如何最好地使用其概率函数模拟任意单变量随机变量?

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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