What is the distribution of absolute value of a normally distributed random variable?

Many would probably say the “truncated normal”. I used to think the same but this answer is wrong. The right answer is another distribution named the “folded normal”. In this short paper I introduce a stochastic frontier model with a *folded normal* inefficiency distribution. I show how it can be estimated using a maximum likelihood approach and apply the model to two data sets and compare the results to those from the truncated normal model.

My little experience with this model indicate that it has a reasonable performance although it does not often outperform the popular truncated normal model. The potential advantage is that it is more tractable where modelling of inefficiencies is of interest (something that I plan to pursue some time in the future).

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Posted by Sriram on October 4, 2015 at 10:38 am

How would Chi-square distribution compare with FN and TN for efficiency analysis?

Posted by Reza on October 5, 2015 at 1:09 am

The standard Chi-squared distribution depends on one parameter and can be used an alternative to half-normal or exponential distributions. There are many one-sided distributions that one can use, the point is that there should be something interesting in a new proposal (I can’t see anything particularly interesting about Chi Squared). In case of folded normal, I have the feeling that it is well-suited for modelling of inefficiency effects e.g. allowing for correlations between the effects.