基於Copula 下的馬可夫鏈模型對於廣義卜瓦松分布之改變點偵測;Change-point Estimation Based on the Copula-based Markov Chain Model for Generalized Poisson Time Series

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/95317

Title:	基於Copula 下的馬可夫鏈模型對於廣義卜瓦松分布之改變點偵測;Change-point Estimation Based on the Copula-based Markov Chain Model for Generalized Poisson Time Series
Authors:	盧弘晉;Lu, Hung-Chin
Contributors:	統計研究所
Keywords:	改變點;廣義卜瓦松分佈;copula;Change point;Generalized Poisson Distribution (GPD);Copula
Date:	2024-07-26
Issue Date:	2024-10-09 16:39:12 (UTC+8)
Publisher:	國立中央大學
Abstract:	檢測隨時間序列數據中的轉變，稱之為改變點估計。在此篇論文當中，我們採用廣義卜瓦松分佈（GPD）來處理計數序列數據。廣義卜瓦松分佈經常性地作為卜瓦松分佈的改進，使其在衡量位置和離散度方面更具有靈活度。加上，我們提出了基於copula的馬可夫鏈模型來解決數據中的非線性依賴關係。接下來利用最大似然估計和牛頓-拉夫遜法，實現了參數和改變點估計。為了說明其有效性，我們將該方法應用於COVID-19及礦坑事故相關數據，並隨後提供相應的實證結果進行說明。;Change-point estimation is to detect shifts in sequential data over time elapsed. We employ the Generalized Poisson Distribution (GPD) to deal with the counting sequential data. Occasionally, the GPD serves as a more flexible alternative to the Poisson distribution with respect to measuring the location and dispersion. We propose a copula-based Markov chain model to tackle the nonlinear dependence in the data. Afterwards, the parameters and change-point estimation are achieved using profile maximum likelihood estimation, along with the application of the Newton-Raphson method. In order to illustrate its effectiveness, we apply the method to the data which concerned the COVID-19 pandemic and coal mining accidents. We subsequently provide the corresponding empirical result for illustration.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

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