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ESTIMATION OF THE PARAMETER OF A POISSON DISTRIBUTION USING A LINEX LOSS FUNCTION
Author(s) -
SadooghiAlvandi S.M.
Publication year - 1990
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1990.tb01033.x
Subject(s) - poisson distribution , estimator , mathematics , statistics , function (biology) , estimation , distribution (mathematics) , sample (material) , mathematical analysis , physics , economics , evolutionary biology , biology , thermodynamics , management
Summary This paper considers estimation of the parameter of a Poisson distribution using Varian's (1975) asymmetric LINEX loss function L (δ) = b{exp(aδ) ‐ aδ ‐ 1}, where δ is the estimation error and b > 0, a 0. It is shown that for a < 0, the sample mean X¯ is admissible whereas for a > 0, X¯ is dominated by c*X¯, where c*= (n/a)log(1+a/n). Practical implications of this result are indicated. More general results, concerning the admissibility of estimators of the form cX¯+ d are also presented.