BAYES ESTIMATION IN A MIXTURE INVERSE GAUSSIAN MODEL

RAMESH C. GUPTA AND H. OLCAY AKMAN

Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752, U.S.A.

(Received February 21, 1994; revised December 13, 1994)

Abstract. In this paper a mixture model involving the inverse Gaussian distribution and its length biased version is studied from a Bayesian view-point. Using proper priors, the Bayes estimates of the parameters of the model are derived and the results are applied on the aircraft data of Proschan (1963, Technometrics, 5, 375–383). The posterior distributions of the parameters are expressed in terms of the confluent-hypergeometric function and the modified Bessel function of the third kind. The integral involved in the expression of the estimate of the mean is evaluated by numerical techniques.

Key words and phrases: Length biased, Birnbaum Saunders model, Lindley approximation.