雙變量伽瑪分配與其對應延伸模型之探討

A Study of the Bivariate Gamma Distribution and the Corresponding Extended Model

謝家柔(Chia-Jou Hsieh)

指導教授 ： 黃怡婷

國立臺北大學/商學院/統計學系/碩士(2015年)

摘要

廣義線性模型能用來分析單一非負反應變數，但隨著科技不斷的進步，資料量正在迅速增長，運用巨量資料 (big data) 所提供的訊息將可為生活各個方面帶來新的價值與創新。因此，分析資料的重點將不再只對單一變量，而會對多個相關變量的關係感興趣。
本文主要目的在於探討與運用 Kibble (1941) 所提出的雙變量伽瑪分配進行建模，去配適兩個相關非負反應變數，使用 R 軟體 NLMINB 函數的數值方法求出參數之最大概似估計值。在不同模擬設定之下，利用蒙地卡羅模擬法 (Monte Carlo simulation) 求取偏誤、估計值標準誤及覆蓋機率去評估估計值的表現。將應用在從銀行獲得的實際資料，用來說明此模型的可行性。

關鍵字

Kibble 雙變量伽瑪分配 ； 非負資料

並列摘要

The generalized linear model can be used to analyze one non-negative response variable. With the advance of technology, the volume of data is increasing rapidly. The information provided by the application of big data can bring new values and innovation to our lives. In turn, the primary key analysis might not be just one single variable, but could be several correlated variables.
The purpose of this thesis is to discuss and propose a new model for two-correlated non-negative response variables based on the Kibble's bivariate gamma distribution proposed by Kibble (1941). The maximum likelihood estimators of parameters are derived numerically using the function NLMINB in R. Under various simulation settings, Monte Carlo simulations are conducted to evaluate the performance of the estimates in terms of bias, standard error and coverage probability. A real application obtained from a bank is used to illustrate the feasibility of the model.

並列關鍵字

Kibble's bivariate gamma distribution ； Non-negative data

參考文獻

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