Discriminating Between Normal and Laplace Distributions

Abstract

Both normal and Laplace distributions can be used to analyze symmetric data. In this chapter, we consider the logarithm of the ratio of the maximized likelihoods to discriminate between these two distributions. We obtain the asymptotic distributions of the test statistics and it is observed that they are independent of the unknown parameters. When the underlying distribution is normal, the asymptotic distribution works quite well even when the sample size is small. But when the underlying distribution is Laplace, the asymptotic distribution does not work well for small sample sizes. In this case, we propose a bias corrected asymptotic distribution which works well even for small sample sizes. Based on the asymptotic distributions, minimum sample size needed to discriminate between these two distributions is obtained for a given probability of correct selection. Monte Carlo simulations are performed to examine how the asymptotic results work for small sample sizes and two data sets are analyzed for illustrative purposes.