Some properties of the generalized TTT transform |
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Authors: | Jarosław Bartoszewicz Magdalena Benduch |
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Affiliation: | Mathematical Institute, University of Wroc?aw, Pl. Grunwaldzki 2/4, 50-384 Wroc?aw, Poland |
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Abstract: | Recently Li and Shaked [2007. A general family of univariate stochastic orders. J. Statist. Plann. Inference 137, 3601–3610] introduced the generalized total time on test (GTTT) transform with respect to a given function ?. In this paper we study some properties of it which are related with stochastic orderings. A concept of Lehmann and Rojo [1992. Invariant directional orderings. Ann. Statist. 20, 2100–2110] is applied to a new setting and the GTTT transform is used to define invariance properties and distances of some stochastic orders. Iterations of the GTTT transforms are also studied and their relations with exponential mixtures of gamma distributions are established. |
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Keywords: | 60E05 60E15 62N05 |
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