Jonas Lindeløv Jonas Lindeløv - 2 months ago 22
R Question

Generate random numbers with fixed mean and sd

When generating random numbers in R using

rnorm
(or
runif
etc.), they seldom have the exact mean and SD as the distribution they are sampled from. Is there any simple one-or-two-liner that does this for me? As a preliminary solution, I've created this function but it seems like something that should be native to R or some package.

# Draw sample from normal distribution with guaranteed fixed mean and sd
rnorm_fixed = function(n, mu=0, sigma=1) {
x = rnorm(n) # from standard normal distribution
x = sigma * x / sd(x) # scale to desired SD
x = x - mean(x) + mu # center around desired mean
return(x)
}


To illustrate:

x = rnorm(n=20, mean=5, sd=10)
mean(x) # is e.g. 6.813...
sd(x) # is e.g. 10.222...

x = rnorm_fixed(n=20, mean=5, sd=10)
mean(x) # is 5
sd(x) # is 10


The reason I want this is that I adjust my analysis on simulated data before applying it to real data. This is nice because with simulated data I know the exact properties (means, SDs etc.) and I avoid p-value inflation because I'm doing inferential statistics. I am asking if there exist anything simple like e.g.

rnorm(n=20, mean=5, sd=10, fixed=TRUE)

Answer

Since you asked for a one-liner:

rnorm2 <- function(n,mean,sd) { mean+sd*scale(rnorm(n)) }
r <- rnorm2(100,4,1)
mean(r)  ## 4
sd(r)    ## 1
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