近年來，由於資料庫系統日益發達，可蒐集大量顧客交易資訊，因此，如何有效利用顧客交易資訊做出對企業有利的行銷手法，已成為企業重要的目標之一。其中，顧客購買間隔時間變數為判斷顧客購買狀態的重要變數。已有研究利用顧客購買期間變數建立顧客行為的預測模型，但著墨於比較伽瑪分配與廣義伽瑪分配兩者之預測結果，並未深入探討應用在顧客購買分析時各參數的代表意義。
本研究以 Stacy(1962) 所提出之廣義伽瑪分配為基礎，並利用危險函數以及條件生存函數等統計分析方法，討論不同參數範圍下顧客購買意涵，得出較能合理解釋購買行為的參數範圍。接著，以兩組 kaggle 上的顧客交易資料進行實證研究，以最大概似法或層級貝氏法估計模型參數，建構出若干組模型，再評估這些模型能否正確預測顧客是否購買。實證結果顯示，預測表現較佳的參數組合與理論探討中得到的合理參數範圍相當吻合，此外，貝氏模型在小樣本資料中的預測表現較佳，大樣本下則為最大概似法預測表現較佳。

In recent years, because database system is advancing as time goes by, we can collect a lot of customer transaction information. Consequently, in order to make effective marketing approach, how to effectively use of information is an important goal for enterprise.Among this information, interpurchase time is the indispensable variable used to judge the behavior of customer. There have been many research literatures addressing the issue of interpurchase time, however, many of them only focused on comparing the results predicted by gamma distribution and generalized gamma distribution. Therefore, the goal of this thesis is to analyze the meaning of the model established by different parameters.
Based on generalized gamma distribution proposed by Stacy(1962), with the use of hazard function and conditional survival function we can analyze the meaning of customer
behavior under different parameter ranges. We used two datasets come from kaggle to make some models by different methods such as likelihood function or hierarchical bayes.
Finally, we found the best model’s parameter range is identical to theoretical discussion. Otherwise, bayes model is better than likehood function method for small samples and the opposite is true for large samples.

第一章 緒論 1
第二章 文獻回顧 3
2.1 廣義伽瑪分配­機率密度函數與危險函數 3
2.1.1 機率密度函數 3
2.1.2 危險函數 4
2.2 廣義伽瑪分配­參數估計方法 7
第三章 研究方法與資料說明 11
3.1 參數估計模擬驗證 11
3.2 顧客購買議題­參數估計方法 16
3.3 顧客購買議題­危險函數與條件生存函數 22
3.3.1 危險函數 22
3.3.2 條件生存函數 24
3.4 顧客購買議題分析流程 27
3.5 研究資料 28
3.5.1 資料一:Acquire Valued Shoppers Challenge 29
3.5.2 資料二:Retailrocket recommender system dataset 32
第四章 研究結果 35
4.1 參數估計結果 35
4.2 模型預測結果 39
4.3 實際預測顧客購買行為結果 41
4.4 較少購買之顧客分析 43
4.5 大量資料之抽樣結果分析 47
第五章 結論與建議 52
5.1 結論與實際應用 52
5.2 限制與未來方向 52
參考文獻 54
程式碼 56

中文部分:
[1] 陳薏棻，“應用層級貝式理論於跨商品類別之顧客購買期間預測模型”，國立臺灣大學商學研究所碩士論文，2006
[2] 郭瑞祥、蔣明晃、陳薏棻、楊凱全，“應用層級貝氏理論於跨商品類別之顧客購買期間預測模型” ，管理學報，2009

英文部分:
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