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Truncated Normal and Student's t-distribution toolbox

version 2.0 (839 KB) by Zdravko Botev
Perfect simulation from the truncated (multivariate) normal and student's t-distribution.


Updated 04 Feb 2016

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The toolbox includes:
1. fast random number generators from the truncated univariate and multivariate student/normal distributions;
2. (Quasi-) Monte Carlo estimator of the cumulative distribution function of the multivariate student/normal;
3. accurate computation of the quantile function of the normal distribution in the extremes of its tails.
Z. I. Botev (2017), The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting, Journal of the Royal Statistical Society, Series B, Volume 79, Part 1, pp. 1-24

Cite As

Zdravko Botev (2020). Truncated Normal and Student's t-distribution toolbox (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (3)


Thanks for your sampling method and it really helped me a lot, but when I tried the scalar case, error always occurred saying that
Inner matrix dimensions must agree.
Error in cholperm (line 20)

Could you please take a look at it?

What can I do to sample from a truncated multivariate Gaussian with non-zero mean when the number of inequality constraints is greater than the dimensionality of the random vector (matrix A is not squared)?

Thanks for sharing. Best regards

Thanks for making this toolbox available!



- toolbox can now deal with multivariate truncated Student's t-distribution
- updated reference

MATLAB Release Compatibility
Created with R2015b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired by: Truncated Normal Generator

Inspired: Truncated Normal Generator