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.

[1] Killick, R., Fearnhead, P., & Eckley, I. A. (2012). Optimal detection of change
points with a linear computational cost. Journal of the American Statistical
Association, 107(500), 1590-1598.

[2] Jakson, B., Sccargle, J. D., Barnes, D., Arabhi, S., Alt, A., Gioumousis, P., Gwin, E.,
Sangtrakulcharoen, P., Tan, L., and Tsai, T. T. (2005). An algorithm for optimal
partitioning of data on an interval. IEEE Signal Processing Letters, 12(2), 105-108.
 
[3] Delignette-Muller, M. L., & Dutang, C. (2015). fitdistrplus: An R package for fitting
distributions. Journal of statistical software, 64, 1-34.

[4] Steenbergen, M. R. (2006). Maximum likelihood programming in R. University of
North Carolina, Chapel Hill.
 
[5] Justus, C., Hargraves, W., Mikhail, A., & Graber, D. (1978). Methods for
estimating. wind speed frequency distributions. Journal of Applied Meteorology
(1962-1982), 350-353.

[6] Climate Monitoring 2018 Annual Report (2019).From
https://www.cwb.gov.tw/Data/service/notice/download/publish_20191104141027.pdf
 
[7] 楊子賢(2021)。風速資料的轉折點分析。未出版之碩士論文，國立陽明交通大學應用數
學系所，新竹市。
 
[8] Tina, S. W., Li-Ching, H., & Yun-Ju, C. (1996). Generating pseudo-random time
series with specified marginal distributions. European Journal of Operational
Research, 94(1), 194-202.
 
[9] Wambui, G. D., Waititu, G. A., & Wanjoya, A. (2015). The power of the pruned
exact linear time (PELT) test in multiple changepoint detection. Am. J. Theor.
Appl. Stat, 4(6), 581-586.
 
[10] Killick, R., & Eckley, I. (2014). changepoint: An R package for changepoint
analysis. Journal of statistical software, 58(3), 1-19.