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題名 應用Conway-Maxwell-Poisson分配預測非契約型顧客之終身價值
Predicting Customer Lifetime Value for Non-Contractual Relations with Application of Conway-Maxwell-Poisson Distribution作者 陳琬珊
Chen, Wan-Shan貢獻者 陳麗霞
Chen, Li-Shya
陳琬珊
Chen, Wan-Shan關鍵詞 顧客終身價值
非契約型關係
過度離散
不足離散
Conway-Maxwell-Poisson分配
Customer lifetime value (CLV)
Non-contractual relations
Overdispersion
Underdispersion
Conway-Maxwell-Poisson (CMP) distribution日期 2021 上傳時間 4-Aug-2021 14:42:22 (UTC+8) 摘要 隨著商業競爭加劇，企業不再單純依靠產品本身差異以維持競爭力，進而將焦點轉向個人化之服務，然而在顧客數眾多的情況下，如何評估個別顧客為企業帶來的終身價值 (customer lifetime value, 簡稱CLV或LTV) 已儼然成為重要的課題。若企業可明確知道顧客流失時點則稱為契約型關係 (contractual relations)，反之則稱為非契約型關係 (non-contractual relations)。本論文探討的是非契約型關係，考慮顧客在企業中存續時間為不可觀測之下，分別建構交易次數與顧客存續時間模型及交易金額模型之後，再依據CLV的計算公式，以預測個別顧客的CLV。不少實證研究顯示，交易次數相較於卜瓦松分配有過度離散 (overdispersion) 或不足離散 (underdispersion) 的現象，本論文乃延續 Mzoughia et al. (2018) 的做法，以Conway-Maxwell-Poisson (CMP) 分配為交易次數之分配，但修正Mzoughia et al. (2018) 的公式，納入顧客間交易次數離散現象之異質性，並進一步推導及計算出兩種CLV估計值，可分別評估顧客未來於一定期間內及至其流失為止的價值。
As business competition intensifies, companies no longer rely solely on the superior products to maintain their competitive edge. Instead, they turn their focuses to personalized services. When having thousands of customers, how to evaluate individual customer’s customer lifetime value (CLV or LTV) is undoubtedly a significant issue. If a company can observe exactly the time of customer dropout, then it belongs to “contractual relations”. Otherwise, it belongs to “non-contractual relations”. This thesis discusses the non-contractual relationship. Considering that the customer`s lifetime in the business is unobservable, models for the number of transactions, the customer’s lifetime and the transaction amount are constructed separately, and then the CLV formula is applied to predict the CLV of each individual customer. Several empirical studies have already shown that the numbers of transactions are sometimes being overdispersion or underdispersion compared to Poisson distribution. This thesis continues the work of Mzoughia et al. (2018) and constructs the model of number of transactions by Conway-Maxwell-Poisson (CMP) distribution, but modifies the formula of Mzoughia et al. (2018), and considers heterogeneous dispersion of the number of transactions among customers. Moreover, we derive and compute two CLV estimates, which can be used to evaluate each individual customer’s future value within a certain period and until customer dropout.參考文獻 Abe, M. (2009). "Counting Your Customers" One by One: A Hierarchical Bayes Extension to the Pareto/NBD Model. Marketing Science, 28(3), 541-553. https://doi.org/10.1287/mksc.1090.0502Berger, P. D., and Nasr, N. I. (1998). Customer Lifetime Value: Marketing Models and Applications [Article]. Journal of Interactive Marketing, 12(1), 17-30. https://doi.org/10.1002/(SICI)1520-6653(199824)12:1<17::AID-DIR3>3.0.CO;2-KBernat, J. R. (2019). Modelling Customer Lifetime Value in a Continuous, Non-Contractual Time Setting. [Master Thesis, Erasmus University]. http://hdl.handle.net/2105/45923Brockett, P. L., Golden, L. L., and Panjer, H. L. (1996) Flexible Purchase Frequency Modeling. Journal