零膨脹

零膨脹模型（英語：Zero-inflated models）是人們在社會科學、自然中的計數資料的實際研究中，觀察事件發生數中含有大量的零值。例如保險索賠次數，索賠數為0的概率很高，否則保險公司就面臨破產風險。這種數據數資料中的零值過多，超出了Poisson分佈等一般離散分佈的預測能力。零膨脹這個概念首先是由 Lambert在1992年的論文「Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing」中提出^[1].。

1994年, Greene根據Lambert的方法提出了零膨脹負二項模型 (ZINB)^[2]。 2000年, Daniel根據Lambert的方法提出了零膨脹二項模型 (ZIB)^[3]。

註釋參考

^ Lambert, Diane. Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics. 1992, 34 (1): 1–14 [2012-12-14]. （原始內容存檔於2021-03-08）.
^ Greene, William H. Some Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models. Working Paper EC-94-10: Department of Economics, New York University. 1994 [2015-02-23]. （原始內容存檔於2020-11-01）.
^ B. Hall, Daniel. Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study. Biometrics. 2000, 56 (4): 1030–1039 [2012-12-14]. （原始內容存檔於2017-11-01）.

[1] Lambert, Diane. Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics. 1992, 34 (1): 1–14 [2012-12-14]. （原始內容存檔於2021-03-08）.

[2] Greene, William H. Some Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models. Working Paper EC-94-10: Department of Economics, New York University. 1994 [2015-02-23]. （原始內容存檔於2020-11-01）.

[3] B. Hall, Daniel. Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study. Biometrics. 2000, 56 (4): 1030–1039 [2012-12-14]. （原始內容存檔於2017-11-01）.

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