Preliminary test shrinkage estimators for the shape parameter of generalized exponential distribution
Keywords:Generalized Exponential Distribution, Maximum Likelihood Estimator, Single Stage Shrinkage Estimator, Mean Squared Error and Relative Efficiency.
The present paper deals with the estimation of the shape parameter Î± of Generalized Exponential GE (Î±, Î») distribution when the scale parameter Î» is known, by using preliminary test single stage shrinkage (SSS) estimator when a prior knowledge available about the shape parameter as initial value due past experiences as well as optimal region R for accepting this prior knowledge.
The Expressions for the Bias [B (.)], Mean Squared Error [MSE] and Relative Efficiency [R.Eff (.)] for the proposed estimator is derived.
Numerical results about conduct of the considered estimator are discussed include study the mentioned expressions. The numerical results exhibit and put it in tables.
Comparisons between the proposed estimator Â withe classical estimator Â as well as with some earlier studies were made to show the effect and usefulness of the considered estimator.
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