New properties of the total time on test transform order (Q2894056)

The total time on test transform (ttt) order was introduced by \textit{S.C. Kochar, X. Li} and \textit{M. Shaked} [Adv. Appl. Probab. 34, No. 4, 826--845 (2002; Zbl 1031.62086)] for non-negative random variables. In this paper the authors extend that definition for the comparison of not necessarily non-negative random variables. Some characterizations of the ttt order are derived, and further properties of this order are extended from the non-negative case to the general case. The connection between the ttt order and the excess wealth order is studied, and a procedure that generates the ttt order is identified. Finally, if the underlying random variables have logconcave density functions, it is shown that the ttt order is closed under convolutions.