On construction of general classes of bivariate distributions

Journal of Multivariate Analysis

Volumn 127, Issue , 2014, Pages 151-159

  Lee, Hyunju ^a   Cha, Ji Hwan ^a  

^a Ewha Womans University   (South Korea)

Author keywords

Conditional failure rate; Covariate process; Degree of dependency; Failure rate process; Freund's bivariate exponential distribution; Stochastic order

Indexed keywords

EID: 84896339738     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2014.02.007     Document Type: Article

References (34)

1. S.V. Amari, R. Bergman, Reliability analysis of k-out-of-n load-sharing systems, in: Proceedings of Reliability and Maintainability Symposium 2008, 2008.
2. Aven T., Jensen U. Stochastic Models in Reliability 1999, Springer, New York.
3. Bain L.J. Analysis for the linear failure rate life testing distribution. Technometrics 1974, 16:551-559.
4. Balakrishnan N., Lai C. Continuous Bivariate Distributions 2009, Springer, New York. second ed.
5. Block H.W., Basu A.P. A continuous bivariate exponential extension. J. Amer. Statist. Assoc. 1974, 69:1031-1037.
6. Carriere J.F. Bivariate survival models for coupled lives. Scand. Act. J. 2000, 1:17-32.
7. Cha J.H., Finkelstein M. On a terminating shock process with independent wear increments. J. Appl. Probab. 2009, 46:353-362.
8. Cha J.H., Finkelstein M. On new classes of extreme shock models and some generalizations. J. Appl. Probab. 2011, 48:258-270.
9. Cha J.H., Mi J. Study of a stochastic failure model in a random environment. J. Appl. Probab. 2007, 44:151-163.
10. Cha J.H., Mi J. On a stochastic survival model for a system under randomly variable environment. Methodol. Comput. Appl. Probab. 2011, 13:549-561.
11. Downton F. Estimation of parametric functions in Downton's bivariate exponential distribution. J. R. Stat. Soc. Ser. B 1970, 32:408-417.
12. Finkelstein M., Cha J.H. Stochastic Modelling for Reliability (Shocks, Burn-in and Heterogeneous Populations) 2013, Springer, London.
13. Freund J.E. A bivariate extension of the exponential distribution. J. Amer. Statist. Assoc. 1961, 56:971-977.
14. P. Georges, A.G. Lamy, G. Nicolas, G. Quibel, T. Roncalli, Multivariate survival modelling: a unified approach with copulas, Working paper, Credit Lyonnias, 2001.
15. Gross A.J., Clark V.A., Liu V. Estimation of survival parameters when one of two organs must function for survival. Biometrics 1971, 27:369-377.
16. Gumbel E.J. Bivariate exponential distribution. J. Amer. Statist. Assoc. 1960, 55:698-707.
17. Hawkes A.G. A bivariate exponential distribution with application to reliability. J. R. Stat. Soc. Ser. B 1972, 34:129-131.
18. Hayakawa Y. The construction of new bivariate exponential distributions from a Bayesian perspective. J. Amer. Statist. Assoc. 1994, 89:1044-1049.
19. Hougaard P. Modelling multivariate survival. Scand. J. Stat. 1987, 14:292-304.
20. Iyer S.K., Manjunath D. Correlated bivariate sequences for queueing and reliability applications. Commun. Stat.-Theory Methods 2004, 33:331-350.
21. Jagger C., Sutton C.J. Death after marital bereavement-is the risk increased?. Stat. Med. 1991, 10:395-404.
22. Kalbfleisch J.D., Prentice R.L. The Statistical Analysis of Failure Time Data 2002, Wiley, New Jersey. second ed.
23. Kebir Y. On hazard rate process. Nav. Res. Logist. 1991, 38:865-876.
24. Kvam P.H., Peña E.A. Estimating load-sharing properties in a dynamic reliability system. J. Amer. Statist. Assoc. 2005, 100:262-272.
25. Lawless J.F. Statistical Models and Methods for Lifetime Data 2003, Wiley, New Jersey.
26. Lee L. Multivariate distributions having Weibull properties. J. Multivariate Anal. 1979, 9:267-277.
27. Marshall A.W., Olkin I. A multivariate exponential distribution. J. Amer. Statist. Assoc. 1967, 62:30-44.
28. Nelson R.B. An Introduction to Copulas 2006, Springer, New York. second ed.
29. Sarhan A.M., Balakrishnan N. A new class of bivariate distributions and its mixture. J. Multivariate Anal. 2007, 98:1508-1527.
30. Sarkar S.K. A continuous bivariate exponential distribution. J. Amer. Statist. Assoc. 1987, 82:667-675.
31. Shaked M. Extension of the Freund distribution with applications in reliability theory. Oper. Res. 1984, 32:917-925.
32. Shaked M., Shanthikumar J.G. Stochastic Orders 2007, Springer, New York.
33. Spurrier J.D., Weier D.R. Bivariate survival model derived from a Weibull distribution. IEEE Trans. Reliab. 1981, R-30:194-197.
34. Yue S., Ouarda T.B.M.J., Bobée B. A review of bivariate Gamma distributions for hydrological application. J. Hydrol. 2001, 246:1-18.