# 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?

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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

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

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