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A NOTE ON BIVARIATE DUAL GENERALIZED MARSHALL–OLKIN DISTRIBUTIONS WITH APPLICATIONS

Published online by Cambridge University Press:  28 March 2013

Rui Fang and
Xiaohu Li
Rui Fang
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China E-mail: mathxhli@hotmail.com; xhli@lzu.edu.cn
Xiaohu Li
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China E-mail: mathxhli@hotmail.com; xhli@lzu.edu.cn
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Abstract

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This note introduces bivariate dual generalized Marshall–Olkin distribution and builds a comparison result on the copula of this distribution. Several applications in survival analysis and actuarial science are presented as well.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 3 , July 2013, pp. 367 - 374
Copyright
Copyright © Cambridge University Press 2013 

References

1.Cheung, K.C. (2007). Optimal allocation of policy limits and deductibles. Insurance: Mathematics and Economics 41: 291–382.Google Scholar
2.Duchateau, L. & Janssen, P. (2008). The frailty models. New York: Springer.Google Scholar
3.Goovaerts, M.J., De Vylder, F.E., & Haezendonck, J. (1984). Insurance premiums: theory and applications. Amsterdam: North Holland.Google Scholar
4.Hua, L. & Cheung, K.C. (2008). Worst allocations of policy limits and deductibles. Insurance: Mathematics and Economics 43: 93–98.Google Scholar
5.Li, H. (2008). Tail dependence comparison of survival Marshall–Olkin copulas. Methodology and Computing in Applied Probability 10: 39–54.CrossRefGoogle Scholar
6.Li, H. (2008). Duality of the multivariate distributions of Marshall–Olkin type and tail dependence. Communictions in Statistics—Theory and Methods 37: 1721–1733.CrossRefGoogle Scholar
7.Li, X. & Pellerey, F. (2011). Generalized Marshall–Olkin distributions, and related bivariate aging properties. Journal of Multivariate Analysis 102: 1399–1409.CrossRefGoogle Scholar
8.Lin, J. & Li, X. (2012). Multivariate generalized Marshall–Olkin distributions and copulas. Methodology and Computation in Applied Probability. DOI: 10.1007/s11009-012-9297-4.Google Scholar
9.Muliere, P. & Scarsini, M. (1987). Characterization of a Marshall–Olkin type class of distributions. Annals of the Institute of Statistical Mathematics 39: 429–441.CrossRefGoogle Scholar
10.Sarhan, A.M., Hamilton, D.C., Smitha, B., & Kundub, D. (2011). The bivariate generalized linear failure rate distribution and its multivariate extension. Computational Statistics and Data Analysis 55: 644–654.CrossRefGoogle Scholar
11.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
12.Marshall, A.W. & Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association 62: 30–41.CrossRefGoogle Scholar