政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/146304

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/146304

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政大機構典藏 > 商學院 > 統計學系 > 學位論文 > Item 140.119/146304

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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:	2023-08-02 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. 30 Murphy, 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
顯示於類別:	[統計學系] 學位論文

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