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Ali E, Diop ML, Diop A. Statistical Inference in a Zero-Inflated Bell Regression Model. MATHEMATICAL METHODS OF STATISTICS 2022. [DOI: 10.3103/s1066530722030012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Ali E. A simulation-based study of ZIP regression with various zero-inflated submodels. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2025840] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Essoham Ali
- LERSTAD, University Gaston Berger, Saint-Louis, Senegal
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EM Estimation for Zero- and k-Inflated Poisson Regression Model. COMPUTATION 2021. [DOI: 10.3390/computation9090094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we provide details for obtaining parameter estimates of the ZkIP regression model using the Expectation–Maximization (EM) algorithm for a given data. We derive the standard errors of the EM estimates by computing the complete, missing, and observed data information matrices. We present the analysis of two real-life data using the methods outlined in the paper.
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Bousselmi B, Dupuy JF, Karoui A. Censored count data regression with missing censoring information. Electron J Stat 2021. [DOI: 10.1214/21-ejs1897] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Bilel Bousselmi
- Univ Rennes, INSA Rennes, CNRS, IRMAR – UMR 6625, F-35000 Rennes, France
| | | | - Abderrazek Karoui
- University of Carthage, Department of Mathematics, Faculty of Sciences of Bizerte, Tunisia
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