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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 鄭克聲(Ke-Sheng Cheng) | |
dc.contributor.author | Ching-Hsiang Hsieh | en |
dc.contributor.author | 謝景翔 | zh_TW |
dc.date.accessioned | 2021-06-17T01:29:43Z | - |
dc.date.available | 2017-08-11 | |
dc.date.copyright | 2017-08-11 | |
dc.date.issued | 2017 | |
dc.date.submitted | 2017-08-04 | |
dc.identifier.citation | 林國峰、張守陽、李汴軍,1994,「台灣地區雨型之研究報告(二)」,國立台灣大學水工試驗所研究報告第 163 號。
林國峰、王俊明、高士傑,2004,區域性設計雨型之建立及應用,國立臺灣大學「台大工程」學刊,第九十二期,第1–9頁。 林維明,2006,水文分析系統觀念與暴雨頻率分析概說,水利技術與實務,第92-105頁 吳進龍,2002,暴雨歷程連續模擬之研究,國立臺灣大學生物環境系統工程學系暨研究所碩士論文。 鄭克聲、許恩菁、葉惠中,1999,具隨機碎形特性之設計暴雨雨型,臺灣水利期刊,第47卷,第3期。 經濟部水利署,2013,氣候變遷水文情境評估研究(2/2)。 Alai, D.H., Landsman, Z., Sherris M. (2013) Lifetime dependence modelling using a truncated multivariate gamma distribution. Insurance: Mathematics and Economics, 52, 542-549 Broeder, G.G. (1955) On parameter estimation of truncated Pearson type III distribution. The Annals of Mathematical Statistics, 26, 659-663. Chapman, D.G. (1956) Estimating the parameters of a truncated gamma distribution. The Annals of Mathematical Statistics, 27, 498-506. Cheng K.S., Hueter I., Hsu E.C., Yeh H.C. (2001) A scale-invariant gauss-markov model for design storm hyetographs. Journal of the American Water Resources Association, 37(3), 723-735. Cheng K.S., Chiang J.L.,Hsu C.W. (2007) Simulation of probability distributions commonly used in hydrological frequency analysis. Hydrological Processes, 21, 51–60. Cheng, K.S., Hou J.C., Liou, J.J., Wu Y.C., Chiang, J.J. (2011) Stochastic simulation of bivariate gamma distribution: a frequency-factor based approach. Stochastic Environmental Research and Risk Assessment, 25, 107–122. Chow, V.T. (1951) A general formula for hydrological frequency analysis. Eos, Transactions American Geophysical Union, 32(2), 231-237. Chow, V.T., Maidment, D.R., and Mays, L.W. (1988) Applied Hydrology. McGraw-Hill: New York. Cohen, A. (1949) On estimating the mean and standard deviation of truncated normal distributions. Journal of the American Statistical Association, 45, 518–525. Cohen, A. (1950) Estimating the mean and variance of normal populations from singly truncated and doubly truncated samples. The Annals of Mathematical Statistics, 21, 557–569. Gross, A.J. (1971) Monotonicity properties of the moments of truncated gamma and weibull density functions. University of California at Los Angeles and The Veterans Administration Western Research Support Center, Sepulveda, CA. Technometrics, 13(4), 851-857. Hattaway, J.T. (2010) Parameter estimation and hypothesis testing for the truncated normal distribution with applications to introductory statistics grades. Department of statistics at Brigham Young University. Horrace,W.C. (2005) Some results on the multivariate truncated normal distribution. Journal of Multivariate Analysis, 94, 209-221. Johnson, A.C., Thomopoulos, N.T. (2002) Characteristics and tables of the left-truncated normal distribution. Proceedings of Midwest Decision Sciences Institute, 133-139. Kite G.W. (1988) Frequency and risk analysis in hydrology. Water Resources Publications. Koutsoyiannis, D., Foufoula-Georgiou, E. (1993) A scaling model of a storm hyetograph. Water Resources Research, 29(7), 2345-2361. Nadarajah, S., Gupta, A.K. (2006) Some bivariate gamma distributions. Applied Mathematics Letters, 19, 767–774. Okasha, M.K., Alqanoo, I.M. (2014) Inference on the doubly truncated gamma distribution for lifetime data. International Journal of Mathematics and Statistics Invention. Wilhelm,S., Manjunath, B.G. (2010) tmvtnorm: A package for the truncated multivariate normal distribution. The R Journal, 2(1), 25-29 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67374 | - |
dc.description.abstract | 雙變數截斷迦瑪分布(Bivariate truncated gamma distribution,簡稱BTG)為一考慮兩隨機變數之相關性和截斷值之機率分布。本研究將颱風降雨事件隨時間之變化視為一非平穩性迦瑪馬可夫歷程,並提出雙變數截斷迦瑪分布之模擬方法,應用於序率模擬繁衍颱風事件之時雨量。
首先,本研究整理常見之單變數截斷分布型式(截斷常態分布、截斷迦瑪分布)及其參數推估法。其二,提出雙變數截斷迦瑪分布之模擬流程,其是根據雙變數截斷迦瑪分布與雙變數截斷標準常態分布的一對應轉換關係,透過模擬雙變數截斷標準常態分布不同之截斷值,建立雙變數截斷標準常態分布之相關係數和雙變數標準常態分布之相關係數,其存在的一關係式(其可表示為截斷值之函數)。並結合Cheng 等人 (2001) 提出之雙變數迦瑪分布與雙變數常態分布之相關係數轉換關係,考慮在給定雙變數迦瑪分布之相關係數下,尋找一對應之雙變數截斷迦瑪分布,並可推估其參數和進行序率模擬。 其三,將上述模擬流程應用到北台灣之宜蘭雨量站,進行該站之颱風事件時雨量模擬。模擬結果顯示本研究所提出之方法可繁衍颱風事件之時雨量,其保留了歷史雨量資料之統計特性(平均值、標準差、偏度、一階自相關係數)。其方法也可作為在極端降雨下對氣候變遷之衝擊評估。 | zh_TW |
dc.description.abstract | Bivariate truncated gamma (BTG) distribution is a probability distribution considering the correlation between two gamma random variables with truncation points. In this study, the temporal variation of typhoon rainfalls is modeled as a non-stationary gamma process. A bivariate truncated gamma simulation approach was proposed and, under the Markovian assumption, used for stochastic simulation of hourly rainfalls of individual typhoon events.
