臺灣博碩士論文加值系統

We derive a probability inequality regarding location parameter with use of Lyapunou's Inequality and Morkov's Inequality.
The new inequality is applied to location estimation.
We obtain a strict confidence interval for the mean.
In addition, the length of the interval is between the one using the Central Limit Theorem and that from using Chebyshev's Inequality.
The result is applied to treat estimation problem on mean failure time.
Edgeworth Expansion and Berry-Esseen Inequality are two alternative ways to
obtain interval estimation for the mean.
A comparison among the five estimation methods is shown the new inequality
and Berry-Esseen Inequality can found to make the obtained confidence intervals
strict and efficient.

Contents
Abstract ………………………………………………2
1 Introduction ………………………………………...4
1.1 Study Motivation . . . . . . . . . . . . . . . . . . . . . . . . . .4
1.2 Related Research Papers . . . . . . . . . . . . . . . . . . . .. 4
2 Three Methods for Interval Estimation …………….6
2.1 CLT and Chebyshev's Inequality . . . . . . . . . . .. . . 6
2.2 A New Inequality . . . . . . . . . . . . . . . . . . . . . . . …. 7
3 The New Inequality on Failure Time ………………12
3.1 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . …12
3.2 Comparison among Three Methods . . . . . . . . . . . . 15
3.3 Property of CI from Using the New Inequality . . 16
4 Edgeworth Expansion and Berry-Ess¶een Inequality 21
4.1 Edgeworth Expansion . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.1 Basic Conditions . . . . . . . . . . . . . . . . . . . . . …….21
4.1.2 The Estimator and its Error . . . . . . . . . . . . . . ….. 22
4.2 Berry-Ess¶een Inequality . . . . . . . . . . . . . . . . . . . . . 24
5 Conclusion and Comment ……………………………27
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …..27
5.2 Comment and Suggestion . . . . . . . . . . . . . . . . . . . . 28
Appendices ……………………………………………..29

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