# When is half normal distribution useful?

Julian Faraway, in his book on linear model with R, used half normal plot to find hat(a value in hat matrix) with too large value.

That's the only example where I saw half normal distribution is used. But other than that, I can't come up with real application of it though I guess it might be useful for approximating some positive numbers whose mean is near zero.

What are real applications of it?

• Because the square root of a $\chi^2(1)$ variable is half normal, most applications involving chi squared values with 1 degree of freedom can be interpreted as applications of a half-normal model. – whuber Dec 27 '11 at 21:10
• The half normal is used in the EGARCH specification for asymmetric volatility modelling. – user11978 Jun 14 '12 at 3:41

## 2 Answers

In quality control, there is something called a moving-range statistic which is the absolute value of successive differences. The half-normal serves as the basis of the chart as discussed in the following article:

http://www.tandfonline.com/doi/abs/10.1080/08982119508904612#preview

In Bayesian statistics the half normal,with a sufficiently large variation parameter, can be used as a noninformative prior distribution on the SD of a standard distribution. This is suggested in, for example:

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian analysis, 1, 515-534.

• It's true that you use it, but if you do it's typically NOT noninformative, since then you could also use a more typical/easier noninformative prior like gamma or the uniform. The half-t makes more sense as a weakly informative prior, which has a distinct tendency but wide enough tails to let itself be overwhelmed by the data in the face of strong evidence. – Erik Nov 13 '12 at 12:00