Tests of fit for the laplace distribution, with applications

Tests are given for the Laplace or double exponential distribution. The tes t statistics are based on the empirical distribution function and include t he families of Cramer-von Mises and Kolmogorov-Smirnov. Asymptotic theory i s given, and asymptotic points are calculated, for the Cramer-von Mises fam ily, and Monte Carlo points for, finite samples are given for all the stati stics. Power studies suggest that the Watson statistic is the most powerful for the common problem of testing Laplace against other symmetric distribu tions. An application of the Laplace distribution is in LAD (or L-1) regres sion. This is also discussed in the article, with two examples.