Closure properties of some partial orderings under mixing

Insurance: Mathematics and Economics

Volumn 22, Issue 2, 1998, Pages 163-170

  Hesselager, Ole ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Equilibrium distributions; Failure rate order; Scale mixtures; Stop loss order; Total positivity

Indexed keywords

EID: 0032090786     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(97)00037-1     Document Type: Article

References (12)

1. [1] Barlow, R.E., Proschan, F., 1981. Statistical theory of reliability and life testing. To Begin With, Silver Springs.
2. [2] Dharmadhikari, S., Joag-dev, K., 1988. Unimodality, Convexity and Applications. Academic Press, London.
3. [3] Fagiuoli, E., Pellerey, F., 1993. New partial orderings and applications. Naval Research Logistics, 40, 829-842.
4. [4] Hesselager, O., 1996. A unification of some order relations. Insurance: Mathematics and Economics 17, 223-224.
5. [5] Hesselager, O., Wang, S., Willmot, G.E., 1998. Exponential and scale mixtures and equilibrium distributions. Scand. Actuarial J. (to appear).
6. [6] Kaas, R., van Heerwaarden, A., Goovaerts, M.J. 1994. Ordering of actuarial risks. Caire Education Series, 1, Brussels.
7. [7] Kaas, R., Hesselager, O., 1995. Ordering claim size distributions and mixed Poisson probabilities. Insurance: Mathematics and Economics 17, 193-201.
8. [8] Karlin, S., 1968. Total positivity. Stanford University Press, Stanford, California.
9. [9] Nanda, A.K., Jain, H., Singh, H., 1996. On closure of some partial orderings under mixtures. Journal of Applied Probability 33, 698-706.
10. [10] Ross, S.M., 1983. Stochastic processes. Wiley, New York.
11. [11] Shaked, M., Shanthikumar, J.G., 1994. Stochastic orders and their Applications. Academic Press.
12. [12] Stoyan, D., 1983. Comparison methods for queque and other stochastic models, Wiley.