An additive property of weak records from geometric distributions

A. Castaño-Martínez (), F. López-Blázquez () and B. Salamanca-Miño ()

Metrika: International Journal for Theoretical and Applied Statistics, 2013, vol. 76, issue 4, 449-458

Abstract: Let $$\{W_m\}{_{m\ge 1}}$$ be the sequence of weak records from a discrete parent random variable, $$X$$ , supported on the non-negative integers. We obtain a new characterization of geometric distributions based on an additive property of weak records: $$X$$ follows a geometric distribution if and only if for certain integers, $$n,\, s\ge 1, W_{n+s}\stackrel{d}{=}W_n+W^{\prime }_s$$ , with $$W^{\prime }_s$$ independent of $$W_n$$ and $$W^{\prime }_s\stackrel{d}{=} W_s$$ . Copyright Springer-Verlag 2013

Keywords: Weak records; Discrete distribution; Geometric distribution; Characterizations (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:76:y:2013:i:4:p:449-458

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DOI: 10.1007/s00184-012-0398-4

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