of Marketing Research, 33(1), 94–107.Borle, S., Singh, S. S., and Jain, D. C. (2008). Customer Lifetime Value Measurement [Article]. Management Science, 54(1), 100-112. https://doi.org/10.1287/mnsc.1070.0746Colombo, R., and Jiang, W. (1999). A Stochastic RFM Model. Journal of Interactive Marketing, 13(3), 2-12. https://doi.org/10.1002/(SICI)1520-6653(199922)13:3<2::AID-DIR1>3.0.CO;2-HConsul, P. C. (1989). Generalized Poisson Distributions: Properties and Applications. New York: M. Dekker.Conway, R. W. and Maxwell, W. L. (1962). A Queuing Model with State Dependent Service Rates, Journal of Industrial Engineering, 12, 132-136.Dziurzynski, L., and Wadsworth, E. (2020). BTYD: Implementing BTYD Models with the Log Sum Exp Patch. R package version 2.4.2.EsmaeiliGookeh, M., and Tarokh, M. J. (2013). Customer Lifetime Value Models: A Literature Survey. International Journal of Industrial Engineering & Production Research, 24(4), 317-336. http://ijiepr.iust.ac.ir/article-1-509-en.htmlFader, P. S., and Hardie, B. G. S. (2001). Forecasting Repeat Sales at CDNOW: A Case Study. INFORMS Journal on Applied Analytics 31 (3_supplement) S94-S107. https://doi.org/10.1287/inte.31.3s.94.9683Fader, P. S., and Hardie, B. G. S. (2009). Probability Models for Customer-Base Analysis. Journal of Interactive Marketing, 23(1), 61-69. https://doi.org/10.1016/j.intmar.2008.11.003Fader, P. S., and Hardie, B. G. S. (2013a). The Gamma-Gamma Model of Monetary. http://brucehardie.com/notes/025/Fader, P. S., and Hardie, B. G. S. (2013b). A Note on the CDNOW Master Data Set. http://www.brucehardie.com/notes/026/Fader, P. S., and Hardie, B. G. S. (2014). What’s Wrong with This CLV Formula? http://brucehardie.com/notes/033/Fader, P. S., Hardie, B. G. S., and Lee, K. L. (2005a). "Counting Your Customers" the Easy Way: An Alternative to the Pareto/NBD Model. Marketing Science, 24(2), 275-284. https://doi.org/10.1287/mksc.1040.0098Fader, P. S., Hardie, B. G. S., and Lee, K. L. (2005b). RFM and CLV: Using Iso-Value Curves for Customer Base Analysis. Journal of Marketing Research, 42(4), 415-430. https://doi.org/10.1509/jmkr.2005.42.4.415Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). Chapman and Hall/CRC. https://doi.org/10.1201/b16018Guo, J., Gabry, J., Goodrich, B., and Weber, S. (2020). rstan: R Interface to Stan. R package version 2.21.2.Jain, D., and Singh, S. S. (2002). Customer Lifetime Value Research in Marketing: A Review and Future Directions [Article]. Journal of Interactive Marketing, 16(2), 34-46. https://doi.org/10.1002/dir.10032Kotler, P., and Armstrong, G. (1996). Principles of Marketing (7th ed.). Prentice-Hall, Englewood Cliffs.Kumar V., and Reinartz, W. (2018). Customer Relationship Management (3rd ed.). Springer-Verlag Berlin Heidelberg.Minka, T. P., Shmeuli, G., Kadane, J. B., Borle, S., and Boatwright, P. (2018). Computing with the COM-Poisson Distribution. Carnegie Mellon University. Journal contribution. https://doi.org/10.1184/R1/6586508.v1Mzoughia, M. B., Borle, S., and Limam, M. (2018). A MCMC Approach for Modeling Customer Lifetime Behavior Using the COM-Poisson Distribution [Article]. Applied Stochastic Models in Business and