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NEW PROPERTIES OF THE TOTAL TIME ON TEST TRANSFORM ORDER

Published online by Cambridge University Press:  17 November 2011

Taizhong Hu ,
Yashi Wang  and
Weiwei Zhuang
Taizhong Hu
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: thu@ustc.edu.cn
Yashi Wang
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of Chinaand Department of Science and Technology, China University of Political Science and Law, Beijing, 100027, China
Weiwei Zhuang
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: weizh@ustc.edu.cn
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Abstract

The total time on test transform (ttt) order was introduced in Kochar, Li, and Shaked (2002) for nonnegative random variables, which has a close connection to the location independent riskier and the excess wealth orders. In this article, the ttt order is redefined for comparing not necessarily nonnegative random variables. Such an extension will lead us to conveniently derive several new intrinsic properties of the ttt order. In particular, we establish an interesting separation result on the connection between the ttt and the excess wealth orders. As two applications of this separation result, we obtain the generating process of the ttt order in terms of mean-decreasing right stretches and the closure property of the ttt order under convolutions. The generating process of the ttt order parallels those of the location independent riskier and the excess wealth orders established by Landsberger and Meilijson (1994).

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 1 , January 2012 , pp. 43 - 60
Copyright
Copyright © Cambridge University Press 2011

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