# painful truncnorm

April 8, 2013
By

(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)

As I wanted to simulate truncated normals in a hurry, I coded the inverse cdf approach:

```truncnorm=function(a,b,mu,sigma){
u=runif(1)
u=qnorm(pnorm((a-mu)/sigma)*(1-u)+u*pnorm((b-mu)/sigma))
return(mu+sigma*u)
}
```

instead of using my own accept-reject algorithm. Poor shortcut as the method fails when a and b are too far from μ

```> truncnorm(1,2,3,4)
[1] -0.4912926
> truncnorm(1,2,13,1)
[1] Inf
```

So I introduced a control (and ended up wasting more time than if I had used my optimised accept-reject version!)

```truncnorm=function(a,b,mu,sigma){
u=runif(1)
if (pnorm((b-mu)/sigma)-pnorm((a-mu)/sigma)>0){
u=qnorm(pnorm((a-mu)/sigma)*(1-u)+u*pnorm((b-mu)/sigma))
}else{
u=-qnorm(pnorm(-(a-mu)/sigma)*(1-u)-u*pnorm(-(b-mu)/sigma))}
return(mu+sigma*u)
}
```

As shown by the above, it works, even when a=1, b=2 and μ=20. However, this eventually collapses as well and I ended up installing the msm R package that includes rtnorm, an R function running my accept-reject version. (This package was written by Chris Jackson from the MRC Unit in Cambridge.)

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