Comparison of some tests of fit for the Laplace distribution

Tests for the Laplace distribution based on the sample skewness and kurtosis coefficients are shown to be related to components of smooth tests of goodness of fit and are compared with a number of tests including the Anderson-Darling test, a new data-driven smooth test, a new empirical characteristic function based test and a new maximum entropy test. This last would be our slight preference as the test of choice for testing for the Laplace distribution.