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JSRI 2020, 16(2): 343-378 Back to browse issues page
Inference about the Marshal-Olkin Bivariate Burr Type III Distribution under Random Left Censoring
Afsaneh Azizi, Abdolreza Sayyareh *1
1- , asayyareh@kntu.ac.ir
Abstract:   (678 Views)
 

In this paper, a Marshal-Olkin bivariate model based on Burr $III$ distribution is considered under random left censoring. The maximum likelihood estimator of the unknown parameters is obtained using the direct method and Expectation Conditional Maximization algorithm. We also obtained the Fisher information matrices. To discuss the properties of the estimators obtained iteratively, a simulation study is carried out. A real data set is used to illustrate the theoretical results.
 
 
Keywords: Marshal-Oklin bivariate distribution, Burr lll distribution, ECM algorithm, pseudo likelihood, random left censoring.
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Type of Study: Research | Subject: General
Received: 2020/10/19 | Accepted: 2021/02/12 | Published: 2021/09/19
References
1. Abdel-Ghaly, A.A., Al-Dayian, G.R., and Al-Kashkari, F.H. (1997). The Use of Burr Type XII Distribution on Software Reliability Growth Modelling. Microelectronics Reliability, 37, 305-313. [DOI:10.1016/0026-2714(95)00124-7]
2. Al-Khedhairi, A., and El-Gohary, A. (2008) A New Class of Bivariate Gompertz Distributions. Internatinal Journal of Mathematics Analysis, 2, 235-253.
3. Azizi, A., and Sayyareh, A. (2019). Estimating the Parameters of the Marshal-Olkin Bivariate Burr Type III Distribution by EM Algorithm. Journal of The Iranian Statistical Society, 18, 133-155. [DOI:10.29252/jirss.18.1.133]
4. Azizi, A., and Sayyareh, A. (2019). Inference about the Bivariate New Extended Weibull Distribution Based on Complete and Censored Data. Communications in Statistics - Simulation and Computation, [DOI:10.1080/03610918.2019.1658779]
5. Asimit, A., Furman, V.E., and Vernic, R. (2016). Statistical Inference for a New Class of Multivariate Pareto Distributions. Communications in Statistics Simulation and Computation, 45, 456-471. [DOI:10.1080/03610918.2013.861627]
6. Bagger, J. (2005). Wage Growth and Turnover in Denmark. University of Aarhus, Denmark.
7. Balakrishnan, N. (1989). Approximate MLE of the Scale Parameter of the Rayleigh Distribution with Censoring. IEEE Transactions on Reliability, 38, 355-357. [DOI:10.1109/24.44181]
8. Balakrishna, N., and Shiji, K. (2014). On a Class of Bivariate Exponential Distributions. Statistics and Probability Letters, 85, 153-160. [DOI:10.1016/j.spl.2013.11.009]
9. Balakrishnan, N., and Varadan, J. (1991). Approximate MLEs for the Location and Scale Parameters of the Extreme Value Distribution with Censoring. IEEE Transactions on Reliability, 40, 146-151. [DOI:10.1109/24.87115]
10. Burr, I.W. (1942). Cumulative Frequency Distributions. Annals of Mathematical Statistics, 13, 215-232. [DOI:10.1214/aoms/1177731607]
11. Chernobai, A.S., Fabozzi, F.J., and Rachev, S.T. (2007). Operational Risk: A Guide to Basel II Capital Requirements. Models and Analysis, John Wiley & Sons, New York, USA.
12. Csoorgo Csorgo, S. and Welsh, A. (1989). Testing for Exponential and Marshall-Olkin Distributions. Journal of Statistical Planning and Inference, 23, 287-300. [DOI:10.1016/0378-3758(89)90073-6]
13. Dagum, C.A. (1977). New Model of Personal Income Distribution: Specification and Estimation. Applied Economics, 30, 413-437.
14. Dey, A.K., Paul, B., and Kundu, D. (2018). An EM Algorithm for Absolute Continuous Bivariate Pareto Distribution. arXiv:1608.02199v4 [stat.CO] 18 Mar 2018.
15. El-Sherpieny, E.A., Ibrahim, S.A., and Bedar, R.E. (2013). A New Bivariate Generalized Gompertz Distribution. Asian Journal of Applied Sciences, 1-4, 2321-0893.
