*WINNER* On the Location-Scale Gaussian Mixture of the Laplace Distribution with Applications

Abstract

The Laplace distribution has historically had statistical applications in image and speech recognition, hydrology, and finance. The distribution is characterized by having a sharper peak at the center than that of the Normal distribution. Ding and Blitzstein (2016) present a novel and simple approach based on moment generating functions and conditioning to show the Laplace distribution could be represented using a mixture of Exponential and standard Normal variables. We extend their approach to include a scale and location parameter and model to fit highway speed data. The symmetry of the Laplace distribution does not appear to represent the data well. Further modeling efforts employ an asymmetric Laplace distribution. We compare the goodness of fit of the symmetric and asymmetric distributions on the speed data using the Akaike information criterion.