An interesting if presumably hopeless question spotted on X validated: a lower-truncated Normal distribution is parameterised by its location, scale, and truncation values, μ, σ, and α. There exist formulas to derive the mean and variance of the resulting distribution, that is, when α=0, and but there is no easy way to choose (μ, σ) […]

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## truncated Normal moments

May 24, 2019## truncated normal algorithms

January 4, 2017Nicolas Chopin (CREST) just posted an entry on Statisfaction about the comparison of truncated Normal algorithms run by Alan Rogers, from the University of Utah. Nicolas wrote a paper in Statistics and Computing about a simulation method, which proposes a Ziggurat type of algorithm for this purpose, and which I do not remember reading, thanks […]

## Simulation of truncated normal variables [reprint]

July 24, 2009As I do get on a very regular basis emailed requests for reprints of my 1995 Statistics and Computing paper “Simulation of truncated normal variables”, I decided to put a reprint of the original version on arXiv. As is (or was), i.e., in the TEX format of 1992… I take the opportunity, though, to recall […]

## truncated mixtures

May 4, 2022A question on X validated about EM steps for a truncated Normal mixture led me to ponder whether or not a more ambitious completion [more ambitious than the standard component allocation] was appropriate. Namely, if the mixture is truncated to the interval (a,b), with an observed sample x of size n, this sample could be […]

## wrapped Normal distribution

April 14, 2020One version of the wrapped Normal distribution on (0,1) is expressed as a sum of Normal distributions with means shifted by all relative integers which, while a parameterised density, has imho no particular statistical appeal over the use of other series. It was nonetheless the centre of a series of questions on X validated in […]