问题
For a normalized probability density function defined on the real line, for example
p(x) = (2/pi) * (1/(exp(x)+exp(-x))
(this is just an example; the solution should apply for any continuous PDF we can define) is there a package in R to simulate from the distribution? I am aware of R's built-in simulators for many distributions.
I could numerically compute the inverse cumulative distribution function at a set of quantiles, store them in a table, and use the table to map from uniform variates to variates from the desired distribution. Is there already a package that does this?
回答1:
Here is a way using the distr package, which is designed for this.
library(distr)
p <- function(x) (2/pi) * (1/(exp(x)+exp(-x))) # probability density function
dist <-AbscontDistribution(d=p) # signature for a dist with pdf ~ p
rdist <- r(dist) # function to create random variates from p
set.seed(1) # for reproduceable example
X <- rdist(1000) # sample from X ~ p
x <- seq(-10,10, .01)
hist(X, freq=F, breaks=50, xlim=c(-5,5))
lines(x,p(x),lty=2, col="red")
You can of course also do this is base R using the methodology described in any one of the links in the comments.
回答2:
If this is the function that you're dealing with, you could just take the integral (or, if you're rusty on your integration rules like me, you could use a tool like Wolfram Alpha to do it for you).
In the case of the function provided, you can simulate with:
draw.val <- function(numdraw) log(tan(pi*runif(numdraw)/2))
A histogram confirms that we're sampling correctly:
hist(draw.val(10000), breaks=100, probability=T)
x <- seq(-10, 10, .001)
lines(x, (2/pi) * (1/(exp(x)+exp(-x))), col="red")
来源：https://stackoverflow.com/questions/23570952/simulate-from-an-arbitrary-continuous-probability-distribution