16. Kundu, D., and Dey, A.K. (2009). Estimating the Parameters of the Marshall-Olkin Bivariate Weibull Distribution by EM Algorithm. Computational Statistics and Data Analysis, 53, 956-965. [DOI:10.1016/j.csda.2008.11.009]
17. Kundu, D., and Gupta, R.D. (2009). Bivariate Generalized Exponential Distribution. Journal of Multivariate Analysis, 100, 581-593. [DOI:10.1016/j.jmva.2008.06.012]
18. Kundu, D., and Gupta, R.D. (2010). Modified Sarhan-Balakrishnan Singular Bivariate Distribution. Journal of Statistical Planning and Inference, 140, 526-538. [DOI:10.1016/j.jspi.2009.07.026]
19. Gove, J.H., Ducey, M.J., Leak, W.B., and Zhang, L. (2008). Rotated Sigmoid Structures in Managed Uneven-aged Northern Hardwork Stands: a Look at the Burr Type III Distribution. Foresty, 81, 161-176. [DOI:10.1093/forestry/cpm025]
20. Jamalizadeh, A., and Kundu, D. (2013). Weighted Marshall-Olkin Bivariate Exponential Distribution. Statistics, 47, 917-928. [DOI:10.1080/02331888.2012.670640]
21. Houggard, P., Harvald, B., and Holm, N.V. (1992). Measuring the Similarities Between the Lifetimes of Adult Danish Twins Born Between 1881-1930. Journal of the American Statistitical Association, 87, 17-24. [DOI:10.1080/01621459.1992.10475170]
22. Lin, D.Y., Sun, W., and Ying, Z. (1999). Nonparametric Estimation of the Gap Time Distribution for Serial Events with Censored Data. Biometrika, 86, 59-70. [DOI:10.1093/biomet/86.1.59]
23. Lindsay, S.R., Wood, G.R., and Woollons, R.C. (1996). Modeling the Diameter Distribution of Forest Stands Using the Burr Distribution. Journal of Applied Statistics, 23, 609-619. [DOI:10.1080/02664769623973]
24. Lee, K.R., Kapadia, C.H., and Dwight, B.B. (1980). On Estimating the Scale Parameter of the Rayleigh Distribution from Doubly Censored Samples. Statistical Hefte, 21, 14-21. [DOI:10.1007/BF02932808]
25. Louis, T.A. (1982). Finding the Observed Information Matrix when Using the EM Algorithm. Journal of the Royal Statistical Society, Series B, 44, 226-233. [DOI:10.1111/j.2517-6161.1982.tb01203.x]
26. Mielke, P.W. (1973). Another Family of Distributions for Describing and Analyzing Precipitation Data. Journal of Applied Meteorology and Climatology, 12, 275-280. https://doi.org/10.1175/1520-0450(1973)012<0275:AFODFD>2.0.CO;2 [DOI:10.1175/1520-0450(1973)0122.0.CO;2]
27. Mitra, S., and Kundu, D. (2008). Analysis of the Left Censored Data from the Generalized Exponential Distribution. Journal of Statistical Computation and Simulation, 78, 669-679. [DOI:10.1080/00949650701344158]
28. Mirhosseini, S.M., Amini, M., Kundu, D., and Dolati, A. (2015). On a New Absolutely Continuous Bivariate Generalized Exponential Distribution. Statistical Methods and Applications, 24, 61-83. [DOI:10.1007/s10260-014-0276-5]
29. Nadarajah, S., and Kotz, S. (2006). Q Exponential is a Burr Distribution. Physics Letters A, 359, 451-456. [DOI:10.1016/j.physleta.2006.07.035]
30. Nadarajah, S., and Kotz, S. (2007). On the Alternative to the Weibull Function. Engineering Fracture Mechanics, 74, 577-579. [DOI:10.1016/j.engfracmech.2006.06.007]
31. Nandi, S., and Dewan, I. (2010). An EM Algorithm for Estimating the Parameters of Bivariate Weibull Distribution under Random Censoring. Computational Statistics and Data Analysis, 54, 1559-1569. [DOI:10.1016/j.csda.2010.01.004]
32. Sarhan, A., and Balakrishnan, N. (2007). A New Class of Bivariate Distribution and its Mixture. Journal of the Multivariate Analysis, 98, 1508-1527. [DOI:10.1016/j.jmva.2006.07.007]
33. Sherrick, B.J., Garcia, P., and Tirupattur, V. (1996). Recovering Probabilistic Information from Option Markets: Tests of Distributional Assumptions. Journal of Futures Markets, 16, 545-560. https://doi.org/10.1002/(SICI)1096-9934(199608)16:5<545::AID-FUT3>3.0.CO;2-G [DOI:10.1002/(SICI)1096-9934(199608)16:53.0.CO;2-G]
34. Tejeda, H.A., and Goodwin, B.K. (2008). Modelling Crop Price Through a Burr Distribution and Analysis of Correlation Between Crop Prices and Yields Using Copula Method. Paper Presented at the Annual Meeting of the Agriculture and Applied Economics Association, Orlanndo, FL, USA.
35. Wingo, D.R. (1983). Maximum Likelihood Methods for Fitting the Burr Type XII Distribution of Life Test Data. Journal of Biomedical Science, 25, 77-84. [DOI:10.1002/bimj.19830250109]
36. Wingo, D.R. (1993). Maximum Likelihood Methods for Fitting the Burr Type XII Distribution to Multiply (Progressively) Censored Life Test Data. Metrika, 40, 203-210. [DOI:10.1007/BF02613681]
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Azizi A, Sayyareh A. Inference about the Marshal-Olkin Bivariate Burr Type III Distribution under Random Left Censoring. JSRI. 2020; 16 (2) :343-378
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