Reproducibility in the one-parameter exponential family

S. K. Bar-Lev, P. Enis

Research output: Contribution to journalArticlepeer-review


Let X1, ..., Xn be i.i.d. random variables with common distribution an element of a linear one-parameter exponential family[Figure not available: see fulltext.] indexed by a natural parameter θ. It is proved that the distribution of {Mathematical expression} is an element of F, for all θ∈Θ and n=1, 2, ... if and only if F is a family of scale transformed Poisson distributions.

Original languageEnglish
Pages (from-to)391-394
Number of pages4
Issue number1
StatePublished - Dec 1985

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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