Abstract
In present paper, the properties of the Bayes Shrinkage estimator is studied for the measure of dispersion of an inverse Gaussian model under the Minimax estimation criteria.
Highlights
The Inverse Gaussian distribution plays an important role in Reliability theory and Life testing problems
The present article proposed Bayes Shrinkage estimator based on the Minimax criteria for the measure of dispersion
The Equation (9) represents the risk of the Bayes estimator of the measure of dispersion, which is independent with the parameter
Summary
The Inverse Gaussian distribution plays an important role in Reliability theory and Life testing problems. It has useful applications in a wide variety of fields such as Biology, Economics, and Medicine. In some estimation problems overestimation is more serious than the underestimation, or vice-versa [7] To deal with such cases, a useful and flexible class of asymmetric loss function (LINEX loss function (LLF)) was introduced by Varian [8]. Some shrinkage estimators for measure of dispersion θ 1 have been obtained by Pandey & Malik [11] and have studied their properties under SELF–criterion. The present article proposed Bayes Shrinkage estimator based on the Minimax criteria for the measure of dispersion.
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