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研究生:謝嘉軒
研究生(外文):HSIEH,CHIA-HSUAN
論文名稱:指數型幾何分配之研究與應用
論文名稱(外文):The study of the Exponentiated Geometric distribution and related applications
指導教授:李強笙
指導教授(外文):Lee, Chiang-Sheng
口試委員:李強笙林希偉吳崇光
口試委員(外文):Lee, Chiang-ShengShi-Woei Lin
口試日期:2017-06-28
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:工業管理系
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:31
中文關鍵詞:指數型幾何分配零膨脹資料
相關次數:
  • 被引用被引用:0
  • 點閱點閱:151
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
在統計學上,數值資料(numerical data)分為以下兩類:連續型資料(continuous data)和計數型資料(count data)。定義上,連續型資料表示資料可以為任意的數值,如身高、體重等。計數型資料則表示為整數型資料,如班級裡的學生人數等。
在以往的資料研究,相關人員常利用傳統的間斷分配去分析一般的計數資料。然而,在實際研究中,往往會發生資料含有大量零觀測值的現象,統計上稱為零膨脹資料(Zero-inflated data)。研究發現傳統的間斷分配並不適用於此類型資料。因此有不同的作者提出不同的方法去分析此類型資料。
本篇文章的主要目的是提出指數型幾何分配(exponentiated geometric distribution)的統計性質及其相關應用。此分配首先由Nadarajah &Baker(2015)提出,但是文章中有不少錯誤的討論,我們修正了原作者在文章中的謬誤之處並延伸了該分配的研究。
在本論文中,除了針對指數型幾何分配的統計性質如累積分配函數、機率質量函數、可靠度函數、危險函數、順序統計量、分位數、隨機變數的生成、參數估計等做詳細探討,也對於修正後的分配進行驗證,判斷其是否適用於零膨脹資料或優於先前常見的分配。
本論文中收集了車險索賠次數、每家住院人數和羔羊胎兒胎動次數等不同類型的零膨脹資料來驗證指數型幾何分配是否適用,並與ZIP、ND及Adjusted GPD做適合度上的比較。
研究結果顯示指數型幾何分配適用於零膨脹資料,可以作為分析零膨脹資料的其中一種選擇。
In statistics, numerical data divided into the following two classifications:continuous data and count data. On definition, continuous data indicates that data can take any values, such as height and weight. Count data indicates that data only can take certain values, such as the number of students in a class.
On a previous data research, relevant people usually use the traditional discrete distribution to analyze the normal count data. But, in the practical research, it usually happens a phenomenon that data with a large amount of zero observation. Statistics call it Zero-inflated data. By the research, we find the traditional distribution is not suitable for this kind of data. So the different author proposed different method to analyze this kind of data.
This paper aims on proposing an exponentiated geometric distribution and related applications. This distribution originally proposed by Nadarajah & Baker (2015).But, there are some wrong discussions in the article. We revised the mistake in the original paper and generalized the distribution’s research.
In this paper, besides making the detailed discussion of statistics properties (CDF, PMF, hazard function, order statistics, quantile) about exponentiated geometric distribution, we also verify the revised distribution, judging whether it is suitable of zero inflated data or greater than the previous common distribution.
This paper collect the different kind of zero inflated data, such as the automobile claim data, Hospitalizations’ data and fetal movement data to verify the exponentiated geometric distribution is suitable or not. And we compare the goodness of fit between exponentiated geometric distribution, ZIP, ND and Adjusted GPD.
The research result shows that exponentiated geometric distribution is suitable for zero inflated data. It can be an alternative to analyze the zero inflated data.
目錄
口試委員會審定書 #
誌謝 i
中文摘要 ii
ABSTRACT iii
目錄 v
圖目錄 vi
表目錄 vii
第一章 緒論 1
第二章 文獻回顧 3
2.1 零膨脹資料的常見分配 3
第三章 研究方法 7
3.1 指數型幾何配的統計性質 7
3.1.1 機率函數和累積分配函數及其相關圖形 7
3.1.2 可靠度函數及危險函數其相關圖形 9
3.1.3 Quantile(分位數) 12
3.1.4 隨機變數的生成 13
3.1.5 指數型幾何分配的展開 15
3.1.6 各類動差函數 15
3.1.7 順序統計量 17
3.2 指數型幾何分配的參數估計 18
3.3 模型的比較方法 20
第四章 資料分析與研究結果 22
4.1 資料研究 22
第五章 結論 28
5.1 結論 28
5.2 研究限制 29
5.3 未來研究建議 29
參考文獻 30
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Gradshteyn, I. S., Ryzhik, I.M., “Table of Integrals, Series, and Products”, seventh ed, Academic Press, San Diego, 2007
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McCullagh, P. & Nelder, J., “Generalized Linear Models”, London: Chapman and Hall. 1989.
Nadarajah, S., Baker, S. A. A., “An exponentiated geometric distribution”, Applied Mathematical Modelling, vol.40, pp. 6775~6784, July 2016
Nelder, J. A., & Wedderburn, R. W. M., “Generalized Linear Models”, Journal of the Royal Statistical Society. Series A (General), Vol. 135, No. 3, pp. 370-384 1972
Ridout, M., Demetrio, C. G. B., Hinde, J., “Models for count data with many zeros”, International Biometric Conference, Cape Town, Dec 1998
Yau, K. K. W., Wang, K., Lee, A. H., “Zero-Inflated Negative Binomial Mixed Regression Modaling of Over-Dispersed Count Data with Extra Zeros”, Biometrical Journal, vol.45,pp.437~452, Jun 2003
Yip, K. C. H. & Yau, K. K. W., “On modeling claim frequency data in general insurance with extra zeros”, Insurance: Mathematics and Economics, vol.36, pp. 153~163, Feb 2005
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