如何最好地使用其概率函数模拟任意单变量随机变量? [英] How do I best simulate an arbitrary univariate random variate using its probability function?

问题描述

在R中，如果仅可用其概率密度函数，那么模拟任意单变量随机变量的最佳方法是什么?

In R, what's the best way to simulate an arbitrary univariate random variate if only its probability density function is available?

推荐答案

在仅提供密度的情况下，这是cdf逆方法的(慢速)实现.

Here is a (slow) implementation of the inverse cdf method when you are only given a density.

den<-dnorm #replace with your own density

#calculates the cdf by numerical integration
cdf<-function(x) integrate(den,-Inf,x)[[1]]

#inverts the cdf
inverse.cdf<-function(x,cdf,starting.value=0){
 lower.found<-FALSE
 lower<-starting.value
 while(!lower.found){
  if(cdf(lower)>=(x-.000001))
   lower<-lower-(lower-starting.value)^2-1
  else
   lower.found<-TRUE
 }
 upper.found<-FALSE
 upper<-starting.value
 while(!upper.found){
  if(cdf(upper)<=(x+.000001))
   upper<-upper+(upper-starting.value)^2+1
  else
   upper.found<-TRUE
 }
 uniroot(function(y) cdf(y)-x,c(lower,upper))$root
}

#generates 1000 random variables of distribution 'den'
vars<-apply(matrix(runif(1000)),1,function(x) inverse.cdf(x,cdf))
hist(vars)

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