Characterization of the Geometric Distribution Via Linear Combinations of Observations and of Records

Barry C. Arnold () and Jose A. Villasenor
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Barry C. Arnold: University of California Riverside
Jose A. Villasenor: Colegio de Postgraduados

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 26, 657 pages

Abstract: Abstract In a sequence of independent identically distributed geometric random variables, the sum of the first two record values is distributed as a simple linear combination of geometric variables. It is verified that this distributional property characterizes the geometric distribution. A related characterization conjecture is also discussed. Related discussion in the context of weak records is also provided.

Keywords: Upper records; convolution; record spacings; weak records.; Primary 60E05; Secondary 62E10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13171-021-00271-2

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