Testing for the generalized normal-Laplace distribution with applications

The generalized normal-Laplace distribution is a useful law for modelling asymmetric data exhibiting excess kurtosis. Goodness-of-fit tests for this distribution are constructed which utilize the corresponding moment generating function, and its empirical counterpart. The consistency and other properties of the test are investigated under general assumptions, and the proposed procedure is applied, following a non-trivial estimation step, to test the fit of some financial data.