Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling
The importance of counting data modeling and its applications to real-world phenomena has been highlighted in several research studies. The present study focuses on a one-parameter discrete distribution that can be derived via the survival discretization approach. The proposed model has explicit for...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/12/737 |
| _version_ | 1797461466937294848 |
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| author | Mahmoud El-Morshedy Hend S. Shahen Bader Almohaimeed Mohamed S. Eliwa |
| author_facet | Mahmoud El-Morshedy Hend S. Shahen Bader Almohaimeed Mohamed S. Eliwa |
| author_sort | Mahmoud El-Morshedy |
| collection | DOAJ |
| description | The importance of counting data modeling and its applications to real-world phenomena has been highlighted in several research studies. The present study focuses on a one-parameter discrete distribution that can be derived via the survival discretization approach. The proposed model has explicit forms for its statistical properties. It can be applied to discuss asymmetric “right skewed” data with long “heavy” tails. Its failure rate function can be used to discuss the phenomena with a monotonically decreasing or unimodal failure rate shape. Further, it can be utilized as a probability tool to model and discuss over- and under-dispersed data. Various estimation techniques are reported and discussed in detail. A simulation study is performed to test the property of the estimator. Finally, three real data sets are analyzed to prove the notability of the introduced model. |
| first_indexed | 2024-03-09T17:19:48Z |
| format | Article |
| id | doaj.art-0f23b2d4ef0948bf9ccbbc7a50bc929c |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T17:19:48Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-0f23b2d4ef0948bf9ccbbc7a50bc929c2023-11-24T13:16:19ZengMDPI AGAxioms2075-16802022-12-01111273710.3390/axioms11120737Discrete Single-Factor Extension of the Exponential Distribution: Features and ModelingMahmoud El-Morshedy0Hend S. Shahen1Bader Almohaimeed2Mohamed S. Eliwa3Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, College of Science, Qassim University, Buraydah 51482, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptThe importance of counting data modeling and its applications to real-world phenomena has been highlighted in several research studies. The present study focuses on a one-parameter discrete distribution that can be derived via the survival discretization approach. The proposed model has explicit forms for its statistical properties. It can be applied to discuss asymmetric “right skewed” data with long “heavy” tails. Its failure rate function can be used to discuss the phenomena with a monotonically decreasing or unimodal failure rate shape. Further, it can be utilized as a probability tool to model and discuss over- and under-dispersed data. Various estimation techniques are reported and discussed in detail. A simulation study is performed to test the property of the estimator. Finally, three real data sets are analyzed to prove the notability of the introduced model.https://www.mdpi.com/2075-1680/11/12/737discretization techniquevarious estimation techniquessimulationcount data |
| spellingShingle | Mahmoud El-Morshedy Hend S. Shahen Bader Almohaimeed Mohamed S. Eliwa Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling Axioms discretization technique various estimation techniques simulation count data |
| title | Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling |
| title_full | Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling |
| title_fullStr | Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling |
| title_full_unstemmed | Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling |
| title_short | Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling |
| title_sort | discrete single factor extension of the exponential distribution features and modeling |
| topic | discretization technique various estimation techniques simulation count data |
| url | https://www.mdpi.com/2075-1680/11/12/737 |
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