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

Author

Listed:
  • Barry C. Arnold

    (University of California Riverside)

  • Jose A. Villasenor

    (Colegio de Postgraduados)

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.

Suggested Citation

  • Barry C. Arnold & Jose A. Villasenor, 2023. "Characterization of the Geometric Distribution Via Linear Combinations of Observations and of Records," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 651-657, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00271-2
    DOI: 10.1007/s13171-021-00271-2
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