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  • 學位論文

迭代平滑在普瓦松分配平均值之研究

Iterative smoothing analysis for poisson mean

指導教授 : 吳建華

摘要


在網路科技蓬勃發展的情況下,人們要統計資料或者建立數據都已成為非常容易的事情,但有些時候我們會發現資料過於粗糙,而導致我們得不到我們想要的資訊,我們為了使資料量變多,讓資料變得更細緻,我們決定用迭代平滑的方法來讓資料量變多。 本論文將會利用普瓦松過程來當成分段常數函數,找出平滑度定義的目標函數,並利用R軟體將圖畫出來,再利用已知的平滑方法來做模擬,並將圖畫下來看看是否有平滑化,並說明已知的模擬方法並不完善的地方,接下來我們會用我們所想出來的新方法,試看看能否克服不完善的地方,並讓分段常數函數平滑化。

並列摘要


With the development of network technology, nowadays, it is easy for people to collect data or statistics. However, we sometimes find that the data might be too rough for us to get the information. To collect more data, we determine to use an iterative smoothing method to make information more detailed and increase the amount of data. In this paper, we will use the Poisson process with a piecewise constant function ,and find the objective function of the smoothness definition. We also use the R software to draw out the picture. then we use the known smooth method to do the simulation, last, we will observe the picture down to see Whether it is smooth, and the simulation that we known is not perfect , so we will use our new method, try to see whether to overcome the imperfections, and let the piecewise constant function smooth.

參考文獻


1.Huifen Chen, Bruce W. Schmeiser: I-SMOOTH: iteratively smoothing piecewise-constant Poisson-process rate functions. Winter Simulation Conference 2011: 469-480
2. Poisson 分配、指數分配與排隊理論-翁秉仁http://episte.math.ntu.edu.tw/applications/ap_poisson/
3. 談談卜松過程 (Poisson Process)-孫自健;石仲拓
http://episte.math.ntu.edu.tw/articles/mm/mm_02_4_01/
4. 陳景祥 (2010)。 R軟體 : 應用統計方法。修訂版。台北市 : 台灣東華。

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