Test of fit for a Laplace distribution against heavier tailed alternatives

Over the last decade there has been a marked interest in a Laplace distribution and its properties and generalizations, especially in the framework of financial applications. Such an interest has led to a revision and discussion of available goodness-of-fit procedures for a Laplace distribution. Indeed, since most of the studies which employ the Laplace distribution are concerned with modelling heavy tailed patterns, the modern class of possible alternatives is way broader than just testing the Laplace vs. normal distribution. In this paper we propose a new test of fit for a Laplace distribution against deviations with heavier tails than that of the reference Laplace distribution. The proposed goodness-of-fit procedure is based on sample skewness and kurtosis and a robust L1L1 estimator of scale about a sample median. The developed test statistic is shown to asymptotically follow a χ2χ2-distribution with two degrees of freedom. Performance of the new goodness-of-fit test is illustrated by simulations and a case study.