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BIVARIATE MARSHALL–OLKIN EXPONENTIAL SHOCK MODEL

Published online by Cambridge University Press:  17 April 2020

H.A. Mohtashami-Borzadaran ,
H. Jabbari Open the ORCID record for H. Jabbari [Opens in a new window]  and
M. Amini
H.A. Mohtashami-Borzadaran
Affiliation:
Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran. E-mail: jabbarinh@um.ac.ir
H. Jabbari
Affiliation:
Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran. E-mail: jabbarinh@um.ac.ir
M. Amini
Affiliation:
Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran. E-mail: jabbarinh@um.ac.ir
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Abstract

The well-known Marshall–Olkin model is known for its extension of exponential distribution preserving lack of memory property. Based on shock models, a new generalization of the bivariate Marshall–Olkin exponential distribution is given. The proposed model allows wider range tail dependence which is appealing in modeling risky events. Moreover, a stochastic comparison according to this shock model and also some properties, such as association measures, tail dependence and Kendall distribution, are presented. The new shock model is analytically quite tractable, and it can be used quite effectively, to analyze discrete–continuous data. This has been shown on real data. Finally, we propose the multivariate extension of the Marshall–Olkin model that has some intersection with the well-known multivariate Archimax copulas.

Keywords

distortion copulaMarshall–Olkin modelshock modelstochastic comparison
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 745 - 765
Copyright
© Cambridge University Press 2020

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References

1Ahmed, A.H.N., Langberg, N.A., Leon, R.V., & Proschan, F. (1978). Two Concepts of Positive Dependence, with Applications in Multivariate Analysis (No. FSU-STATISTICS-M486). Florida State University Tallahassee, Department of Statistics, USA.CrossRefGoogle Scholar
2Al-Khedhairi, A., & El-Gohary, A. (2008). A new class of bivariate Gompertz distributions and its mixture. International Journal of Mathematical Analysis 2: 235–253.Google Scholar
3Arnold, B.C. (1975). Multivariate exponential distributions based on hierarchical successive damage. Journal of Applied Probability 12(1): 142–147.CrossRefGoogle Scholar
4Balakrishnan, N., & Basu, A. (1995). The exponential distribution: Theory, methods and applications. USA: CRC Press.Google Scholar
5Charpentier, A., Fougères, A.L., Genest, C., & Nešlehová, J.G. (2014). Multivariate Archimax copulas. Journal of Multivariate Analysis 126: 118–136.CrossRefGoogle Scholar
6Cherubini, U., Durante, F., & Mulinacci, S. (2015). Marshall–Olkin distributions–advances in theory and applications. Springer Proceedings in Mathematics & Statistics. Italy: Springer International Publishing.CrossRefGoogle Scholar
7Cuadras, C.M., & Augé, J. (1981). A continuous general multivariate distribution and its properties. Communications in Statistics – Theory and Methods 10(4): 339–353.CrossRefGoogle Scholar
8Durante, F., Foschi, R., & Sarkoci, P. (2010). Distorted copulas: Constructions and tail dependence. Communications in Statistics – Theory and Methods 39(12): 2288–2301.CrossRefGoogle Scholar
9Elouerkhaoui, Y. (2007). Pricing and hedging in a dynamic credit model. International Journal of Theoretical and Applied Finance 10(04): 703–731.CrossRefGoogle Scholar
10Genest, C., & Rivest, L.P. (2001). On the multivariate probability integral transformation. Statistics & Probability Letters 53(4): 391–399.CrossRefGoogle Scholar
11Gupta, R.C., Kirmani, S.N.U.A., & Balakrishnan, N. (2013). On a class of generalized Marshall–Olkin bivariate distributions and some reliability characteristics. Probability in the Engineering and Informational Sciences 27(2): 261–275.CrossRefGoogle Scholar
12Kundu, D., & Dey, A.K. (2009). Estimating the parameters of the Marshall–Olkin bivariate Weibull distribution by EM algorithm. Computational Statistics & Data Analysis 53(4): 956–965.CrossRefGoogle Scholar
13Kundu, D., & Gupta, R.D. (2010). Modified Sarhan–Balakrishnan singular bivariate distribution. Journal of Statistical Planning and Inference 140(2): 526–538.CrossRefGoogle Scholar
14Li, H. (2008). Tail dependence comparison of survival Marshall–Olkin copulas. Methodology and Computing in Applied Probability 10(1): 39–54.CrossRefGoogle Scholar
15Li, X., & Pellerey, F. (2011). Generalized Marshall–Olkin distributions and related bivariate ageing properties. Journal of Multivariate Analysis 102(10): 1399–1409.CrossRefGoogle Scholar
16Li, Y., Sun, J., & Song, S. (2012). Statistical analysis of bivariate failure time data with Marshall–Olkin Weibull models. Computational statistics & Data Analysis 56(6): 2041–2050.CrossRefGoogle Scholar
17Lindskog, F., & McNeil, A.J. (2003). Common Poisson shock models: Applications to insurance and credit risk modelling. ASTIN Bulletin: The Journal of the IAA 33(2): 209–238.CrossRefGoogle Scholar
18Marshall, A.W., & Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association 62(317): 30–44.CrossRefGoogle Scholar
19Meintanis, S.G. (2007). Test of fit for Marshall–Olkin distributions with applications. Journal of Statistical Planning and Inference 137(12): 3954–3963.CrossRefGoogle Scholar
20Mu, J., & Wang, Y. (2010). Multivariate generalized exponential distribution. Journal of Dynamical Systems and Geometric Theories 8(2): 189–199.CrossRefGoogle Scholar
21Nagaraja, H.N., & He, Q. (2015). Fisher information in censored samples from the Marshall–Olkin bivariate exponential distribution. Communications in Statistics – Theory and Methods 44(19): 4172–4184.CrossRefGoogle Scholar
22Nelsen, R.B. (2007). An introduction to copulas. USA: Springer Science & Business Media.Google Scholar
23Sarhan, A.M., & Balakrishnan, N. (2007). A new class of bivariate distributions and its mixture. Journal of Multivariate Analysis 98(7): 1508–1527.CrossRefGoogle Scholar