Reproducibility in the one-parameter exponential family

S. K. Bar-Lev; P. Enis

doi:10.1007/BF01897827

Reproducibility in the one-parameter exponential family

S. K. Bar-Lev, P. Enis

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Let X₁, ..., X_n 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 language	English
Pages (from-to)	391-394
Number of pages	4
Journal	Metrika
Volume	32
Issue number	1
DOIs	https://doi.org/10.1007/BF01897827
State	Published - Dec 1985

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/BF01897827

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title = "Reproducibility in the one-parameter exponential family",

abstract = "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.",

author = "Bar-Lev, {S. K.} and P. Enis",

year = "1985",

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AU - Enis, P.

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N2 - 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.

AB - 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.

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DO - 10.1007/BF01897827

M3 - Article

AN - SCOPUS:34250113867

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VL - 32

SP - 391

EP - 394

JO - Metrika

JF - Metrika

IS - 1

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Reproducibility in the one-parameter exponential family

Abstract

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