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    题名: The Generalized Gamma Distribution with Application to the Modeling of Customers’ Purchase Times
    廣義伽瑪分配於顧客購買時間模型之應用
    作者: 翁久幸;蔣宛蓉;陳麗霞
    Weng, Chiu-hsing;Jiang, Wan-rong;Chen, Li-shya
    贡献者: 統計系
    关键词: Hierarchical Bayesian;Conditional survival functions;Generalized gamma distribution;Hazard function;Profile likelihood
    階層貝氏模型;條件存活函數;廣義伽瑪分配;危險函數;剖面概似法
    日期: 2021-12
    上传时间: 2022-07-07 11:24:07 (UTC+8)
    摘要: The generalized gamma (GG) distribution is an extensive family that includes as special cases several distributions: the exponential, the gamma, the log-normal, and the Weibull. It extends the gamma distribution by introducing an additional shape parameter γ , with γ = 1 giving the gamma distribution. While the taxonomy of the hazard functions of the GG family has been studied and applied to areas such as clinical trials and reliability analysis, the application to customers` purchase times is less studied. In this paper, we characterize the properties of hazard functions and conditional survival functions from the aspect of customers` buying behavior. We show how purchase behavior varies with γ and the other shape parameter. We also compare the maximum likelihood estimation via the profile likelihood methods and the hierarchical Bayesian estimation. Some real-world examples are presented for illustration.
    廣義伽瑪分配是個廣泛的模型，它涵蓋指數、伽瑪、對數常態、以及韋伯等分配。它藉由引入一個形狀參數γ來延伸伽瑪分配，而當γ=1時則為伽瑪分配。雖然廣義伽瑪分配的危險函數已有許多探討，也應用於臨床試驗、可靠度分析等領域，但是在顧客購買時間之應用仍然不多。本研究從顧客購買行為來探討，說明廣義伽瑪分配的危險函數與條件存活函數之特色，如何對應到不同之購買行為，以及購買行為與廣義伽瑪分配形狀參數之關係。我們也會比較透過剖面概似法求得的最大概似估計與使用階層貝氏模型得到之估計。若干實際資料將用來說明。
    關聯: Journal of the Chinese Statistical Association(中國統計學報), Vol.59, No.4, pp.255-279
    数据类型: article
    显示于类别:[統計學系] 期刊論文

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