Industry, 34(2), 113-127. https://doi.org/10.1002/asmb.2276Mzoughia, M. B., and Limam, M. (2014). An Improved BG/NBD Approach for Modeling Purchasing Behavior Using COM-Poisson Distribution. International Journal of Modeling and Optimization, 4(2), 141-145. https://doi.org/10.7763/IJMO.2014.V4.362Platzer, M. (2021). BTYDplus: Probabilistic Models for Assessing and Predicting Your Customer Base. R package version 1.2.0.Pfeifer, P. E., Haskins, M. E., and Conroy, R. M. (2005). Customer Lifetime Value, Customer Profitability, and the Treatment of Acquisition Spending [Article]. Journal of Managerial Issues, 17(1), 11-25. https://www.scopus.com/inward/record.uri?eid=2-s2.0-28444488787&partnerID=40&md5=98858b4efd66a0815a0de6cbce1dc71bRosset, S., Neumann, E., Eick, U., and Vatnik, N. (2003). Customer Lifetime Value Models for Decision Support. Data Mining and Knowledge Discovery, 7(3), 321-339. https://doi.org/10.1023/A:1024036305874Schmittlein, D. C., and Peterson, R. A. (1994). Customer Base Analysis: An Industrial Purchase Process Application. Marketing Science, 13(1), 41-67. http://www.jstor.org/stable/183755Schmittlein, 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. https://doi.org/10.1287/mnsc.33.1.1Shmueli, G., Minka, T. P., Kadane, J. B., Borle, S., and Boatwright, P. (2005). A Useful Distribution for Fitting Discrete Data: Revival of the Conway-Maxwell-Poisson Distribution [Article]. Journal of the Royal Statistical Society. Series C: Applied Statistics, 54(1), 127-142. https://doi.org/10.1111/j.1467-9876.2005.00474.xSingh, S. S., Borle, S., and Jain, D. C. (2009). A Generalized Framework for Estimating Customer Lifetime Value When Customer Lifetimes Are Not Observed [Article]. Quantitative Marketing and Economics, 7(2), 181-205. https://doi.org/10.1007/s11129-009-9065-0Thomas, J. S. (1997). Customer Equity: Managing the Customer-Firm Relationship. [Doctor Dissertation, Kellogg School of Management, Northwestern University].Xie, S.-M. (2020). Comparative Models in Customer Base Analysis: Parametric Model and Observation-Driven Model. Journal of Business Economics and Management, 21(6), 1731-1751. https://doi.org/10.3846/jbem.2020.13194Zhu, L., Sellers, K. F., Morris, D. S., and Shmueli, G. (2017). Bridging the Gap: A Generalized Stochastic Process for Count Data [Article]. American Statistician, 71(1), 71-80. https://doi.org/10.1080/00031305.2016.1234976 描述 碩士
國立政治大學
統計學系
108354016資料來源 http://thesis.lib.nccu.edu.tw/record/#G0108354016 資料類型 thesis dc.contributor.advisor 陳麗霞 zh_TW dc.contributor.advisor Chen, Li-Shya en_US dc.contributor.author (Authors) 陳琬珊 zh_TW dc.contributor.author (Authors) Chen, Wan-Shan en_US dc.creator (作者) 陳琬珊 zh_TW dc.creator (作者) Chen, Wan-Shan en_US dc.date (日期) 2021 en_US dc.date.accessioned 4-Aug-2021 14:42:22 (UTC+8) - dc.date.available 4-Aug-2021 14:42:22 (UTC+8) - dc.date.issued (上傳時間) 4-Aug-2021 14:42:22 (UTC+8) - dc.identifier (Other Identifiers) G0108354016 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/136320 - 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) 108354016 zh_TW dc.description.abstract (摘要) 隨著商業競爭加劇，企業不再單純依靠產品本身差異以維持競爭力，進而將焦點轉向個人化之服務，然而在顧客數眾多的情況下，如何評估個別顧客為企業帶來的終身價值 (customer lifetime value, 簡稱CLV或LTV) 已儼然成為重要的課題。