| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 周宗翰 | zh_TW |
| DC.creator | Tsung-han Chou | en_US |
| dc.date.accessioned | 2007-7-17T07:39:07Z | |
| dc.date.available | 2007-7-17T07:39:07Z | |
| dc.date.issued | 2007 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=942201016 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.abstract | 穩定型分布之冪數因未出現於密度函數或分布函數，故不易估計，本文介紹一些估計冪數的方法。我們發現，單峰穩定型分布之冪數為密度函數或分布函數之泛函，故可由核密度函數估計式或經驗分布估計之。我們將討論這些估計式的性質及應用。 | zh_TW |
| dc.description.abstract | The collection of stable distributions is a particular class of distributions studied in probability and statistics. Let $X,X_1,ldots,X_k$ denote a sequence of i.i.d. random variables with a common distribution $R$. If for all positive integer $k$, $X$ and $frac{X_1+cdots+X_k}{k^alpha}$ have the same distribution for
some constant $alpha$, then $R$ is a stable distribution with exponent $frac{1}{alpha}$. It is difficult to estimate exponent $alpha$ since $alpha$ does not appear in probability density function. The purpose of this paper is to study some estimators of $alpha$ and their applications. We find that under unimodal assumption $alpha$ is a functional of probability density function
or distribution function. Consequently, $alpha$ can be estimated by kernel density estimators or empirical distributions. | en_US |
| DC.subject | 經驗分布 | zh_TW |
| DC.subject | 密度函數估計式 | zh_TW |
| DC.subject | 冪數 | zh_TW |
| DC.subject | 穩定型分布 | zh_TW |
| DC.subject | stable distributions | en_US |
| DC.subject | empirical distributions | en_US |
| DC.subject | kernel density estimators | en_US |
| DC.subject | exponent | en_US |
| DC.title | 單峰穩定型分布之冪數的經驗分布及核密度函數估計法 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | Exponent Estimations for Unimodal Stable Distribution based on Empirical Distributions and Kernel Density Estimators | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |