class.https://www.mdpi.com/2227-7390/11/5/1125discretizationBayesian estimationmetropolis-hastingsmaximum likelihoodCramér-von-MisesMarkov chain Monte Carlo |
| spellingShingle | Walid Emam Yusra Tashkandy G.G. Hamedani Mohamed Abdelhamed Shehab Mohamed Ibrahim Haitham M. Yousof A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference Mathematics discretization Bayesian estimation metropolis-hastings maximum likelihood Cramér-von-Mises Markov chain Monte Carlo |
| title | A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference |
| title_full | A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference |
| title_fullStr | A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference |
| title_full_unstemmed | A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference |
| title_short | A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference |
| title_sort | novel discrete generator with modeling engineering agricultural and medical count and zero inflated real data with bayesian and non bayesian inference |
| topic | discretization Bayesian estimation metropolis-hastings maximum likelihood Cramér-von-Mises Markov chain Monte Carlo |
| url | https://www.mdpi.com/2227-7390/11/5/1125 |
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