| dc.contributor.advisor | 姜志銘<br>宋傳欽 | zh_TW |
| dc.contributor.author (Authors) | 郭俊佑 | zh_TW |
| dc.creator (作者) | 郭俊佑 | zh_TW |
| dc.date (日期) | 2012 | en_US |
| dc.date.accessioned | 2-Sep-2013 16:46:19 (UTC+8) | - |
| dc.date.available | 2-Sep-2013 16:46:19 (UTC+8) | - |
| dc.date.issued (上傳時間) | 2-Sep-2013 16:46:19 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0099972003 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/59434 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系數學教學碩士在職專班 | zh_TW |
| dc.description (描述) | 99972003 | zh_TW |
| dc.description (描述) | 101 | zh_TW |
| dc.description.abstract (摘要) | Chen(2010)提出如何用勝率函數來判斷給定的連續條件分配是否相容，以及相容時如何求對應的聯合分配。本研究提出，在二維有限的情形下，如何用勝率矩陣來判斷給定的條件機率矩陣是否相容，以及相容時如何求對應的聯合機率矩陣。又給定的條件機率矩陣不相容時，我們介紹了四種修改勝率矩陣的方法，同時在使用幾何平均法調整勝率矩陣的過程中，也發現選取最佳參考點以獲得最佳近似聯合機率矩陣之方法，並且給予理論證明。最後以模擬的方式發現，在修改勝率矩陣的四種方法中，以幾何平均法所得到的近似聯合機率矩陣，其條件機率矩陣最常接近所給定的條件機率矩陣。 | zh_TW |
| dc.description.abstract (摘要) | Chen (2010) provides the representations of odds ratio function to examine the compatibility of conditional probability density functions and gives the correspondingjoint probability density functions if they are compatible. In this research, we provide the representations of odds ratio matrix to examine the compatibility of two discreteconditional probability matrices and give the corresponding joint probability matrix if they are compatible. For incompatible situations, we offer four methods to revise odds ratio matrices to find near joint probability matrices so that their conditional probability matrices are not far from the two given ones. That is, we provide four methods so that the sums of error squares are small. For each method, the sum of error squares may depend on the same reference point of two odds ratio matrices. We firstdiscover by example that only the geometric method out of these four methods has a pattern to get the best reference point so that the sum of error squares is smallest. Wethen prove this finding in general. In addition, through simulation results, the geometric method would provide the smallest sum of error squares most often among these four methods. Hence, we suggest using geometric method. Its strategy to find the best reference point is also given. | en_US |
| dc.description.tableofcontents | 中文摘要………………………………………………………………………1Abstract……………………………………………………………………21. 簡介1.1 研究動機……………………………………………………………… 31.2 研究目的……………………………………………………………… 31.3 研究架構……………………………………………………………… 42. 勝率矩陣之探討2.1 條件機率矩陣之介紹………………………………………………… 52.2 勝率矩陣之定義及功能……………………………………………… 52.3 四種修正勝率矩陣之方法…………………………………………… 93. 最佳參考點之尋找3.1 以實例探討算術平均法下之最佳參考點………………………… 123.2 以實例探討幾何平均法下之最佳參考點………………………… 143.3 以實例探討最大值法下之最佳參考點…………………………… 163.4 以實例探討最小值法下之最佳參考點…………………………… 183.5 幾何平均法下尋找最佳參考點之理論基礎……………………… 203.6 四種修正勝率矩陣方法之模擬比較……………………………… 244. 結論……………………………………………………………………26參考文獻……………………………………………………………………27附錄：實驗模擬之數據……………………………………………………28 | zh_TW |
| dc.format.extent | 5895233 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0099972003 | en_US |
| dc.subject (關鍵詞) | 勝率矩陣 | zh_TW |
| dc.subject (關鍵詞) | 相容 | zh_TW |
| dc.subject (關鍵詞) | 條件機率矩陣 | zh_TW |
| dc.subject (關鍵詞) | 參考點 | zh_TW |
| dc.subject (關鍵詞) | odds ratio matrix | en_US |
| dc.subject (關鍵詞) | compatibility | en_US |
| dc.subject (關鍵詞) | conditional probability matrix | en_US |
| dc.subject (關鍵詞) | reference point | en_US |
| dc.title (題名) | 修正條件分配勝率矩陣時最佳參考點之選取方法 | zh_TW |
| dc.title (題名) | The best reference point method for the modification of the conditional distribution odds ratio matrices | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | Chen, Hua Yun. (2010) Compatibility of conditionally specified models. Statistics andProbability Letters, 80, 670-677.Ip, Edward H., Wang, Yuchung J. (2009) Canonical representation of conditionallyspecified multivariate discrete distributions. Journal of Multivariate Analysis,100,1282-1290. | zh_TW |
