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2005•Communication in Statistics- Theory and MethodsRequires access

A Characterization of Geometric Distribution Throughkth Weak Records

Anna Dembińska, Fernando López-Blázquez

Open publisher page 17 citations

Abstract

Let be the sequence of kth weak records from a distribution F having support on non negative integers. We show that is a constant almost surely (a.s.) iff the underlying distribution is geometric. We also prove that for n ≥ 1 and k ≥ 2 the property (a.s.) does not hold in the geometric case.

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What this paper is about

Let be the sequence of kth weak records from a distribution F having support on non negative integers. We show that is a constant almost surely (a.s.) iff the underlying distribution is geometric. We also prove that for n ≥ 1 and k ≥ 2 the property (a.s.) does not hold in the geometric case.

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OpenAlex reports 17 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Let be the sequence of kth weak records from a distribution F having support on non negative integers. We show that is a constant almost surely (a.s.) iff the underlying distribution is geometric. We also prove that for n ≥ 1 and k ≥ 2 the property (a.s.) does not hold in the geometric case.

Key concepts: Characterization (materials science), Geometric distribution, Distribution (mathematics), Mathematics, Sequence (biology), Combinatorics, Property (philosophy), Geometric progression

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