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Properties of some stochastic orders: A unified study
Author(s) -
Hu Taizhong,
Nanda Asok K.,
Xie Huiliang,
Zhu Zegang
Publication year - 2004
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.10111
Subject(s) - residual , stochastic ordering , mathematics , hazard , hazard ratio , statistics , closure (psychology) , integer (computer science) , order (exchange) , degree (music) , computer science , algorithm , economics , physics , confidence interval , chemistry , organic chemistry , finance , acoustics , market economy , programming language
The notions of the likelihood ratio order of degree s ( s ≥ 0) are introduced for both continuous and discrete integer‐valued random variables. The new orders for s = 0, 1, and 2 correspond to the likelihood ratio, hazard rate, and mean residual life orders. We obtain some basic properties of the new orders and their up shifted stochastic orders, and derive some closure properties of them. Such a study is meaningful because it throws an important light on the understanding of the properties of the likelihood ratio, hazard rate, and mean residual life orders. On the other hand, the properties of the new orders have potential applications. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.