Stochastic orders generated by integrals: A unified study

Advances in Applied Probability

Volumn 29, Issue 2, 1997, Pages 414-428

  Müller, Alfred ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Closure properties; Integral stochastic orders; Likelihood ratio order; Maximal generator

Indexed keywords

EID: 0001674310     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800028068     Document Type: Article

References (17)

1. CHOQUET, G. (1969) Lectures on Analysis II. Benjamin, New York.
2. DUDLEY, R. M. (1989) Real Analysis and Probability. Wadsworth and Brooks, Belmont, CA.
3. KAMAE, T., KRENGEL, U. AND O'BRIEN, G. L. (1977) Stochastic inequalities on partially ordered spaces. Ann. Prob. 5, 899-912.
4. KARLIN, S. AND RINOTT, Y. (1980) Classes of orderings of measures and related correlation inequalities. J. Multivar. Anal. 10, 467-498.
5. LEHMANN, E. (1955), Ordered families of distributions. Ann. Math. Statist. 26, 399-419.
6. MARSHALL, A. W. (1991) Multivariate stochastic orderings and generating cones of functions. In Stochastic Orders and Decision Under Risk. (IMS Lecture Notes - Monograph Series 19.) ed. K. Mosler and M. Scarsini. IMS, New York. pp. 231-247.
7. MOSLER, K. AND SCARSINI, M. (1991) Some theory of stochastic dominance. In Stochastic Orders and Decision Under Risk. (IMS Lecture Notes - Monograph Series 19.) ed. K. Mosler and M. Scarsini. IMS, New York. pp. 261-284.
8. MOSLER, K. AND SCARSINI, M. (1994) Stochastic Orders and Applications: A Classified Bibliography. (Lecture Notes in Econ. Math. Syst. 401.)
9. NACHBIN, L. (1965) Topology and Order. (Van Nostrand Math. Studies 4.) Van Nostrand, Princeton, NJ.
10. REUTER, H. AND RIEDRICH, T. (1981) On maximal sets of functions compatible with a partial ordering for distribution functions. Math. Operationsforsch. Statist. 12, 597-605.
11. SHAKED, M. AND SHANTHIKUMAR, J. G. (1994) Stochastic Orders and their Applications. Academic Press, London.
12. SHANTHIKUMAR, J. G. AND YAO, D. D. (1986). The preservation of likelihood ratio ordering under convolution. Stoch. Proc. Appl. 23, 259-267.
13. STOYAN, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, Chichester.
14. SZEKLI, R. (1995) Stochastic Ordering and Dependence in Applied Probability. (Lecture Notes in Statistics 97.) Springer, New York.
15. SZEKLI, R., DISNEY, R. L. AND S. HUR (1994) MR/GI/1 queues with positively correlated arrival streams. J. Appl. Prob. 31, 497-514.
16. WHEEDEN, R. L. AND ZYGMUND, A. (1977) Measure and Integral. Dekker, New York.
17. WHITT, W. (1986) Stochastic comparisons for non-Markov processes. Math. Operat. Res. 11, 608-618.