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:: Volume 15, Issue 1 (9-2018) ::
JSRI 2018, 15(1): 119-146 Back to browse issues page
Poisson-Beta Exponential Distribution: Properties and Applications
Eisa Mahmoudi 1, Hossein Zamani2 , RahmatSadat Meshkat3
1- Yazd University , emahmoudi@yazd.ac.ir
2- Hormozgan University
3- Yazd University
Abstract:   (2421 Views)
A new generalized version of the mixed Poisson distribution, called the Poisson-beta exponential (PBE) distribution, is obtained by mixing the Poisson and the beta exponential (BE) distributions. Estimation of the parameters, using the method of moments and maximum likelihood estimators, is discussed. We show the consistency of the new model parameters using simulation study. Examples are given for fitting the PBE distribution to data, and the fit model is compared with that obtained using other distributions.
Keywords: Beta exponential distribution, mixed distributions, Poisson mixtures, truncated distributions, weighted distributions
Full-Text [PDF 777 kb]   (2292 Downloads)    
Type of Study: Research | Subject: General
Received: 2018/02/16 | Accepted: 2018/11/14 | Published: 2019/03/3
References
1. Albrecht, P. (1982). On Some Statistical Methods Connected with the Mixed Poisson Process. Scandinavian Actuarial Journal, 9, 1-14. [DOI:10.1080/03461238.1982.10405427]
2. Albrecht, P. (1984). Laplace Transforms, Mellin Transforms and Mixed Poisson Process. Scandinavian Actuarial Journal, 11, 58-64. [DOI:10.1080/03461238.1984.10413753]
3. Al-Awadhi, S.A. and Ghitany, M.E. (2001). Statistical Properties of Poisson Lomax Distribution and Its Application to Repeated Accident Data. Journal of Applied Statistical Science, 10, 365-372.
4. Bhattacharya, S.K. (1966). Confluent Hypergeometric Distributions of Discrete and Continuous Type with Application to Accident Proneness. Bulletin of the Calcutta Statistical Association, 15, 20-31. [DOI:10.1177/0008068319660103]
5. Bulmer, M.G. (1974). On Fitting the Poisson Lognormal Distribution to Species Abundance Data. Biometrics, 30, 101-110. [DOI:10.2307/2529621]
6. Chakraborty, S. (2010). On Some Distributional Properties of the Family of Weighted Generalized Poisson Distribution. Communications in Statistics-Theory and Methods, 39, 2767-2788. [DOI:10.1080/03610920903129141]
7. Denuit, M., Marechal, X., Pitrebois, S. and Walhin, J.F. (2007). Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Scales. Wiley, New York. [DOI:10.1002/9780470517420]
8. Denuit, M. (1997). A New Distribution of Poisson-type for the Number of Claims. ASTIN Bulletin: The Journal of the IAA, 27, 229-242. [DOI:10.2143/AST.27.2.542049]
9. Douglas, J.B. (1980). Analysis with Standard Contagious Distributions, Statistical Distributions in Scientific Work Series 4, International Cooperative Publishing House.
10. Gaver, D. and O'Muircheartaigh, I.G., (1987). Robust Empirical Bayes Analysis of Event Rates. Technometrics, 29, 1-15. [DOI:10.1080/00401706.1987.10488178]
11. Ghitany, M.E. and Al-Mutairi, D.K. (2008). Size-biased Poisson-Lindley Distribution and Its Application. METRON-International Journal of Statistics, 66(3), 299-311.
12. Ghitany, M.E., Al-Mutari, D.K. and Nadarajah, S. (2008). Zero-truncated Poisson-Lindley Distribution and Its Application. Mathematics and Computers in Simulation , 79, 279-287. [DOI:10.1016/j.matcom.2007.11.021]
13. Gomez-Deniz, E. and Calderin-Ojeda, E. (2015). Parameters Estimation for a New Generalized Geometric Distribution. Communications in Statistics -Simulation and Computation, 44(8). [DOI:10.1080/03610918.2013.835410]
14. Gomez-Deniz, E., Hernandez-Bastida, A. and Fernandez-Sanchez, M.P. (2016). A Suitable Discrete Distribution for Modelling Automobile Claim Frequencies. Bulletin of the Malaysian Mathematical Sciences Society, 39, 633-647. [DOI:10.1007/s40840-015-0189-y]
15. Greenwood, M. and Yule, G. (1920). An Enquiry into the Nature of Frequency Distributions Representative of Multiple Happenings with Particular Reference to the Occurrence of Multiple Attacks of Disease or of Repeated Accidents. Journal of the Royal Statistical Society, 83, 255-279. [DOI:10.2307/2341080]
16. Gupta, R.C. and Ong, S.H. (2005). Analysis of Long-tailed Count Data by Poisson Mixtures. Communications in Statistics-Theory and Methods, 34, 557-573. [DOI:10.1081/STA-200052144]
17. Gurland J. (1958). A Generalized Class of Contagious Distributions. Biometrics, 14, 229-249. [DOI:10.2307/2527787]
18. Holla, M.S. and Bhattacharya, S.K. (1965). On a Discrete Compound Distribution. Annals of the Institute of Statistical Mathematics, 15, 377-384. [DOI:10.1007/BF02868181]
19. Hougard, P. (1997). Analysis of Over Dispersed Count Data by Mixture of Poisson Variables and Poisson Processes. Biometrics, 53, 1225-1238. [DOI:10.2307/2533492]
20. Irwin, J. (1975). The Generalized Waring Distribution, Parts I, II,III. Journal of the Royal Statistical Society A, 18-31(Part I), 204-227(Part II), 374-384(Part III).
