Estimating common dispersion parameter of several inverse Gaussian populations : A simulation study

Abstract

Suppose we have k(≥ 2) inverse Gaussian populations with a common dispersion parameter λ and possibly different location parameters μi, i = 1, 2, … , k. Estimation of λ is considered when the other nuisance parameters μ1, μ2, … , μk are unknown and unequal. First, we derive the maximum likelihood estimator (MLE) of λ. Using the fisher information matrix, an asymptotic confidence interval for λ as well as other k location parameters has been obtained. Further Bayes estimators with respect to non-informative, Jeffrey’s and conjugate priors have been considered. We observe that unlike the MLE, the closed form of these Bayes estimators do not exist. Using certain approximations for the ratio of the integrals, approximate Bayes estimators have been obtained. All the proposed estimators are compared in terms of their bias and mean squared errors (MSEs) through simulation in the case of k = 2 and k = 3 populations. Finally a real data set has been considered to demonstrate the potential application of our model.