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ESTIMATION OF A COMMON MEAN OF SEVERAL UNIVARIATE

INVERSE GAUSSIAN POPULATIONS

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MANZOOR AHMAD^{1}, Y. P. CHAUBEY^{2}* AND B. K. SINHA^{3}

^{1} *Department de Mathematique et Informatique, Université du Québec à Montréal,*

CP 8888, Suc. A, Montreal, Quebec, Canada H3C 3P8

^{2} *Department of Mathematics, Concordia University, Montreal, Quebec, Canada H3G 1M8*

^{3} *Department of Mathematics and Statistics, The University of Maryland, Baltimore,*

MD 21228, U.S.A.
(Received July 1, 1989; revised April 2, 1990)

**Abstract.**
The problem of estimating the common mean *mu* of
*k* independent and univariate inverse Gaussian populations
*IG*(*mu*, *lambda*_{i}), *i* = 1,...., *k* with unknown and unequal
*lambda*'s is considered. The difficulty with the maximum likelihood
estimator of *mu* is pointed out, and a natural estimator ^{~}*mu* of
*mu* along the lines of Graybill and Deal is proposed. Various finite
sample properties and some decision-theoretic properties of ^{~}*mu*
are discussed.

*Key words and phrases*:
Inverse-Gaussian population,
Graybill-Deal type estimate, squared error loss, equivariant estimator,
admissibility.

**Source**
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