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

Suppose we have k(>= 2) inverse Gaussian populations with a common dispersion parameter lambda and possibly different location parameters mu(i), i = 1, 2, ..., k. Estimation of lambda is considered when the other nuisance parameters mu(1), mu(2), ...,mu(k) are unknown and unequal. First, we derive the maximum likelihood estimator (MLE) of lambda. Using the fisher information matrix, an asymptotic confidence interval for lambda 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.