On characterization results based on the number of observations near the k-records |
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| Authors: | M Akbari |
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| Institution: | Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran |
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| Abstract: | In this paper, using the completeness properties of the sequence of functions {hn(x)=(?log x)n, 0<x<1, n≥1}, some characterization results are established. The results are based on the number of observations near the k-records. It is shown that the equality of the moment of the appropriate subsequence of the number of observations near to upper and lower k-records is a characteristic property of symmetric distributions. Since ordinary record values are contained in the k-records, the results hold for usual records as a particular case. |
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| Keywords: | completeness properties Müntz-Szász theorem symmetric distribution upper and lower record values |
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