穩定型分布之參數的經驗分布估計法

Parameter Estimations for some stable Distributions based on Empirical Distributions

張庭耀(Ting-yao Chang)

指導教授 ： 許玉生

國立中央大學/理學院/數學系/碩士(2007年)

摘要

經驗分布在機率論及統計學都很重要，經驗分布為非母數統計之重要工具，本文研究經驗分布在母數統計之表現，以常態、柯西和Levy等穩定型分布為例，用經驗分布作參數估計並和常用統計量比較。

關鍵字

經驗分布 ； 參數估計 ； 穩定型分布

並列摘要

Empirical distribution has important theoretical property like Glivenko-Cantelli theorem from which statistical inference for distribution function is possible. Empirical distribution is optimal in nonparametric framework. However, it is unknown if empirical distribution is optimal in parametric models. In this paper, we will investigate the efficiency of empirical distribution in parametric framework. The distributions considered include normal, Cauchy and Levy that are all stable.

並列關鍵字

parametric estimation ； Stable distribution ； Empirical distribution

參考文獻

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[5]Tapia, R. A. and Thompson, J. R. (1977). "Nonparametric Probability Density Estimation." Johns Hopkins University Press.