R：从概率密度分布生成数据

Question

Say I have a simple array, with a corresponding probability distribution.

library(stats)    
data <- c(0,0.08,0.15,0.28,0.90)
pdf_of_data <- density(data, from= 0, to=1, bw=0.1)

Is there a way I could generate another set of data using the same distribution. As the operation is probabilistic, it need not exactly match the initial distribution anymore, but will be just generated from it.

I did have success finding a simple solution on my own. Thanks!

Answer 1

From the examples in the documentation of ?density you (almost) get the answer.

So, something like this should do it:

library("stats")    
data <- c(0,0.08,0.15,0.28,0.90)
pdf_of_data <- density(data, from= 0, to=1, bw=0.1)

# From the example.
N <- 1e6
x.new <- rnorm(N, sample(data, size = N, replace = TRUE), pdf_of_data$bw)

# Histogram of the draws with the distribution superimposed.
hist(x.new, freq = FALSE)
lines(pdf_of_data)

You can just reject the draws outside your interval as in rejection sampling. Alternatively, you can use the algorithm described in the link.

Answer 2

Your best bet is to generate the empirical cumulative density function, approximate the inverse, and then transform the input.

The compound expression looks like

random.points <- approx(
  cumsum(pdf_of_data$y)/sum(pdf_of_data$y),
  pdf_of_data$x,
  runif(10000)
)$y

Yields

hist(random.points, 100)

Answer 3

从曲线中画出：

sample(pdf_of_data$x, 1e6, TRUE, pdf_of_data$y)