Improved Estimation of Inverse Gaussian Shape Parameter and Measure of Dispersion with Prior Information

Abstract

This paper is intended to propose an improved class of shrinkage estimators for estimating the general parameter P _(α) = λ^α (α, being an integer) of the Inverse Gaussian distribution using prior information λ^α ₀ of the parameter P _(α) = λ^α under investigation. The properties of the suggested class of shrinkage estimators are studied and compared with the usual unbiased estimator, minimum mean squared error (MMSE) estimator and Singh and Pandit's (2006) estimator. Realistic condition have been obtained under which the proposed class of shrinkage estimators are better than these estimators. In particular, the study has been concentrated over the problem of estimation of shape parameter P ₍₁₎ = λ and the measure of dispersion P _(-1) = 1/λ of the Inverse Gaussian distribution. Numerical illustrations are given in the support of the proposed study.

Key Words:

• Inverse Gaussian distribution
• Shrinkage estimator
• Bias
• Mean squared error