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INTRINSIC AGING AND CLASSES OF NONPARAMETRIC DISTRIBUTIONS

Published online by Cambridge University Press:  14 July 2009

Rhonda Righter ,
Moshe Shaked  and
J. George Shanthikumar
Rhonda Righter
Affiliation:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720 E-mail: rrighter@ieor.berkeley.edu
Moshe Shaked
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721 E-mail: shaked@math.arizona.edu
J. George Shanthikumar
Affiliation:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720 E-mail: shanthikumar@ieor.berkeley.edu
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Abstract

We develop a general framework for understanding the nonparametric (aging) properties of nonnegative random variables through the notion of intrinsic aging. We also introduce some new notions of aging. Many classical and more recent results are special cases of our general results. Our general framework also leads to new results for existing notions of aging, as well as many results for our new notions of aging.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 4 , October 2009 , pp. 563 - 582
Copyright
Copyright © Cambridge University Press 2009

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References

1.Ammann, M. (2001). Credit risk valuation, 2nd ed.New York: Springer.CrossRefGoogle Scholar
2.Barlow, R.E. & Proschan, F. (1975). Mathematical theory of reliability, 2nd ed.Silver Spring, MD: SIAM.Google Scholar
3.Belzunce, F., Candel, J. & Ruiz, J.M. (1995). Ordering of truncated distributions through concentration curves. Sankhyā 57(Series A): 375–383.Google Scholar
4.Belzunce, F., Candel, J. & Ruiz, J.M. (1998). Ordering and asymptotic properties of residual income distributions. Sankhyā 60(Series B): 331–348.Google Scholar
5.Çinlar, E. & Ozekici, S. (1987). Reliability of complex devices in random environments. Probability in the Engineering and Informational Sciences 1: 97–115.CrossRefGoogle Scholar
6.Çinlar, E., Shaked, M. & Shanthikumar, J.G. (1989). On lifetimes influenced by a common environment. Stochastic Processes and Their Applications 33: 347–359.CrossRefGoogle Scholar
7.Chandra, N.K. & Roy, D. (2001). Some results on reversed hazard rate. Probability in the Engineering and Informational Sciences 15: 95–102.CrossRefGoogle Scholar
8.Lariviere, M. (1999). Supply chain contracting and coordination with stochastic demand. In Tayur, E.S., Ganeshan, R., & Magazine, M.J. (eds.), Quantitative models for supply chain management. Boston: Kluwer, pp. 233–268.CrossRefGoogle Scholar
9.Lariviere, M. (2006). A note on probability distributions with increasing generalized failure rates. Operations Research 54: 602–604.CrossRefGoogle Scholar
10.Lariviere, M. & Porteus, E. (2001). Selling to the newsvendor: an analysis of price only contracts. Manufacturing and Service Operations Management 3: 293–305.CrossRefGoogle Scholar
11.Ma, C. (1999). Uniform stochastic ordering on a system of components with dependent lifetimes induced by a common environment. Sankhyā 61(Series A): 218–228.Google Scholar
12.Marshall, A.W. & Olkin, I. (1979). Inequalities: Theory of majorization and its applications. New York: Academic Press.Google Scholar
13.Marshall, A.W. & Olkin, I. (2007). Life distributions. New York: Springer Science+Business Media.Google Scholar
14.Paul, A. (2005). A note on closure properties of failure rate distributions. Operations research 53: 733–734.CrossRefGoogle Scholar
15.Porteus, E.L. (2002). Foundations of stochastic inventory theory. Stanford, CA: Stanford Business Books.CrossRefGoogle Scholar
16.Ross, S.M. (1996). Stochastic processes, 2nd ed.New York: Wiley.Google Scholar
17.Sengupta, D. & Nanda, A.K. (1999). Log-concave and concave distributions in reliability. Naval Research Logistics 46: 419–433.3.0.CO;2-B>CrossRefGoogle Scholar
18.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
19.Singh, S.K. & Maddala, G.S. (1976). A function for size distributions of incomes. Econometrica 44: 963–970.CrossRefGoogle Scholar