The double half-normal distribution and its extensions

Abstract

We use the difference of two half-normal random variables as a device to generate a class of distributions whose members have Gaussian functional forms but possess the characteristic kink of the Laplace distribution and exhibit positive excess kurtosis. These distributions provide data-modeling tools alternative to the use of the Laplace distribution, but they also have applications wherever absolute values of normal random variables appear, for example in relation to the absolute error of estimators and predictors, but also in Brownian motion theory. We provide Monte Carlo evidence related to the performance of maximum likelihood estimation of the distribution.