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).
Similar content being viewed by others
References
Aliev FA (1998) Characterization of distributions through weak records. J Appl Statist Sci 8:13–16
Aliev FA (1999) New characterization of discrete distributions through weak records. Theory Probab Appl 44:756–761 (English translation)
Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New York
Franco M, Ruiz JM (2001) Characterizations of discrete distributions based on conditional expectations of record values. Statist Papers 42:101–110
López-Blázquez F, Wesołowski J (2001) Discrete distributions for which the regression of the first record on the second is linear. Test 10:121–131
Stepanov AV (1993) A characterization theorem for weak records. Theory Probab Appl 38:762–764 (English translation)
Wesołowski J, Ahsanullah M (2001) Linearity of regression for non-adjacent weak records. Statistica Sinica 11:39–52
Wesołowski J, López-Blázquez F (2004) Linearity of regression for the past weak and ordinary records. Statistics 38:457–464
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Danielak, K., Dembińska, A. On characterizing discrete distributions via conditional expectations of weak record values. Metrika 66, 129–138 (2007). https://doi.org/10.1007/s00184-006-0100-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-006-0100-9