A summarized description of parameter estimation and stochastic simulation of univariate truncated normal and gamma distributions was given. The proposed BTG simulation approach is based on a transformation between the BTG and a corresponding bivariate truncated standard normal distribution. Through stochastic simulation of bivariate truncated standard normal distribution with various truncation points, an empirical relationship, as a function of truncation points, between correlation coefficient of the bivariate standard normal distribution and correlation coefficient of bivariate truncated standard normal distribution were established. By coupling this empirical relationship and a correlation coefficients conversion between bivariate gamma distribution and bivariate standard normal distribution derived by Cheng et al. (2001), correlation coefficient of the bivariate gamma distribution, which corresponds to the bivariate truncated gamma distribution under investigation, can be estimated and used for stochastic simulation of the bivariate truncated gamma distribution. The proposed BTG simulation approach was applied to simulation of hourly rainfalls of individual typhoon events at Yilan rainfall station in northern Taiwan. The simulation results demonstrate that the proposed approach is capable of generating hourly rainfall realizations of typhoons which preserve statistical properties (mean, standard deviation, skewness and lag-1 autocorrelation coefficient) of historical rainfall data. The proposed approach can also be used for assessing the impact of climate change on rainfall extremes. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T01:29:43Z (GMT). No. of bitstreams: 1 ntu-106-R04h41003-1.pdf: 6127977 bytes, checksum: 540899a46a92bf8ca0c64de3df5300ba (MD5) Previous issue date: 2017 | en |
dc.description.tableofcontents | 摘要 I
ABSTRACT II 目錄 III 圖目錄 V 表目錄 VI 壹 緒論 1 一 研究動機及目的 1 二 研究架構及流程 2 貳 文獻回顧 4 一 文獻綜述 4 二 常見之截斷分布型式 5 (一) 截斷常態分布 6 (二) 截斷迦瑪分布 9 三 頻率因子法 12 四 無因次雨型 16 參 研究方法 19 一 截斷常態分布之參數推估 19 二 截斷迦瑪分布之參數推估 22 三 雙變數截斷迦瑪分布之參數推估 23 (一) 相關係數的關係式推衍 23 (二) 雙變數截斷迦瑪分布之模擬 25 四 序率暴雨模擬 27 五 水文頻率分析 32 肆 研究區域與研究資料 35 伍 結果與討論 37 一 截斷常態分布之模擬實證 37 二 截斷迦瑪分布之模擬實證 42 三 雙變數截斷迦瑪分布之模擬實證 44 四 序率暴雨之模擬實證 46 陸 結論與建議 56 參考文獻 57 附錄A 截斷分布之參數推估值 59 附錄B 與降雨百分率有關之統計量 64 附錄C截斷和未截斷相關係數之關係式 68 附錄D 程式碼 69 | |
dc.language.iso | zh-TW | |
dc.title | 應用雙變數截斷迦瑪分布於序率暴雨模擬 | zh_TW |
dc.title | Simulation of Bivariate Truncated Gamma Distribution-Application to Storm Rainfall Modeling | en |
dc.type | Thesis | |
dc.date.schoolyear | 105-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 黃文政(Wen-Cheng Huang),蔡政安(Chen-An Tsai),盧孟明(Mong-Ming Lu),陳莉(Li Chen) | |
dc.subject.keyword | 截斷分布,雙變數迦瑪分布,無因次雨型,馬可夫歷程,參數推估, | zh_TW |
dc.subject.keyword | Truncated distribution,Bivariate gamma distribution,Dimensionless hydrograph,Markov process,Parameter estimation, | en |
dc.relation.page | 90 | |
dc.identifier.doi | 10.6342/NTU201702243 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2017-08-04 | |
dc.contributor.author-college | 共同教育中心 | zh_TW |
dc.contributor.author-dept | 統計碩士學位學程 | zh_TW |
顯示於系所單位: | 統計碩士學位學程 |
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