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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/130962
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/130962


    Title: 廣義伽瑪分配於顧客購買時間模型之應用
    The Generalized Gamma Distribution with Application to the Modeling of Customers’ Purchase Times
    Authors: 蔣宛蓉
    Jiang, Wan-Rong
    Contributors: 翁久幸
    陳麗霞

    蔣宛蓉
    Jiang, Wan-Rong
    Keywords: 危險函數
    條件生存函數
    廣義伽瑪分配
    購買間隔時間
    Hazard function
    Conditional survival function
    Generalized gamma distribution
    Interpurchase time
    Date: 2020
    Issue Date: 2020-08-03 17:32:33 (UTC+8)
    Abstract: 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.
    Reference: 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:
    [3] E. W. Stacy. “A generalization of the Gamma distribution.” Annals of Mathematical Statistics(1962);33:1187–1192.
    [4] E. W. Stacy and G. A. Mihram. “Parameter estimation for a Generalized Gamma distribution.” Technometrics (1965);7:349–358.
    [5] R. E. Glaser. “Bathtub and related failure rate characterizations.” Journal of the American Statistical Association(1980);75:667­672.
    [6] G. M. Allenby, R. P. Leone and L. Jen. “A dynamic model of purchase timing with application to direct marketing.” Journal of the American Statistical Association(1999);
    94:365­374.
    [7] C. Cox, H. Chu, M. F. Schneider and A. Mun˜oz. “Parametric survival analysis and taxonomy of hazard functions for the Generalized Gamma distribution.” Statistics in Medicine(2007);26:4352–4374.
    [8] O. Gomes, C. Combes and A. Dussauchoy. “Parameter estimation of the Generalized Gamma distribution.” Mathematics and Computers in Simulation(2008);79:955­963.
    [9] V. Kumar and G. Shukla. “Maximum likelihood estimation in Generalized Gamma type model.” Journal of Reliability and Statistical Studies(2010);3:43­51.
    [10] A. Noufaily and M. C. Jones. “On maximization of the likelihood for the Generalized Gamma distribution.” Computational Statistics(2013);28:505–517.
    [11] R. Shanker, K. K. Shukla, R. Shanker and T. A. Leonida. “On modeling of lifetime data using three­parameter generalized lindley and generalized gamma distributions” Biometrics & Biostatistics International Journal(2016);4:283­288.
    [12] M. H. Ling. “A comparison of estimation methods for Generalized Gamma distribution with one­shot device testing data” International Journal of Applied & Experimental
    Mathematics(2018);3:1­7.
    [13] J. F. Lawless. “Statistical Models and Methods for Lifetime Data” Wiley­Interscience(2011);2:306­308.
    [14] S. H. Jung, H. Y. Lee and S. C. Chow. “Statistical Methods for Conditional Survival Analysis” Journal of Biopharmaceutical Statistics(2018);28:927–938.
    [15] D. C. Schmittlein, D. G. Morrison and R. Colombo. “Counting Your Customers: Who Are They and What Will They Do Next?” Management Science(1987);33:1­24.
    Description: 碩士
    國立政治大學
    統計學系
    107354021
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0107354021
    Data Type: thesis
    DOI: 10.6814/NCCU202001093
    Appears in Collections:[統計學系] 學位論文

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