Optimal Shrinkage Estimations for the Parameters of Exponential Distribution Based on Record Values

Optimal Shrinkage Estimations for the Parameters of Exponential Distribution Based on Record Values

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This paper studies shrinkage estimation after the preliminary test for the parameters of exponential distribution Cookie based on record values.The optimal value of shrinkage coefficients is also obtained based on the minimax regret criterion.The maximum likelihood, pre-test, and shrinkage estimators are compared using a simulation study.The results to estimate the scale parameter show that the optimal shrinkage estimator is better than the maximum likelihood estimator in all 144 cases, and when the prior guess is near the true value, the pre-test estimator is better than shrinkage estimator.

The results to estimate the location parameter show that the optimal shrinkage estimator is better than maximum likelihood estimator when a prior guess is close to the true value.All estimators are illustrated by a numerical example.