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    题名: 基於混合廣義伽瑪分配之顧客購買間隔時間模型
    Customer interpurchase-­time models based on mixture generalized gamma distributions
    作者: 柯瀚鈞
    Ke, Han-Jun
    贡献者: 黃子銘
    Huang, Tzee-Ming
    柯瀚鈞
    Ke, Han-Jun
    关键词: 購買間隔時間
    混合模型
    乘法模型
    馬可夫鏈
    interpurchase times
    mixture model
    multiplicative model
    Markov chain
    日期: 2021
    上传时间: 2021-08-04 14:42:59 (UTC+8)
    摘要: 　　本論文以廣義伽瑪分配作為顧客購買間隔時間之母體分配，建立混合模型推估顧客處於非常活躍、活躍及非活躍狀態的比例，並導入乘法模型探討商品類型在各狀態下對購買間隔時間的影響。除此之外，運用馬可夫鏈的特性建立轉移矩陣收集顧客狀態轉移的變化，並考慮多組馬可夫鏈模型以更精準的捕捉顧客消費行為。資料驗證方面，生成模擬資料以最大概似估計法及是否考慮最大期望演算法估計上述模型之參數來檢視估計優劣，並以 kaggle 中的網路商城交易資料來展現本文方法運用在實際資料的成果。根據模擬實驗顯示，考慮最大期望演算法估計結果較優異但所耗費的時間較長，不使用最大期望演算法估計結果相對較差，然而計算時間則大幅減少。
    In this thesis, a model for customer interpurchase times is proposed, where the generalized gamma distribution is used. In the proposed model, each customer has three states: very active, active and inactive state, and interpurchase times of a customer at different state may obey different distributions. The impact of product types on the interpurchase times is also considered. In addition, the customer states are allowed to change overtime, according to a Markov chain model. Model parameters are estimated using maximum likelihood estimation and consider whether to adopt the expectationmaximization algorithm. According to simulation experiments, using the expectation­maximization algorithm gives a better result but takes a longer
    time, the result without using the expectation­maximization algorithm is relatively poor, but the calculation time is greatly reduced.
    參考文獻: Akaike, H. (1974). A new look at the statistical model identification. IEEE transactions on automatic control, 19(6), 716–723.
    Allenby, G. M., Leone, R. P., & Jen, L. (1999). A dynamic model of purchase timing with application to direct marketing. Journal of the American Statistical Association, 94(446), 365–374.
    Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 1–22.
    Giraud, C. (2015). Introduction to high­dimensional statistics. Monographs on Statistics and Applied Probability, 139, 139.
    Hughes, A. M. (1994). Strategic database marketing. Chicago: Probus Publishing Company.
    Markov, A. A. (1971). Extension of the limit theorems of probability theory to a sum of variables connected in a chain. Dynamic probabilistic systems, 1, 552–577.
    Schwarz, G., et al. (1978). Estimating the dimension of a model. Annals of statistics, 6(2), 461–464.
    Stacy, E. W., et al. (1962). A generalization of the gamma distribution. The Annals of mathematical statistics, 33(3), 1187–1192.
    Wilks, S. S. (1938). The large­sample distribution of the likelihood ratio for testing composite hypotheses. The annals of mathematical statistics, 9(1), 60–62.
    郭瑞祥, 蔣明晃, 陳薏棻, & 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.
    林倉億. (2014). 「轉移矩陣」二三事 (2)：歷年高中課本中的穩定狀態. HPM 通訊, 17(6).
    描述: 碩士
    國立政治大學
    統計學系
    108354022
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0108354022
    数据类型: thesis
    DOI: 10.6814/NCCU202100840
    显示于类别:[統計學系] 學位論文

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