包装以适合学生t分布的混合 [英] package to fit mixtures of student-t distributions

问题描述

我正在寻找一款软件(首选python，但实际上是存在jupyter内核的任何软件)，以使数据样本适合t分布的混合.

I am looking for a piece of software (python preferred, but really anything for which a jupyter kernel exists) to fit a data sample to a mixture of t-distributions.

我已经搜索了很长一段时间，这似乎是一种模糊的尝试，因为大多数搜索结果都出现了高斯混合现象(对此我不感兴趣).

I searched quite a while already and it seems to be that this is a somehwat obscure endeavor as most search results turn up for mixture of gaussians (what I am not interested here).

T迄今为止，最有前途的候选人是"AdMit"和"MitSEM" R软件包.但是我不了解R，并且发现这些软件包的描述相当复杂，似乎它们的核心目标不是拟合t的混合物，而是将其用作完成其他任务的步骤.

TThe most promising candidates so far are the "AdMit" and "MitSEM" R packages. However I do not know R and find the description of these packages rather comlple and it seems their core objective is not the fitting of mixtures of t’s but instead use this as a step to accomplish something else.

这简而言之就是我要软件完成的工作:

This is in a nutshell what I want the software to accomplish:

为某些数据拟合t分布的混合，并估计每个数据的位置"，比例"和自由度".

Fitting a mixture of t-distributions to some data and estimate the "location" "scale" and "degrees of freedom" for each.

我希望有人可以将我指向一个简单的程序包，我不敢相信这是一个晦涩的用例.

I hope someone can point me to a simple package, I can’t believe that this is such an obscure use case.

推荐答案

这似乎可行(在R中):

This seems to work (in R):

模拟示例:

 set.seed(101)
 x <- c(5+ 3*rt(1000,df=5),
        10+1*rt(10000,df=20))

适合:

 library(teigen)
 tt <- teigen(x,
        Gs=2,   # two components
        scale=FALSE,dfupdate="numeric",
        models=c("univUU")  # univariate model, unconstrained scale and df
        # (i.e. scale and df can vary between components)
 )

所有参数都相当接近(第二个组件的df除外，但这很难估计...)

The parameters are all reasonably close (except for the df for the second component, but this is a very tough thing to estimate ...)

 tt$parameters[c("df","mean","sigma","pig")]
 ## $df    ## degrees of freedom
 ## [1]  3.578491 47.059841  
 ## $mean  ## ("location")
 ##           [,1]
 ## [1,]  4.939179
 ## [2,] 10.002038
 ## $sigma    ## reporting variance rather than sd (I think?)
 ## , , 1
 ##          [,1]
 ## [1,] 8.763076
 ## , , 2
 ##          [,1]
 ## [1,] 1.041588
 ## $pig     ## mixture probabilities
 ## [1] 0.09113273 0.90886727

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