在 R 中模拟给定的概率密度函数

Question

The following pdf is given:

f(x)=2x/k^2, where 0 <= x <= k

Let k=10, I'm trying to simulate 100 times for this pdf, then print the first 5 results and find the mean for all 100 times results.

Answer 1

If you want to simulate with a uniform distribution between 0 and k , then you can pass runif(n, min, max) into your pdf.

f <- function(x, k) {
  return(2*x/k^2)
}

k <- 10
res <- f(runif(100, 0, k), k)
print(res[1:5])
print(mean(res))

Per MrFlick's comments, if you were instead wanting to do inverse transform sampling, this should suffice.

pdf <- function(x, k) {
  return(2*x/k^2)
}

cdf <- function(x, k){
  return(x^2/k^2)
}

icdf <- function(y, k){
  return(sqrt(k^2*y))
}

k <- 10
res <- icdf(runif(100,0,1), k)
print(res[1:5])
print(mean(res))