来自R中的自定义分发的样本 [英] Sample from custom distribution in R

问题描述

我已经在R中实现了负二项式分布的替代参数化，例如(另请参见这里):

I have implemented an alternate parameterization of the negative binomial distribution in R, like so (also see here):

nb = function(n, l, a){
  first = choose((n + a - 1), a-1)
  second = (l/(l+a))^n
  third = (a/(l+a))^a
  return(first*second*third)
}

其中n是计数，lambda是均值，a是超分散项.

Where n is the count, lambda is the mean, and a is the overdispersion term.

我想从此分布中抽取随机样本，以验证我对负二项式混合模型的实现，但不确定如何执行此操作.此功能的CDF定义不容易，因此我考虑了按

I would like to draw random samples from this distribution in order to validate my implementation of a negative binomial mixture model, but am not sure how to go about doing this. The CDF of this function isn't easily defined, so I considered trying rejection sampling as discussed here, but that didn't work either (and I'm not sure why- the article says to first draw from a uniform distribution between 0 and 1, but I want my NB distribution to model integer counts...I'm not sure if I understand this approach fully.)

感谢您的帮助.

推荐答案

您似乎可以:

1)在0和1之间绘制一个统一的随机数.

1) Draw a uniform random number between zero and one.

2)在数值上积分概率密度函数(这实际上只是一个和，因为分布是离散的且下界为零).

2) Numerically integrate the probability density function (this is really just a sum, since the distribution is discrete and lower-bounded at zero).

3)积分中的任何一个值都会使CDF超过随机数，这就是您的随机抽奖.

3) Whichever value in your integration takes the cdf past your random number, that's your random draw.

因此，一起执行以下操作:

So all together, do something like the following:

r <- runif(1,0,1)
cdf <- 0
i <- -1
while(cdf < r){
  i <- i+1
  p <- PMF(i)
  cdf <- cdf + p
}

其中PMF(i)是i计数上的概率质量，由分布参数指定.当while循环结束时的i值就是您的样本.

Where PMF(i) is the probability mass over a count of i, as specified by the parameters of the distribution. The value of i when this while-loop finishes is your sample.

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