On characterizing discrete distributions via conditional expectations of weak record values |
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| Authors: | Katarzyna Danielak Anna Dembińska |
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| Affiliation: | (1) Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21 (Śniadeckich 8), 00-956 Warsaw, Poland;(2) Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland |
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| Abstract: | Let (W n ,n ≥ 0) denote the sequence of weak records from a distribution with support S = { α0,α1,...,α N }. In this paper, we consider regression functions of the form ψ n (x) = E(h(W n ) |W n+1 = x), where h(·) is some strictly increasing function. We show that a single function ψ n (·) determines F uniquely up to F(α0). Then we derive an inversion formula which enables us to obtain F from knowledge of ψ n (·), ψ n-1(·), h(·) and F(α0). |
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| Keywords: | Characterization Weak records Regression function |
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