Association of multivariate phase-type distributions, with applications to shock models

Statistics and Probability Letters

Volumn 64, Issue 4, 2003, Pages 381-392

  Li, Haijun ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Associated in time; Association of probability measures on partially ordered spaces; Multivariate phase type distribution; Shock model

Indexed keywords

EID: 0041381122     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(03)00182-2     Document Type: Article

References (22)

1. Assaf D. Langberg N. Savits T. Shaked M. Multivariate phase-type distributions Oper. Res. 32 1984 688-701
2. Barlow R.E. Proschan F. 1981 Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.
3. Becker P.J. Roux J.J. A bivariate extension of the gamma distribution S. Afr. Statist. J. 15 1981 1-12
4. Billingsley P. Convergence of Probability Measures 1968 Wiley New York
5. Brown M. Chaganty N.R. On the first passage time distribution for a class of Markov chains Ann. Prob. 8 1983 1000-1008
6. Esary J.D. Proschan T. A reliability bound for systems of maintained, interdependent components J. Amer. Statist. Assoc. 65 1970 329-338
7. Esary J.D. Proschan F. Walkup D.W. Association of random variables, with applications Ann. Math. Statist. 38 1967 1466-1474
8. Freund J.E. A bivariate extension of the exponential distribution J. Amer. Statist. Assoc. 56 1961 971-977
9. Harris T.E. A correlation inequality for Markov processes in partially ordered state spaces Ann. Probab. 5 1977 451-454
10. Kamae T. Krengel U. O'Brien G.L. Stochastic inequalities on partially ordered spaces Ann. Probab. 5 1977 899-912
11. Kulkarni V.G. A new class of multivariate phase type distributions Oper. Res. 37 1989 151-158
12. Li H. Xu S.H. Stochastic bounds and dependence properties of survival times in a multi-component shock model J. Multivariate Anal. 76 2001 63-89
13. Lindqvist H. Monotone and associated Markov chains, with applications to reliability theory J. Appl. Probab. 24 1987 679-695
14. Lindqvist H. Association of probability measures on partially ordered spaces J. Multivariate Anal. 26 1988 111-132
15. Marshall A.W. Olkin I. A multivariate exponential distribution J. Amer. Statist. Assoc. 2 1967 84-98
16. Marshall A.W. Shaked M. Multivariate shock models for distributions with increasing hazard rate average Ann Probab. 7 1979 343-358
17. Neuts M.F. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach 1981 The Johns Hopkins University Press Baltimore
18. Rüschendorf L. Stochastically ordered distributions and monotonicity of OC-functions of sequential probability ratio tests Math. Operationsforsch. Statist. Ser. Statist. 12 1981 327-338
19. Shaked M. Extensions of the Freund distribution with applications in reliability theory Oper. Res. 32 1984 917-925
20. Shaked M. Shanthikumar J.G. The multivariate hazard construction Stochastic Process. Appl. 24 1987 241-258
21. Stone C. Weak convergence of stochastic processes defined on semi-infinite time intervals Proc. Amer. Math. Soc. 14 1963 694-697
22. Tong Y.L. Probability Inequalities in Multivariate Distributions 1980 Academic Press New York