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JSRI 2019, 15(2): 275-300 Back to browse issues page
On Properties of a Class of Bivariate FGM Type Distributions
Zahra Sharifonnasabi1, Mohammad Hosein Alamatsaz2, Iraj Kazemi1
1- University of Isfahan
2- University of Isfahan , alamatho@sci.ui.ac.ir
Abstract:   (1921 Views)
In this paper, we consider a new class of bivariate copulas and study their measures of association. Specifically, we propose a bivariate copula based distribution and obtain explicit expressions for the corresponding marginal and joint distributions of concomitants of generalized order statistics. Using these results, we provide the minimum variance linear unbiased estimator for the location and scale parameters of the concomitants of order statistics of Burr and logistic distributions. Then, we introduce a class of absolutely continuous bivariate distributions whose univariate margins are exponential distributions. In addition, we discuss their properties such as moment generating function, stress-strength probability and reliability of two component systems. Monte Carlo simulations are performed to highlight properties of the parameters estimates. Finally, we analyze two data sets to illustrate the flexibility and potential of the proposed distribution compared to several competing models.
Keywords: Burr distribution, concomitants, exponential distribution, generalized order statistics, minimum variance, Monte Carlo simulation, reversed hazard rate.
Full-Text [PDF 648 kb]   (1147 Downloads)    
Type of Study: Research | Subject: General
Received: 2018/01/17 | Accepted: 2019/11/18 | Published: 2019/12/12
1. Akaike, H. (1974). A New Look At The Statistical Model Identification. IEEE Transactions on Automatic Control, 19, 716-723. [DOI:10.1109/TAC.1974.1100705]
2. Amblard, C. and Girard, S. (2009). A New Extension of Bivariate FGM Copulas. Metrika, 70, 1-17. [DOI:10.1007/s00184-008-0174-7]
3. Amini, M., Jabbari, H. and Mohtashami Borzadaran, G.R. (2011). Aspects of Dependence in Generalized Farlie-Gumbel-Morgenstern Distribution. Communications in Statistics - Simulation and Computation, 40, 1192-1205. [DOI:10.1080/03610918.2011.568149]
4. Balakrishnan, N. and Basu, A.P. (1995). Exponential Distribution: Theory, Methods and Applications. Taylor and Francis, Philadelphia.
5. Balakrishnan, N. and Lai, C.D. (2009). Continuous Bivariate Distribution, 2nd ed. Springer, New York. [DOI:10.1007/b101765_12]
6. Basu, A.P. (1988). Multivariate Exponential Distributions and their Applications in Reliability. In Handbook of Statistics, vol. 7, Balakrishnan, N. and Rao, C.R. pp. 467-477. [DOI:10.1016/S0169-7161(88)07025-7]
7. Beg, M.I. and Ahsanullah, M. (2008). Concomitants of Generalized Order Statistics from Falie-Gumbel-Morgenstern Distributions. Statistical Methodology, 5, 1-20. [DOI:10.1016/j.stamet.2007.04.001]
8. Bozdogan, H. (1987). Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analytical Extensions. Psychometrika, 52, 345-370. [DOI:10.1007/BF02294361]
9. David, H.A. and Nagaraja, H.N. (1998). Concomitants of Order Statistics, In Handbook of Statistics, vol.16, Balakrishnan, N. and Rao, C.R. pp. 487-513. [DOI:10.1016/S0169-7161(98)16020-0]
10. David, H.A. and Nagaraja, H.N. (2003). Order Statistics, Wiley, New York. [DOI:10.1002/0471722162]
11. Fischer, M. , and Klein, I. (2007). Constructing Generalized FGM Copulas by Means of Certain Univariate Distributions. Metrika, 60, 243-260. [DOI:10.1007/s00184-006-0075-6]
12. Genest, C., Remillard, B. and Beaudion, D. (2009). Goodness-of-fit tests for Copulas: A Review and a Power Study. Insurance: Mathematics and Economics, 44(2), 199-213. [DOI:10.1016/j.insmatheco.2007.10.005]
13. Hannan, E.J. and Quinn, B.G. (1979). The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society, Series B, 41, 190-195. [DOI:10.1111/j.2517-6161.1979.tb01072.x]
14. Hurvich, C. and Tasi, C.L. (1989). Regression and Time Series Model Selection in Small Samples. Biometrika, 76, 297-307. [DOI:10.1093/biomet/76.2.297]
15. Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman and Hall, New York. [DOI:10.1201/b13150]
