DistributionFitTest[] 用于 Mathematica 中的自定义分布 [英] DistributionFitTest[] for custom distributions in Mathematica

问题描述

我有两个自定义分布的 PDF 和 CDF，一种为每个分布生成 RandomVariates 的方法，以及用于将参数拟合到数据的代码.我之前在以下位置发布了一些代码:

I have PDFs and CDFs for two custom distributions, a means of generating RandomVariates for each, and code for fitting parameters to data. Some of this code I've posted previously at:

在 Mathematica 中计算自定义分布的期望

其中一些如下:

nlDist /: PDF[nlDist[alpha_, beta_, mu_, sigma_], 
   x_] := (1/(2*(alpha + beta)))*alpha* 
   beta*(E^(alpha*(mu + (alpha*sigma^2)/2 - x))* 
      Erfc[(mu + alpha*sigma^2 - x)/(Sqrt[2]*sigma)] + 
     E^(beta*(-mu + (beta*sigma^2)/2 + x))* 
      Erfc[(-mu + beta*sigma^2 + x)/(Sqrt[2]*sigma)]); 

nlDist /: 
  CDF[nlDist[alpha_, beta_, mu_, sigma_], 
   x_] := ((1/(2*(alpha + beta)))*((alpha + beta)*E^(alpha*x)* 
        Erfc[(mu - x)/(Sqrt[2]*sigma)] - 
       beta*E^(alpha*mu + (alpha^2*sigma^2)/2)*
        Erfc[(mu + alpha*sigma^2 - x)/(Sqrt[2]*sigma)] + 
       alpha*E^((-beta)*mu + (beta^2*sigma^2)/2 + alpha*x + beta*x)*
        Erfc[(-mu + beta*sigma^2 + x)/(Sqrt[2]*sigma)]))/ 
   E^(alpha*x);         

dplDist /: PDF[dplDist[alpha_, beta_, mu_, sigma_], x_] := 
  PDF[nlDist[alpha, beta, mu, sigma], Log[x]]/x;
dplDist /: CDF[dplDist[alpha_, beta_, mu_, sigma_], x_] := 
  CDF[nlDist[alpha, beta, mu, sigma], Log[x]];

nlDist /: DistributionDomain[nlDist[alpha_, beta_, mu_, sigma_]] := 
 Interval[{-Infinity, Infinity}]

nlDist /: 
    Random`DistributionVector[
    nlDist [alpha_, beta_, mu_, sigma_], n_, prec_] :=
    RandomVariate[ExponentialDistribution[alpha], n, 
        WorkingPrecision -> prec] - 
      RandomVariate[ExponentialDistribution[beta], n, 
        WorkingPrecision -> prec] + 
      RandomVariate[NormalDistribution[mu, sigma], n, 
        WorkingPrecision -> prec];

dplDist /: 
    Random`DistributionVector[
    dplDist[alpha_, beta_, mu_, sigma_], n_, prec_] :=
    Exp[RandomVariate[ExponentialDistribution[alpha], n, 
         WorkingPrecision -> prec] - 
       RandomVariate[ExponentialDistribution[beta], n, 
         WorkingPrecision -> prec] + 
       RandomVariate[NormalDistribution[mu, sigma], n, 
         WorkingPrecision -> prec]];

如果有人需要查看代码，我可以发布更多代码，但我认为以上内容可以很好地说明目前的方法.

I can post more of the code if someone needs to see it, but I think the above gives a good sense of the approach so far.

现在我需要一种方法来将 DistributionFitTest[] 与这些分布一起使用，如下所示:

Now I need a way to use DistributionFitTest[] with these distributions in something like this:

DistributionFitTest[data, dplDist[3.77, 1.34, -2.65, 0.40],"HypothesisTestData"]  

啊，但这行不通.相反，我收到一条错误消息，开头为:

Ah, but this doesn't work. Instead I get an error message that starts out as:

"论据dplDist[3.77,1.34,-2.65,0.4] 应该是一个有效的分布..."

"The argument dplDist[3.77,1.34,-2.65,0.4] should be a valid distribution..."

因此 DistributionFitTest[] 似乎无法将这些分布识别为分布.

So it appears that DistributionFitTest[] doesn't recognize these distributions as distributions.

我不认为在这种情况下使用 TagSet 会有什么帮助，除非可以使用 TagSet 为 DistributionFitTest[] 提供识别这些自定义分布所需的信息.

I don't see how using TagSet would help in this instance, unless one can use TagSet to give DistributionFitTest[] what it needs to identify these custom distributions.

谁能告诉我让这个工作的方法?我想将 DistributionFitTest[] 与这样的自定义分布一起使用，或者找到一些解决方法来评估拟合优度.

Can anyone advise me of a way to get this to work? I'd like to use DistributionFitTest[] with custom distributions like this or find some work around to assess goodness of fit.

Thx -- Jagra

Thx -- Jagra

推荐答案

由于这个问题已经出现很多次了，我认为现在是提供一些如何正确地为 v8 定制发行版的食谱的最佳时机.

Since this question has come up many times, I think it's prime time to furnish some recipes for how to properly cook a custom distribution for v8.

使用 TagSet 为您的发行版定义:

Use TagSet to define for your distribution:

1. DistributionParameterQ、DistributionParameterAssumptions、DistributionDomain
2. 定义PDF、CDF、SurvivalFunction、HazardFunction
3. 通过编码Random`DistributionVector来定义随机数生成代码

这样做将使除参数估计外的所有内容都适用于您的分布.

Doing so will make everything but parameter estimation work for your distribution.

你的错误是 dplDist 没有 DistributionDomain 定义，nlDist 和 dplDist 都没有DistributionParameterQ 和 DistributionParameterAssumptions 定义.

Your mistake was that dplDist had no DistributionDomain definition, and both nlDist and dplDist did not have DistributionParameterQ and DistributionParameterAssumptions definitions.

我在您的定义中添加了以下内容:

I added to your definitions the following:

dplDist /: DistributionDomain[dplDist[alpha_, beta_, mu_, sigma_]] := 
 Interval[{-Infinity, Infinity}]

nlDist /: 
 DistributionParameterQ[nlDist[alpha_, beta_, mu_, sigma_]] := ! 
  TrueQ[Not[
    Element[{alpha, beta, sigma, mu}, Reals] && alpha > 0 && 
     beta > 0 && sigma > 0]]

dplDist /: 
 DistributionParameterQ[dplDist[alpha_, beta_, mu_, sigma_]] := ! 
  TrueQ[Not[
    Element[{alpha, beta, sigma, mu}, Reals] && alpha > 0 && 
     beta > 0 && sigma > 0]]

nlDist /: 
 DistributionParameterAssumptions[
  nlDist[alpha_, beta_, mu_, sigma_]] := 
 Element[{alpha, beta, sigma, mu}, Reals] && alpha > 0 && beta > 0 && 
  sigma > 0

dplDist /: 
 DistributionParameterAssumptions[
  dplDist[alpha_, beta_, mu_, sigma_]] := 
 Element[{alpha, beta, sigma, mu}, Reals] && alpha > 0 && beta > 0 && 
  sigma > 0

现在它起作用了:

In[1014]:= data = RandomVariate[dplDist[3.77, 1.34, -2.65, 0.40], 100];

In[1015]:= DistributionFitTest[data, dplDist[3.77, 1.34, -2.65, 0.40],
  "HypothesisTestData"]

Out[1015]= HypothesisTestData[<<DistributionFitTest>>]

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