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題名 廣義伽瑪分配和 BG/NBD 模型於顧客購買期間之比較研究
A Comparison of Generalized Gamma Distributions and BG/NBD Models for Customers’ Purchase Times作者 鄧喻安
Teng, Yu-An貢獻者 翁久幸
Weng, Chiu-Hsing
鄧喻安
Teng, Yu-An關鍵詞 購買間隔時間
廣義伽瑪分配
危險函數
條件生存函數
BG/NBD 模型
跨商品類別
Interpurchase times
Generalized gamma distribution
Hazard function
Conditional survival function
BG/NBD model
Product categories日期 2023 上傳時間 2-Aug-2023 13:03:34 (UTC+8) 摘要 透過搜集顧客每次消費資料作為顧客的資料庫系統，得以分析數據了解顧客的交易樣貌，進而達到銷售預測、精準行銷或產品推薦等目標，其中顧客每次交易的回購間隔時間是分析顧客購買行為的其中一個指標。先前已有研究利用廣義伽瑪分配應用於顧客購買間隔天數，其中分配的參數估計方法使用最大概似估計法，並透過廣義伽瑪分配的危險函數圖形表現為顧客的購買行為進行分類，加上條件存活函數預測顧客在未來幾天內是否會回來購買，另有研究使用BG/NBD模型用來預測顧客回購，其模型假設購買間隔天數、交易機率、交易次數和流失機率各自服從不同的統計分配。本研究探討廣義伽瑪分配與BG/NBD模型在顧客購買間隔時間的應用，比較兩者模型差異，包含分配假設、預測回購機率與參數估計方法的比較，接著以顧客交易的實證資料建構模型，透過預測不同類別商品的回購時間差異，分析個別方法較適用於何種類型商品，以作為分析顧客回購商品分析之參考。實證結果顯示，高購買頻率商品的未來短期內回購以廣義伽瑪分配的預測表現較佳，而未來較長期的回購情形BG/NBD模型預測表現較佳；購買頻率不高商品的未來長短期內回購都以廣義伽瑪分配的預測表現較佳。
By collecting customer transaction data as a customer database system, it is possible to analyze the data to understand customer buying patterns, thereby achieving goals such as sales forecasting, precision marketing, or product recommendations. One of the indicators for analyzing customer purchasing behavior is the repurchase interval between each customer transaction. Previous studies have utilized the generalized gamma distribution for modeling customer purchase interarrival times, with parameter estimation performed using the maximum likelihood estimation method. Hazard function of the generalized gamma distribution is used to classify customer buying behavior, and the conditional survival function predicts whether a customer will make a future purchase within a certain number of days. Other studys have used the BG/NBD model for predicting customer repurchases.This study investigates the application of the generalized gamma distribution and the BG/NBD model to customer purchase interarrival times and compares the differences between the two models, including distribution assumptions, prediction of repurchase probabilities, and parameter estimation methods. Subsequently, empirical data on customer transactions is used to construct the models, and the differences in predicting repurchase times for different product categories are analyzed to determine which method is more suitable for analyzing customer repurchasing behavior for specific types of products. The empirical results show that for high-frequency purchasing products, the generalized gamma distribution performs better in short-term repurchase predictions, while the BG/NBD model performs better for longer-term repurchases. For products with low purchase frequency, the generalized gamma distribution performs better in predicting both short-term and long-term repurchases.參考文獻 Allenby, G. M., Leone, R. P., and Jen, L. (1999). A dynamic model of purchase timing with application to direct marketing. Journal of the American Statistical Association, 94(446):365–374.Cole, S. R., Chu, H., and Greenland, S. (2014). Maximum likelihood, profile likelihood, and penalized likelihood: a primer. American journal of epidemiology, 179(2):252– 260.Cox, C., Chu, H., Schneider, M. F., and Munoz, A. (2007). Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in medicine, 26(23):4352–4374.Fader, P. S. and Hardie, B. G. (2007). How to project customer retention. Journal of Interactive Marketing, 21(1):76–90.Fader, P. S., Hardie, B. G., and Lee, K. L. (2005). “counting your customers”the easy way: An alternative to the pareto/nbd model. Marketing science, 24(2):275–284.Glaser, R. E. (1980). Bathtub and related failure rate characterizations. Journal of the American Statistical Association, 75(371):667–672.Jiang, W.