若企業可明確知道顧客流失時點則稱為契約型關係 (contractual relations)，反之則稱為非契約型關係 (non-contractual relations)。本論文探討的是非契約型關係，考慮顧客在企業中存續時間為不可觀測之下，分別建構交易次數與顧客存續時間模型及交易金額模型之後，再依據CLV的計算公式，以預測個別顧客的CLV。不少實證研究顯示，交易次數相較於卜瓦松分配有過度離散 (overdispersion) 或不足離散 (underdispersion) 的現象，本論文乃延續 Mzoughia et al. (2018) 的做法，以Conway-Maxwell-Poisson (CMP) 分配為交易次數之分配，但修正Mzoughia et al. (2018) 的公式，納入顧客間交易次數離散現象之異質性，並進一步推導及計算出兩種CLV估計值，可分別評估顧客未來於一定期間內及至其流失為止的價值。 zh_TW dc.description.abstract (摘要) As business competition intensifies, companies no longer rely solely on the superior products to maintain their competitive edge. Instead, they turn their focuses to personalized services. When having thousands of customers, how to evaluate individual customer’s customer lifetime value (CLV or LTV) is undoubtedly a significant issue. If a company can observe exactly the time of customer dropout, then it belongs to “contractual relations”. Otherwise, it belongs to “non-contractual relations”. This thesis discusses the non-contractual relationship. Considering that the customer`s lifetime in the business is unobservable, models for the number of transactions, the customer’s lifetime and the transaction amount are constructed separately, and then the CLV formula is applied to predict the CLV of each individual customer. Several empirical studies have already shown that the numbers of transactions are sometimes being overdispersion or underdispersion compared to Poisson distribution. This thesis continues the work of Mzoughia et al. (2018) and constructs the model of number of transactions by Conway-Maxwell-Poisson (CMP) distribution, but modifies the formula of Mzoughia et al. (2018), and considers heterogeneous dispersion of the number of transactions among customers. Moreover, we derive and compute two CLV estimates, which can be used to evaluate each individual customer’s future value within a certain period and until customer dropout. en_US dc.description.tableofcontents 第一章 緒論 11.1 研究背景與動機 11.2 研究目的 2第二章 文獻回顧 42.1 CLV計算公式 42.2 交易次數與顧客存續時間模型 72.2.1 Pareto/NBD模型 72.2.2 BG/NBD模型 92.2.3 BG/GaCMP模型與Pareto/GaCMP模型 112.3 交易金額機率分配模型 172.3.1 常態分配模型 172.3.2 對數常態分配模型 182.3.3 Gamma-Gamma分配模型 19第三章 研究方法 203.1 Pareto /GaCMP模型之概似函數與相關公式推導 203.2 模型參數估計方法: MCMC法 253.3 CLV之計算 303.4 預測指標 31第四章 模擬驗證 324.1 模擬資料 324.2 模型估計結果 374.3 模型預測結果 40第五章 實證分析 495.1 資料介紹 495.2 Pareto/GaCMP模型參數估計結果 565.3 交易次數模型預測結果 595.4 CLV 預測結果 66第六章 結論與建議 73參考文獻 75 zh_TW dc.format.extent 4148873 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0108354016 en_US dc.subject (關鍵詞) 顧客終身價值 zh_TW dc.subject (關鍵詞) 非契約型關係 zh_TW dc.subject (關鍵詞) 過度離散 zh_TW dc.subject (關鍵詞) 不足離散 zh_TW dc.subject (關鍵詞) Conway-Maxwell-Poisson分配 zh_TW dc.subject (關鍵詞) Customer lifetime value (CLV) en_US dc.subject (關鍵詞) Non-contractual relations en_US dc.subject (關鍵詞) Overdispersion en_US dc.subject (關鍵詞) Underdispersion en_US dc.subject (關鍵詞) Conway-Maxwell-Poisson (CMP) distribution en_US dc.title (題名) 應用Conway-Maxwell-Poisson分配預測非契約型顧客之終身價值 zh_TW dc.title (題名) Predicting Customer Lifetime Value for Non-Contractual Relations with Application of Conway-Maxwell-Poisson Distribution