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Semi- Minimax Estimations on the Exponential Distribution Under Symmetric and Asymmetric Loss Functions | ||
| Al-Rafidain University College For Sciences | ||
| Article 1, Volume 0, Issue 36, 2017, Pages 245-270 | ||
| Authors | ||
| ; J. Al-Obedy | ||
| Abstract | ||
| In this paper the semi-minimax estimators of the scale parameter of the exponential distribution are presented by applying the theorem of Lehmann under symmetric (quadratic) loss function and asymmetric (entropy, mlinex , precautionary) loss functions .The results of comparison between these estimators are compared empirically using Monte-Carlo simulation study with respect to the mean square error(MSE) and the mean percentage error(MPE). In general, the results showed that the semi-minimax estimator under quadratic loss function is the best estimator by MSE and MPE for all sample sizes. We can notice that, when the values of the parameters β ,θ increasing the semi-minimax estimator under quadratic loss function is the best estimator by MSE while comparison by MPE showed that the semi-minimax estimator under mlinex loss function when the value of c positive is the best, but they both get worse as α ,θ increases. Also the results showed that when α, β together increase the semi-minimax estimator under entropy loss function is the best by MSE while by MPE the semi-minimax estimator under precautionary loss function is the best estimator. | ||
| Keywords | ||
| semi; minimax estimator; Exponential Distribution; Bayes estimator; Monte; Carlo simulation; semi; minimax | ||
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