Tests of fit for the asymmetric Laplace distribution

Tests based on the empirical distribution function (EDF) are given for the goodness-of-fit of the three-parameter asymmetric Laplace distribution. Asymptotic distributions of the test statistics are derived and their critical values are computed. For finite samples, simulated critical values of these tests are approximated by simple polynomial functions of the sample size and the shape parameter. Good matches between the asymptotic critical values and the extrapolated critical values from finite samples validate the procedure with finite samples. Power studies are reported to compare among these tests. The Anderson-Darling statistic $A^2$ gives the overall most powerful EDF tests followed by the Cramér-Von Mises statistic $W^2$.

Keywords

asymmetric Laplace distribution, empirical distribution function, goodness of fit, maximum likelihood estimation

2010 Mathematics Subject Classification

62F03

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Published 9 September 2014