en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Abe, M. (2009). "Counting Your Customers" One by One: A Hierarchical Bayes Extension to the Pareto/NBD Model. Marketing Science, 28(3), 541-553. https://doi.org/10.1287/mksc.1090.0502Berger, P. D., and Nasr, N. I. (1998). Customer Lifetime Value: Marketing Models and Applications [Article]. Journal of Interactive Marketing, 12(1), 17-30. https://doi.org/10.1002/(SICI)1520-6653(199824)12:1<17::AID-DIR3>3.0.CO;2-KBernat, J. R. (2019). Modelling Customer Lifetime Value in a Continuous, Non-Contractual Time Setting. [Master Thesis, Erasmus University]. http://hdl.handle.net/2105/45923Brockett, P. L., Golden, L. L., and Panjer, H. L. (1996) Flexible Purchase Frequency Modeling. Journal of Marketing Research, 33(1), 94–107.Borle, S., Singh, S. S., and Jain, D. C. (2008). Customer Lifetime Value Measurement [Article]. Management Science, 54(1), 100-112. https://doi.org/10.1287/mnsc.1070.0746Colombo, R., and Jiang, W. (1999). A Stochastic RFM Model. Journal of Interactive Marketing, 13(3), 2-12. https://doi.org/10.1002/(SICI)1520-6653(199922)13:3<2::AID-DIR1>3.0.CO;2-HConsul, P. C. (1989). Generalized Poisson Distributions: Properties and Applications. New York: M. Dekker.Conway, R. W. and Maxwell, W. L. (1962). A Queuing Model with State Dependent Service Rates, Journal of Industrial Engineering, 12, 132-136.Dziurzynski, L., and Wadsworth, E. (2020). BTYD: Implementing BTYD Models with the Log Sum Exp Patch. R package version 2.4.2.EsmaeiliGookeh, M., and Tarokh, M. J. (2013). Customer Lifetime Value Models: A Literature Survey. International Journal of Industrial Engineering & Production Research, 24(4), 317-336. http://ijiepr.iust.ac.ir/article-1-509-en.htmlFader, P. S., and Hardie, B. G. S. (2001). Forecasting Repeat Sales at CDNOW: A Case Study. INFORMS Journal on Applied Analytics 31 (3_supplement) S94-S107. https://doi.org/10.1287/inte.31.3s.94.9683Fader, P. S., and Hardie, B. G. S. (2009). Probability Models for Customer-Base Analysis. Journal of Interactive Marketing, 23(1), 61-69. https://doi.org/10.1016/j.intmar.2008.11.003Fader, P. S., and Hardie, B. G. S. (2013a). The Gamma-Gamma Model of Monetary. http://brucehardie.com/notes/025/Fader, P. S., and Hardie, B. G. S. (2013b). A Note on the CDNOW Master Data Set. http://www.brucehardie.com/notes/026/Fader, P. S., and Hardie, B. G. S. (2014). What’s Wrong with This CLV Formula? http://brucehardie.com/notes/033/Fader, P. S., Hardie, B. G. S., and Lee, K. L. (2005a). "Counting Your Customers" the Easy Way: An Alternative to the Pareto/NBD Model. Marketing Science, 24(2), 275-284. https://doi.org/10.1287/mksc.1040.0098Fader, P. S., Hardie, B. G. S., and Lee, K. L. (2005b). RFM and CLV: Using Iso-Value Curves for Customer Base Analysis. Journal of Marketing Research, 42(4), 415-430. https://doi.org/10.1509/jmkr.2005.42.4.415Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). Chapman and Hall/CRC. https://doi.org/10.1201/b16018Guo, J., Gabry, J., Goodrich, B., and Weber, S. (2020). rstan: R Interface to Stan. R package version 2.21.2.Jain, D., and Singh, S. S. (2002). Customer Lifetime Value Research in Marketing: A Review and Future Directions [Article]. Journal of Interactive Marketing, 16(2), 34-46. https://doi.org/10.1002/dir.10032Kotler, P., and Armstrong, G. (1996). Principles of Marketing (7th ed.). Prentice-Hall, Englewood Cliffs.Kumar V., and Reinartz, W. (2018). Customer Relationship Management (3rd ed.). Springer-Verlag Berlin Heidelberg.Minka, T. P., Shmeuli, G., Kadane, J. B., Borle, S., and Boatwright, P. (2018). Computing with the COM-Poisson Distribution. Carnegie Mellon University. Journal contribution. https://doi.org/10.1184/R1/6586508.v1Mzoughia, M. B., Borle, S., and Limam, M. (2018). A MCMC Approach for Modeling Customer Lifetime Behavior Using the COM-Poisson Distribution [Article]. Applied Stochastic Models in Business and Industry, 34(2), 113-127. https://doi.org/10.1002/asmb.2276Mzoughia, M. B., and Limam, M. (2014). An Improved BG/NBD Approach for Modeling Purchasing Behavior Using COM-Poisson Distribution. International Journal of Modeling and Optimization, 4(2), 141-145. https://doi.org/10.7763/IJMO.2014.V4.362Platzer, M. (2021). BTYDplus: Probabilistic Models for Assessing and Predicting Your Customer Base. R package version 1.2.0.Pfeifer, P. E., Haskins, M. E., and Conroy, R. M. (2005). Customer Lifetime Value, Customer Profitability, and the Treatment of Acquisition Spending [Article]. Journal of Managerial Issues, 17(1), 11-25. https://www.scopus.com/inward/record.uri?eid=2-s2.0-28444488787&partnerID=40&md5=98858b4efd66a0815a0de6cbce1dc71bRosset, S., Neumann, E., Eick, U., and Vatnik, N. (2003). Customer Lifetime Value Models for Decision Support. Data Mining and Knowledge Discovery, 7(3), 321-339. https://doi.org/10.1023/A:1024036305874Schmittlein, D. C., and Peterson, R. A. (1994). Customer Base Analysis: An Industrial Purchase Process Application. Marketing Science, 13(1), 41-67. http://www.jstor.org/stable/183755Schmittlein, 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. https://doi.org/10.1287/mnsc.33.1.1Shmueli, G., Minka, T. P., Kadane, J. B., Borle, S., and Boatwright, P. (2005). A Useful Distribution for Fitting Discrete Data: Revival of the Conway-Maxwell-Poisson Distribution [Article]. Journal of the Royal Statistical Society. Series C: Applied Statistics, 54(1), 127-142. https://doi.org/10.1111/j.1467-9876.2005.00474.xSingh, S. S., Borle, S., and Jain, D. C. (2009). A Generalized Framework for Estimating Customer Lifetime Value When Customer Lifetimes Are Not Observed [Article]. Quantitative Marketing and Economics, 7(2), 181-205. https://doi.org/10.1007/s11129-009-9065-0Thomas, J. S. (1997). Customer Equity: Managing the Customer-Firm Relationship. [Doctor Dissertation, Kellogg School of Management, Northwestern University].Xie, S.-M. (2020). Comparative Models in Customer Base Analysis: Parametric Model and Observation-Driven Model. Journal of Business Economics and Management, 21(6), 1731-1751. https://doi.org/10.3846/jbem.2020.13194Zhu, L., Sellers, K. F., Morris, D. S., and Shmueli, G. (2017). Bridging the Gap: A Generalized Stochastic Process for Count Data [Article]. American Statistician, 71(1), 71-80. https://doi.org/10.1080/00031305.2016.1234976 zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202101152 en_US
