Testing goodness-of-fit for Laplace distribution based on maximum entropy

Abstract

This article presents the goodness-of-fit tests for the Laplace distribution based on its maximum entropy characterization result. The critical values of the test statistics estimated by Monte Carlo simulations are tabulated for various window and sample sizes. The test statistics use an entropy estimator depending on the window size; so, the choice of the optimal window size is an important problem. The window sizes for yielding the maximum power of the tests are given for selected sample sizes. Power studies are performed to compare the proposed tests with goodness-of-fit tests based on the empirical distribution function. Simulation results report that entropy-based tests have consistently higher power than EDF tests against almost all alternatives considered.

Keywords:

• Laplace distribution
• Maximum entropy
• Entropy estimator
• Goodness-of-fit test

Acknowledgements

The authors would like to thank the referees for their invaluable comments and suggestions that improved much of the original article. The second author was supported by the Korea University Research Fund.