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Author: 李宜蓁
Li, I-Chen
Thesis Title: 韋伯分配下轉折點的分析
Detection of Change Points For Weibull Distribution
Advisor: 蔡碧紋
Tsai, Pi-Wen
Committee: 呂翠珊
Tsui, Shan Lu
鄭宗記
Cheng, Tsung-Chi
蔡碧紋
Tsai, Pi-Wen
Approval Date: 2022/07/26
Degree: 碩士
Master
Department: 數學系
Department of Mathematics
Thesis Publication Year: 2022
Academic Year: 110
Language: 中文
Number of pages: 35
Keywords (in Chinese): 時間序列轉折點風速韋伯分配常態分配
Keywords (in English): Time series, Change point, Computational Cost, Pruned Exact Linear Time (PELT), Normal Distribution, Weibull Distribution
DOI URL: http://doi.org/10.6345/NTNU202201259
Thesis Type: Academic thesis/ dissertation
Reference times: Clicks: 112Downloads: 12
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  • 轉折點檢測是一個廣泛研究的統計學領域,它是估計數據集的統計特性發生轉折點的問題,檢測這類的變化在許多不同的應用領域都很重要,包含氣候學、金融學、海洋學。在本文中我們專注於單轉折點檢測,利用Pruned Exact Linear Time(PELT)方法檢定在韋伯分配下轉折點的分析,再以模擬的方法比較PELT以常態分配和韋伯分配去辨識轉折點位置和求出參數的估計值的結果。最後,我們會將分析一組實際的風速資料。

    Change point detection is a widely studied field of statistics. It is the problem of estimating change points in the statistical properties of datasets. Detecting such changes is important in many different application fields, including climatology, finance, and oceanography. In this paper, we focus on single change point detection, using Pruned Exact Linear Time(PELT)method to verify the analysis of change point under Weibull distribution, and then use simulation method to compare PELT with normal distribution and Weibull distribution to identify the change point locations and find the estimated value of the parameter. Finally, we will analyze a set of true wind speed data.

    第一章 緒論1 第二章 方法 2 2.1 辨識轉折點的方法 2 2.1.1 轉折點檢測的背景 2 2.1.2 Optimal Partitioning Method 3 2.1.3 Pruned Exact Linear Time Method 4 2.1.4 評估準則 6 第三章 不同模型下轉折點的估計 7 3.1 常態模型轉折點的估計 7 3.1.1 常態分佈模型與最大概似估計方法 7 3.2韋伯模型轉折點的估計 10 3.2.1 韋伯分佈 10 3.2.2 韋伯分佈模型的最大概似估計方法 11 第四章 模擬和實例分析 12 4.1 模擬結果 12 4.2 實際風速資料的分析 26 4.2.1 資料描述 26 4.2.2 分析結果 27 第五章 結論 33 參考文獻 35

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