-R., Chen, L.-S., and Weng, C.-H. (2021). The generalized gamma distribu- tion with application to the modeling of customers’ purchase times. 中國統計學報, 59(4):255–279.Jung, S.-H., Lee, H. Y., and Chow, S.-C. (2018). Statistical methods for conditional sur- vival analysis. Journal of biopharmaceutical statistics, 28(5):927–938.30Murphy, S. A. and Van der Vaart, A. W. (2000). On profile likelihood. Journal of the American Statistical Association, 95(450):449–465.Schmittlein, D. C., Morrison, D. G., and Colombo, R. (1987). Counting your customers: Who-are they and what will they do next? Management science, 33(1):1–24.Stacy, E. W. (1962). A generalization of the gamma distribution. The Annals of mathe- matical statistics, pages 1187–1192.蔣宛蓉 (2020). 廣義伽瑪分配於顧客購買時間模型之應用.郭瑞祥, 蔣明晃, 陳薏棻, and 楊凱全 (2009). 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, 26(3):291–308. 描述 碩士
國立政治大學
統計學系
110354009資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110354009 資料類型 thesis dc.contributor.advisor 翁久幸 zh_TW dc.contributor.advisor Weng, Chiu-Hsing en_US dc.contributor.author (Authors) 鄧喻安 zh_TW dc.contributor.author (Authors) Teng, Yu-An en_US dc.creator (作者) 鄧喻安 zh_TW dc.creator (作者) Teng, Yu-An en_US dc.date (日期) 2023 en_US dc.date.accessioned 2-Aug-2023 13:03:34 (UTC+8) - dc.date.available 2-Aug-2023 13:03:34 (UTC+8) - dc.date.issued (上傳時間) 2-Aug-2023 13:03:34 (UTC+8) - dc.identifier (Other Identifiers) G0110354009 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/146304 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 110354009 zh_TW dc.description.abstract (摘要) 透過搜集顧客每次消費資料作為顧客的資料庫系統，得以分析數據了解顧客的交易樣貌，進而達到銷售預測、精準行銷或產品推薦等目標，其中顧客每次交易的回購間隔時間是分析顧客購買行為的其中一個指標。先前已有研究利用廣義伽瑪分配應用於顧客購買間隔天數，其中分配的參數估計方法使用最大概似估計法，並透過廣義伽瑪分配的危險函數圖形表現為顧客的購買行為進行分類，加上條件存活函數預測顧客在未來幾天內是否會回來購買，另有研究使用BG/NBD模型用來預測顧客回購，其模型假設購買間隔天數、交易機率、交易次數和流失機率各自服從不同的統計分配。本研究探討廣義伽瑪分配與BG/NBD模型在顧客購買間隔時間的應用，比較兩者模型差異，包含分配假設、預測回購機率與參數估計方法的比較，接著以顧客交易的實證資料建構模型，透過預測不同類別商品的回購時間差異，分析個別方法較適用於何種類型商品，以作為分析顧客回購商品分析之參考。實證結果顯示，高購買頻率商品的未來短期內回購以廣義伽瑪分配的預測表現較佳，而未來較長期的回購情形BG/NBD模型預測表現較佳；購買頻率不高商品的未來長短期內回購都以廣義伽瑪分配的預測表現較佳。 zh_TW dc.description.abstract (摘要) By collecting customer transaction data as a customer database system, it is possible to analyze the data to understand customer buying patterns, thereby achieving goals such as sales forecasting, precision marketing, or product recommendations. One of the indicators for analyzing customer purchasing behavior is the repurchase interval between each customer transaction. Previous studies have utilized the generalized gamma distribution for modeling customer purchase interarrival times, with parameter estimation performed using the maximum likelihood estimation method. Hazard function of the generalized gamma distribution is used to classify customer buying behavior, and the conditional survival function predicts whether a customer will make a future purchase within a certain number of days. Other studys have used the BG/NBD model for predicting customer repurchases.This study investigates the application of the generalized gamma distribution and the BG/NBD model to customer purchase interarrival times and compares the differences between the two models, including distribution assumptions, prediction of repurchase probabilities, and parameter estimation methods. Subsequently, empirical data on customer transactions is used to construct the models, and the differences