ESTIMATION OF A COMMON MEAN OF SEVERAL UNIVARIATE
INVERSE GAUSSIAN POPULATIONS

MANZOOR AHMAD1, Y. P. CHAUBEY2* AND B. K. SINHA3

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, lambdai), 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.

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