A note on preservation of the generalized TTT transform order

• Autorzy: Kamińska-Zabierowska M.
• Języki publikacji: EN

Abstrakty

EN

The generalized total time on test (GTTT) transform with respect to the nonnegative function was introduced by Li and Shaked (2007). Comparing GTTT transforms of two distributions is useful in reliability theory and actuarial science, see, e.g., Li and Shaked (2007), Shaked et al. (2010). In 2009, Bartoszewicz and Benduch formulated the preserving theorem for some orders under the GTTT transform. We complete it with result for the GTTT transform order with respect to the nonnegative function. We give also some conditions for preservation under mixtures of exponential distributions and extend the theorem proved by Bartoszewicz and Skolimowska (2006).

Słowa kluczowe

EN

total time on test transform; dispersive order; convex order; stochastic order; mixture; IFR

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2014
• Tom: Vol. 34, Fasc. 2
• Strony: 273--278
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Kamińska-Zabierowska M.

• Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] R. E. Barlow and F. Proschan, Statistische Theorie der Zuverlässigkeit, Akademie-Verlag, Berlin 1978.
• [2] J. Bartoszewicz, Dispersive functions and stochastic orders, Appl. Math. (Warsaw) 24 (1997), pp. 429-444.
• [3] J. Bartoszewicz and M. Benduch, Some properties of the generalized TTT transform, J. Statist. Plann. Inference 139 (2009), pp. 2208-2217.
• [4] J. Bartoszewicz and M. Skolimowska, Preservation of stochastic orders under mixtures of exponential distributions, Probab. Engrg. Inform. Sci. 20 (2006), pp. 655-666.
• [5] I. Jewitt, Choosing between risky prospects: the characterization of comparative statics results, and location independent risk, Management Sci. 35 (1989), pp. 60-70.
• [6] X. Li and M. Shaked, A general family of univariate stochastic orders, J. Statist. Plann. Inference 137 (2007), pp. 3601-3610.
• [7] M. Shaked and J. G. Shanthikumar, Stochastic Orders, Springer, New York 2007.
• [8] M. Shaked, M. A. Sordo, and A. Suárez-Llorens, A class of location-independent variability orders, with applications, J. Appl. Probab. 47 (2010), pp. 407-425.

Uwagi

Dedicated to deceased Professor Jarosław Bartoszewicz

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).