in predicting repurchase times for different product categories are analyzed to determine which method is more suitable for analyzing customer repurchasing behavior for specific types of products. The empirical results show that for high-frequency purchasing products, the generalized gamma distribution performs better in short-term repurchase predictions, while the BG/NBD model performs better for longer-term repurchases. For products with low purchase frequency, the generalized gamma distribution performs better in predicting both short-term and long-term repurchases. en_US dc.description.tableofcontents 第一章 緒論 1第二章 文獻回顧 3第三章 研究方法 53.1 廣義伽瑪分配與危險函數 53.2 危險函數與條件存活函數於顧客購買行為的意義 63.2.1 危險函數的意義 63.2.2 條件存活函數的意義 73.3 廣義伽瑪分配之參數估計 83.4 BG/NBD模型與其參數估計 93.4.1 BG/NBD模型假設 9 3.4.2 BG/NBD個人層面的概似函數 11 3.4.3 P(X(t)=x)推導 12 3.4.4 E(X(t))推導 12 3.4.5 BG/NBD的概似函數 133.5 廣義伽瑪分配與BG/NBD模型比較 14第四章 實證結果 164.1 資料說明 164.2 廣義伽瑪分配參數估計與預測結果 224.3 BG/NBD模型參數估計與預測結果 26第五章 結論與未來方向 295.1 結論與實際應用 295.2限制與未來方向 30參考文獻 31 zh_TW dc.format.extent 1290347 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110354009 en_US dc.subject (關鍵詞) 購買間隔時間 zh_TW dc.subject (關鍵詞) 廣義伽瑪分配 zh_TW dc.subject (關鍵詞) 危險函數 zh_TW dc.subject (關鍵詞) 條件生存函數 zh_TW dc.subject (關鍵詞) BG/NBD 模型 zh_TW dc.subject (關鍵詞) 跨商品類別 zh_TW dc.subject (關鍵詞) Interpurchase times en_US dc.subject (關鍵詞) Generalized gamma distribution en_US dc.subject (關鍵詞) Hazard function en_US dc.subject (關鍵詞) Conditional survival function en_US dc.subject (關鍵詞) BG/NBD model en_US dc.subject (關鍵詞) Product categories en_US dc.title (題名) 廣義伽瑪分配和 BG/NBD 模型於顧客購買期間之比較研究 zh_TW dc.title (題名) A Comparison of Generalized Gamma Distributions and BG/NBD Models for Customers’ Purchase Times en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Allenby, G. M., Leone, R. P., and Jen, L. (1999). A dynamic model of purchase timing with application to direct marketing. Journal of the American Statistical Association, 94(446):365–374.Cole, S. R., Chu, H., and Greenland, S. (2014). Maximum likelihood, profile likelihood, and penalized likelihood: a primer. American journal of epidemiology, 179(2):252– 260.Cox, C., Chu, H., Schneider, M. F., and Munoz, A. (2007). Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in medicine, 26(23):4352–4374.Fader, P. S. and Hardie, B. G. (2007). How to project customer retention. Journal of Interactive Marketing, 21(1):76–90.Fader, P. S., Hardie, B. G., and Lee, K. L. (2005). “counting your customers”the easy way: An alternative to the pareto/nbd model. Marketing science, 24(2):275–284.Glaser, R. E. (1980). Bathtub and related failure rate characterizations. Journal of the American Statistical Association, 75(371):667–672.Jiang, W.-R., Chen, L.-S., and Weng, C.-H. (2021). The generalized gamma distribu- tion with application to the modeling of customers’ purchase times. 中國統計學報, 59(4):255–279.Jung, S.-H., Lee, H. Y., and Chow, S.-C. (2018). Statistical methods for conditional sur- vival analysis. Journal of biopharmaceutical statistics, 28(5):927–938.30Murphy, S. A. and Van der Vaart, A. W. (2000). On profile likelihood. Journal of the American Statistical Association, 95(450):449–465.Schmittlein, D. C., Morrison, D. G., and Colombo, R. (1987). Counting your customers: Who-are they and what will they do next? Management science, 33(1):1–24.Stacy, E. W. (1962). A generalization of the gamma distribution. The Annals of mathe- matical statistics, pages 1187–1192.蔣宛蓉 (2020). 廣義伽瑪分配於顧客購買時間模型之應用.郭瑞祥, 蔣明晃, 陳薏棻, and 楊凱全 (2009). 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, 26(3):291–308. zh_TW