16. Kamps, U. (1995). A Concept of Generalized Order Statistics. Teubner, Stuttgart. [DOI:10.1007/978-3-663-09196-7]
17. Klein, J.P. and Moeschberger, M.L. (2003). Survival Analysis. Second edition. Springer, New York.
18. Klein, I. and Christa, F. (2011). Families of Copulas Closed under the Construction of Generalized Linear Means. IWQW discussion paper series, 4.
19. Krall, J.M., Uthoff, V.A. and Harley, J.B. (1975). A Step-up Procedure for Selecting Variables Associated with Survival. Biometrics, 31, 49-57. [DOI:10.2307/2529709]
20. Lallena, J.A.R. and Ubeda-Flores, M. (2010). Multivariate Copulas with Quadratic Sections in One Variable. Metrika, 72, 331-349. [DOI:10.1007/s00184-009-0256-1]
21. Mirhosseini, S.M., Amini, M., Kundu, D. and Dolati, A. (2015). On a New Absolutely Continuous Bivariate Generalized Exponential Distribution. Statistical Methods and Applications, 4, 1-26. [DOI:10.1007/s10260-014-0276-5]
22. Mohie El-Din, M.M. , Amein, M.M. and Mohamed, M.S. (2015). Concomitants of Case-II of Generalized Order Statistics from Farlie-Gumbel-Morgenstern Distributions. Journal of Statistics Applications and Probability, 3, 345-353. [DOI:10.1007/s40065-015-0133-x]
23. Morillas, P.M. (2005). A Method to Obtain New Copulas from a Given One. Metrika, 61, 169-184. [DOI:10.1007/s001840400330]
24. Nelsen, R.B. (2006). An Introduction to Copulas. Springer, New York.
25. Schwarz, G. (1978). Estimating the Dimension of a Model. The Annals of Statistics, 6, 461-464. [DOI:10.1214/aos/1176344136]
26. Sharifonnasabi, Z., Alamatsaz, M.H. and Kazemi, I. (2018). A Large Class of New Bivariate Copulas and their Properties. Brazilian Journal of Probability and statistics, 3, 497-524. [DOI:10.1214/17-BJPS351]
27. Shiau, J.T. (2006). Fitting Drought Duration and Severity with Two Dimensional Copulas. Water Resources Management, 20, 795-815. [DOI:10.1007/s11269-005-9008-9]
28. Sklar, A. (1959). Functions de repartition a n Dimensions et Leurs Marges. Publ. Inst. Statist. Univ. Paris, 8, 229-331.
29. Tahmasebi, S. and Behboodian, J. (2010). Entropy for Concomitants of Order Statistics in Generalized Morgenstern (GM) Sub-family and Pseudo-weibull Distribution. World Applied Sciences journal, 8, 789-791.
30. Yilmaz, M. (2011). The Hazard Rate Properties of Parallel and Series Systems for Bivariate Exponential Distribution. Hacettepe Journal of Mathematics and Statistics, 40, 895-9-6.
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Sharifonnasabi Z, Alamatsaz M H, Kazemi I. On Properties of a Class of Bivariate FGM Type Distributions. JSRI 2019; 15 (2) :275-300
URL: http://jsri.srtc.ac.ir/article-1-311-en.html

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Volume 15, Issue 2 (3-2019) Back to browse issues page
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