In 2005, we developped a first method to generate random variables distributed from a Gaussian distribution defined on a semi-finite interval [a,+∞[. This method was implemented in Scilab, Matlab and Java.

Following the article published in 2011 by Nicolas Chopin, we have developped a method to simulate a Gaussian distribution defined on a finite interval [a,b]. This method is still able to consider semi-finite interval by setting b=+∞. The principle is to divide the interval into regions with the same area where acceptation-reject algorithms with appropriate distributions are used.

Nicolas Chopin's methodis coded in C, but only on a semi-finite interval [a,+∞[. We extend his method to a finite interval [a,b], following its recommandations. The method is implemented in Matlab and C++; it is faster than our former implementation and also allows to consider a finite interval. However, it is still not able to generate a random vector, contrary to the version of 2005.

The following table summarize the implementations and their characteristics, as well as similar implementations in other languages :

I did not compare theses implementations with the truncnorm function in Scipy.

• N. Chopin, « Fast simulation of truncated Gaussian distributions », Statistics and Computing 21, 2011.
• V. Mazet, « Simulation d'une distribution gaussienne tronquée sur un intervalle fini », technical report, Université de Strasbourg/CNRS, 2012