Why Mixture of Probability Distributions?

If we have two random variables ξ_1 and ξ_2, then we can form their mixture if we take ξ_1 with some probability w and ξ_2 with the remaining probability 1-w. The probability density function (pdf ). ϱ(x) of the mixture is a convex combination of the pdfs of the original variables: ϱ(x) = w．ϱ_1(x) + (1 - w)．ϱ_2(x). A natural question is: can we use other functions f(ϱ_1, ϱ_2) to combine the pdfs, i.e., to produce a new pdf ϱ(x) = f(ϱ_1(x), ϱ_2(x))? In this paper, we prove that the only combination operations that always lead to a pdf are the operations f(ϱ_1, ϱ_2) = w．ϱ_1 + (1 - w)．ϱ_2 corresponding to mixture.

關鍵字

Probability distribution ； Mixture

被引用紀錄

葉昇龍（2001）。線狀液晶摻雜碳奈管的光耦合效應〔碩士論文，中原大學〕。華藝線上圖書館。https://doi.org/10.6840/cycu200100323

楊世忠（2007）。低能量雷射照射對皮膚傷口癒合之探討〔碩士論文，中山醫學大學〕。華藝線上圖書館。https://doi.org/10.6834/CSMU.2007.00008

徐英綺（2014）。動態線掃描頻域光學同調斷層掃描儀即時監測塗膜品質之研究〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2014.10906

蔡宏隆（2007）。含1,2,4-三氮唑結構之聚芳香醚之合成和性質〔碩士論文，國立臺北科技大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0006-1308200719443700

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Why Mixture of Probability Distributions?

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