Subsample to follow a normal distribution

I have a problem, that sounds very simple in theory but I fail to implement a good solution.

Let my data be a sample of a continuous variable that that follows a normal distribution (m1,v1), associated with some other variables for each point. I want to get a subsample of this data where this variable will follow a different normal distribution (m2,v2). I am interested in the other associated variables, so my aim is just how to subsample my dataset.

m1, v1, m2, v2 are known.

In all the examples, we sample from a normal distribution with mean 10 and target a distribution with mean 8.

Following random subsample with uniform distribution in R which is closer to my question I tried to adapt the method from the answer:

## simulate a sample normally distributed
m1=10
v1=3
N=10000
dist1=rnorm(N,m1,v1)
## define my target distribution
m2=8
v2=3

d=dnorm(dist1,m1,v1)
dist2=dist1[sample(1:N,N,replace=T,dnorm(dist1,m2,v2)*1/d)]
## check
mean(dist2)
 8.04835
sd(dist2)
 2.982235

And this seems to work ... BUT I noticed we were slightly off, so I performed 10000 such simulations to check

d=dnorm(dist1,m1,v1)
meantot=0
sdtot=0
for(i in 1:10000)
{dist2=dist1[sample(1:N,N,replace=T,dnorm(dist1,m2,v2)*1/d)]
## check
meantot=mean(dist2)+meantot
sdtot=sd(dist2)+sdtot
}
meantot/10000
 8.046662
sdtot/10000
 2.982252

And I repeat this procedure several times, and we stay slightly above the mean. My intuition is that we may fail to have enough numbers before 8 to match exactly the distribution. This small discrepancy could potentially be a problem for my study. Are there any better method for this ? Surely there must have been some work in the past on such problems ?

• I do not understand your problem description. Data does not "follow a distribution". It was sampled from a distribution and the distribution can often be sufficiently described by a standard distribution model. You can sample conditionally from a sample, even in a way that ensures certain properties, but I don't understand how that does relate to "a different normal distribution". – Roland Feb 21 '17 at 13:00
• Ok my bad, I must have used the wrong terminology, but I have my sample that happens to fit a normal distribution (m1,v1) and I want to obtain a subsample that happens to follow a normal distribution (m2,v2). I am not equipped to say it in better terms than this, but please help me rephrase if you think that's necessary – z_fly_away Feb 21 '17 at 13:09
• I can't help with terminology because I don't get what you are trying to do. – Roland Feb 21 '17 at 13:29