从密度对象(或更广泛地从一组数字)生成随机数 [英] Generate a random number from a density object (or more broadly from a set of numbers)

问题描述

比方说，我怀疑有一组数字来自同一分布.

Let's say I have a set of numbers that I suspect come from the same distribution.

set.seed(20130613)
x <- rcauchy(10)

我想要一个函数，该函数从相同的未知分布中随机生成一个数字.我想到的一种方法是创建一个density对象，然后从中获取CDF并采用随机均匀变量(请参阅维基百科).

I would like a function that randomly generates a number from that same unknown distribution. One approach I have thought of is to create a density object and then get the CDF from that and take the inverse CDF of a random uniform variable (see Wikipedia).

den <- density(x)

#' Generate n random numbers from density() object
#' 
#' @param n The total random numbers to generate
#' @param den The density object from which to generate random numbers
rden <- function(n, den)
{
        diffs <- diff(den$x)
        # Making sure we have equal increments
        stopifnot(all(abs(diff(den$x) - mean(diff(den$x))) < 1e-9))
        total <- sum(den$y)
        den$y <- den$y / total
        ydistr <- cumsum(den$y)
        yunif <- runif(n)
        indices <- sapply(yunif, function(y) min(which(ydistr > y)))
        x <- den$x[indices]

        return(x)
}

rden(1, den)
## [1] -0.1854121

我的问题如下:

1. 是否有更好的(或内置于R中)从密度对象生成随机数的方法?
2. 关于如何从一组数字中生成随机数(除sample之外)还有其他想法吗?

1. Is there a better (or built into R) way to generate a random number from a density object?
2. Are there any other ideas on how to generate a random number from a set of numbers (besides sample)?

推荐答案

要从密度估算值生成数据，您只需随机选择一个原始数据点，然后根据密度估算值的内核添加一个随机的错误"片段，对于默认的高斯"，这意味着从原始向量中选择一个随机元素，并添加均值0和sd等于所使用带宽的随机法线:

To generate data from a density estimate you just randomly choose one of the original data points and add a random "error" piece based on the kernel from the density estimate, for the default of "Gaussian" this just means choose a random element from the original vector and add a random normal with mean 0 and sd equal to the bandwidth used:

den <- density(x)

N <- 1000
newx <- sample(x, N, replace=TRUE) + rnorm(N, 0, den$bw)

另一种选择是使用logspline包中的logspline函数拟合密度(使用另一种估算密度的方法)，然后在该包中使用rlogspline函数从估算的值中生成新数据密度.

Another option is to fit a density using the logspline function from the logspline package (uses a different method of estimating a density), then use the rlogspline function in that package to generate new data from the estimated density.

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