A small sample comparison of maximum likelihood, moments and L-moments methods for the asymmetric exponential power distribution

Three methods of estimation, namely maximum likelihood, moments and LL-moments, when data come from an asymmetric exponential power distribution are considered. This is a very flexible four-parameter family exhibiting variety of tail and shape behaviours. The analytical expression of the first four L-moments of these distributions are derived, allowing for the use of L-moments estimators. A simulation study compares the three estimation methods in small samples.