21. Johnson, N.L., Kotz, S. and Kemp A.W. (2005). Univariate Discrete Distributions, Second Edition, John Wiley and Sons. [DOI:10.1002/0471715816]
22. Kempton, R.A. (1975). A Generalized form of Fisher's Logarithmic Series. Biometrics, 62, 29-38. [DOI:10.1093/biomet/62.1.29]
23. Kling, B. and Goovaerts, M. (1993). A Note on Compound Generalized Distributions. Scandinavian Actuarial Journal, 20, 60-72. [DOI:10.1080/03461238.1993.10413913]
24. Mahmoudi, E. and Zakerzadeh, H. (2010). Generalized Poisson-Lindley Distribution. Communications in Statistics-Theory and Methods, 39, 1785-1798. [DOI:10.1080/03610920902898514]
25. Nadarajah, S. and Kotz, S. (2006). The Beta Exponential Distribution. Reliability Engineering and System Safety, 91, 689-697. [DOI:10.1016/j.ress.2005.05.008]
26. Ong, S.H. and Muthaloo, S. (1995). A Class of Discrete Distribution Suited to Fitting very Long Tail Data. Communication in Statistics-Simulation and Computation, 24, 929-945. [DOI:10.1080/03610919508813285]
27. Patil, G.P. (1964). On Certain Compound Poisson and Compound Binomial Distributions. Sankha A, 27, 929-945.
28. Pielou, E. (1962). Run of One Species with Respect to Another in Transects Through Plant Population. Biometrics, 18, 579-593. [DOI:10.2307/2527903]
29. Rai, G. (1971). A Mathematical Model for Accdent Proneness. Trabajos Estadistica, 22, 207-212. [DOI:10.1007/BF03005278]
30. Rao, C.R. (1965). On Discrete Distributions Arising Out of Methods of Ascertainment. In Classical and Contagious Discrete Distributions, Ed. G. P. Patil. Calcutta: Pergamon Press and Statistical Publishing Society, 320-332.
31. Ruohonen M. (1988). A Model for the Claim Number Process. ASTIN Bulletin, 18, 57-68. [DOI:10.2143/AST.18.1.2014960]
32. Sankaran, M. (1969). On Certain Properties of a Class of Compound Poisson Distributions. Sankha B, 32, 353-362.
33. Sankaran, M. (1970). The Discrete Poisson-Lindley Distribution. Biometrics, 26, 145-149. [DOI:10.2307/2529053]
34. Sichel, H.S. (1974). On a Distribution Representing Sentence-Length in Written Prose. Journal of The Royal Statistical Society A, 137, 25-34. [DOI:10.2307/2345142]
35. Sichel, H.S. (1974). On a Distribution Law for Word Frequencies. Journal of the American Statistical Association, 70, 542-547.
36. Simon, P. (1955). On a Class of Skew Distributions. Biometrika, 42, 425-440. [DOI:10.1093/biomet/42.3-4.425]
37. Willmot, G.E. (1986). Mixed Poisson Distribution. ASTIN Bulletin Supplement, 16, 59-79. [DOI:10.2143/AST.16.3.2014993]
38. Willmot, G.E. (1993). On Recursive Evaluation of Mixed Poisson Probabilities and Related Quantities. Scandinavian Actuarial Journal, 18, 114-133.
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Mahmoudi E, Zamani H, Meshkat R. Poisson-Beta Exponential Distribution: Properties and Applications. JSRI 2018; 15 (1) :119-146
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Volume 15, Issue 1 (9-2018) Back to browse issues page
مجله‌ی پژوهش‌های آماری ایران Journal of Statistical Research of Iran JSRI
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