(This article was first published on

**Xi'an's Og » R**, and kindly contributed to R-bloggers)**A**s 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

**S**o 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) }

**A**s 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.)

Filed under: R, Statistics Tagged: Monte Carlo Statistical Methods, msm package, quantile function, R, rtnorm function, simulation, truncated normal

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