# Statistical tolerance interval for half-normal or folded normal

I've a half-normal distribution with its $\theta$ parameter defined and I would need to compute a tolerance interval for a certain proportion of this population with a certain level of confindence. Do you know if these results are published or how may I derive them?

thanks!

• One alternative option - there are always nonparametric tolerance intervals, which should apply here as much as anywhere else. Commented Feb 25, 2016 at 6:43
• (1) Do you need a one-sided or two-sided interval? (2) If $\theta$ is truly "defined," then there's no need for a tolerance interval. A TI applies only when $\theta$ is estimated from data. It really matters how $\theta$ was estimated and what assumptions you are making about the data. Could you supply this information?
– whuber
Commented Feb 25, 2016 at 15:08
• I have estimated theta from data using maximum likelihood. By the way, the data fits really well to the half-normal distribution. I want to know if there's some closed form, but I've just used a non-parametric method. Commented Feb 25, 2016 at 15:48

## 1 Answer

The half-normal is entirely characterized by one parameter: the standard-deviation of the underlying normal distribution. One way to tackle your problem could thus be to first establish bounds on the mean of the half-normal using a method as e.g. described in 1. You could then proceed to calculate confidence intervals for quantiles/proportions or whatever you are interested by converting the upper/lower limits of the confidence interval to your measure of interest using standard-equations from 2.

Disclosure: I am not a statistician, if this procedure is wrong, please feel free to correct me.