ESTIMATION OF A COMMON MEAN OF SEVERAL UNIVARIATE INVERSE GAUSSIAN POPULATIONS

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

1Department de Mathematique et Informatique, Université du Québec à Montréal,

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

2Department of Mathematics, Concordia University, Montreal, Quebec, Canada H3G 1M8

3Department 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 μ of k independent and univariate inverse Gaussian populations IG(μ, λ_{i}), i = 1, …, k with unknown and unequal λ’s is considered. The difficulty with the maximum likelihood estimator of μ is pointed out, and a natural estimator μ̃ of μ along the lines of Graybill and Deal is proposed. Various finite sample properties and some decision-theoretic properties of μ̃ are discussed.

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