臺灣博碩士論文加值系統

在水文學上，以往總以單變量的統計方法分析資料。Nadarajah(2009)針對乾旱資料提出了伽瑪-貝他二元混合模型來分析乾旱持續時間與其發生比例。本文利用強韌概似函數的概念建立強韌二元負二項模型，並利用模擬與乾旱資料比較此模型與伽瑪-貝他二元混合模型，在分析具相關性的連續與比例資料時的差異與優劣。

Traditionally, analysis of Hydrology employs only one hydrological variable. Nadarajah (2009) proposed a bivariate model with gamma and beta as marginal distributions to analyze the drought duration and the proportion of drought events.
We demonstrate that the gamma-beta model is sensitive to model misspecification, and propose using the robust bivariate negative binomial model to make inference for data of this type. One obtains legitimate inference without worrying about the true underlying distribution of the bivariate data.
Simulations and the analysis of the drought data from the State of Nebraska, USA, are provided to make contrasts between our robust approach and the gamma-beta model.

摘要i
Abstract ii
目錄iii
表目次v
第一章緒論1
第二章伽瑪−貝他模型2
2.1 建立模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 參數估計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 伽瑪−貝他模型對於乾旱資料的應用. . . . . . . . . . . . . . . . . . . . . . 5
第三章強韌二元負二項模型與伽瑪−貝他模型之比較7
3.1 強韌概似函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 伽瑪−貝他二元混合模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 二元負二項模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4 二元負二項模型的修正項. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.5 實作模型為二元負二項之強韌概似比檢定. . . . . . . . . . . . . . . . . . . 14
第四章模擬研究15
4.1 邊際分配期望值之估計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 複迴歸模型下之二元反應變數. . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 模擬結果分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
第五章實例分析29
5.1 資料介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2 資料分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
第六章結論與展望43
參考文獻44

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