A new two-parameter family of discrete distributions
This paper introduces a new family of discrete distributions with two shape parameters, termed the Generalized Two-Parameter Discrete Distribution (GTPDD). The raw and central moments are derived from a general expression for its rth factorial moments. Additionally, the paper provides expressions fo...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844024174907 |
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| author | Allaeddine Haddari Halim Zeghdoudi Reza Pakyari |
| author_facet | Allaeddine Haddari Halim Zeghdoudi Reza Pakyari |
| author_sort | Allaeddine Haddari |
| collection | DOAJ |
| description | This paper introduces a new family of discrete distributions with two shape parameters, termed the Generalized Two-Parameter Discrete Distribution (GTPDD). The raw and central moments are derived from a general expression for its rth factorial moments. Additionally, the paper provides expressions for the moment generating function, coefficient of variation, skewness, kurtosis, index of dispersion and the hazard function. Parameter estimation is addressed using the maximum likelihood estimation method, and the uniqueness of the maximum likelihood estimators is also verified. The applicability of the proposed distribution is illustrated through the modeling of two real data sets, one from engineering and the other from survival analysis. |
| format | Article |
| id | doaj-art-7ac526559f564e3189772fba95a1b138 |
| institution | Kabale University |
| issn | 2405-8440 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj-art-7ac526559f564e3189772fba95a1b1382025-01-30T05:14:33ZengElsevierHeliyon2405-84402025-02-01113e41459A new two-parameter family of discrete distributionsAllaeddine Haddari0Halim Zeghdoudi1Reza Pakyari2Mathematics Department, Faculty of Mathematics and Computer Science, Batna 2 University, Batna, AlgeriaLaPS Laboratory, Badji Mokhtar–Annaba University, Annaba 23000, AlgeriaStatistics Program, Department of Mathematics and Statistics, College of Arts and Sciences, Qatar University, 2713, Doha, Qatar; Corresponding author.This paper introduces a new family of discrete distributions with two shape parameters, termed the Generalized Two-Parameter Discrete Distribution (GTPDD). The raw and central moments are derived from a general expression for its rth factorial moments. Additionally, the paper provides expressions for the moment generating function, coefficient of variation, skewness, kurtosis, index of dispersion and the hazard function. Parameter estimation is addressed using the maximum likelihood estimation method, and the uniqueness of the maximum likelihood estimators is also verified. The applicability of the proposed distribution is illustrated through the modeling of two real data sets, one from engineering and the other from survival analysis.http://www.sciencedirect.com/science/article/pii/S2405844024174907Maximum likelihood estimationMomentsMonte Carlo simulationPoisson distributionPoisson-Lindley distribution |
| spellingShingle | Allaeddine Haddari Halim Zeghdoudi Reza Pakyari A new two-parameter family of discrete distributions Heliyon Maximum likelihood estimation Moments Monte Carlo simulation Poisson distribution Poisson-Lindley distribution |
| title | A new two-parameter family of discrete distributions |
| title_full | A new two-parameter family of discrete distributions |
| title_fullStr | A new two-parameter family of discrete distributions |
| title_full_unstemmed | A new two-parameter family of discrete distributions |
| title_short | A new two-parameter family of discrete distributions |
| title_sort | new two parameter family of discrete distributions |
| topic | Maximum likelihood estimation Moments Monte Carlo simulation Poisson distribution Poisson-Lindley distribution |
| url | http://www.sciencedirect.com/science/article/pii/S2405844024174907 |
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