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 :
| Code | Author | Year | Size | Language | Dimensions | Truncation Interval |
|---|---|---|---|---|---|---|
| truncgauss | N. Chopin | 2011 | 462 kb | C/Python | 1/2 | semi-finite/semi-finite or finite |
| rpnorm | V. Mazet | 2005 | 2 kb | Matlab | 1 or greater | semi-finite |
| rpnorm | V. Mazet | 2005 | 2 kb | Scilab | 1 or greater | semi-finite |
| rpnorm | B. Perret, V. Mazet | 2010 | 4 kb | Java | 1 or greater | semi-finite |
| rtnorm | V. Mazet | 2012 | 58 kb | Matlab | 1 | semi-finite or finite |
| rtnorm | G. Dollé, V. Mazet | 2012 | 67 kb | C++ | 1 | semi-finite or finite |
| rtnorm | C. Lassner | 2013 | 60 kb | Python | 1 | semi-finite or finite |
| dtnorm | Alan R. Rogers | 2016 | 232 kb | C | 1 | finite |
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