This paper is to find the estimators of the mean
For the population that is distributed as normal with mean
Arnholt and Hebert [
This paper focuses on improving the estimators of
The paper is organized as follows. The improved estimators are proposed in Section
Let
(1) Let
(2) Let
(3) Bayes estimator
The likelihood function of
Then, the prior distribution is
(1) For asymptotic comparison, the estimators are compared based on the relative efficiency (RE) of MSEs. The RE of
The
Therefore, from (
(2) The simulation results are shown for the comparison MSEs among the three proposed estimators,
MSEs of the proposed estimators
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0.01 |
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5 | 0.09 |
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0.25 |
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0.01 |
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10 | 0.09 |
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0.25 |
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0.01 |
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15 | 0.09 |
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0.25 |
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MSEs of the proposed estimators
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0.01 |
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5 | 0.09 |
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0.25 |
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0.01 |
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10 | 0.09 |
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0.25 |
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0.01 |
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15 | 0.09 |
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0.25 |
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MSEs of the proposed estimators
|
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|
---|---|---|---|---|
0.01 |
|
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5 | 0.09 |
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0.25 |
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0.01 |
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10 | 0.09 |
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0.25 |
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0.01 |
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15 | 0.09 |
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0.25 |
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From Tables
These estimators
The authors would like to thank Computational Science Research Group, Faculty of Science, Khon Kaen University for the financial support.