Laplace distribution : Properties, regression model and simulation

摘要

The Laplace distribution with two parameters is studied here. Some properties were demonstrated, such as, quantile function, media, mode, variance, analytical expressions for generating function of moments and cumulants. The estimators of the method of moments and maximum likelihood were discussed, with a comparison between these two methods using Monte Carlo simulation. Subsequently, we propose the Laplace regression model, where the parameter estimates are made by maximum likelihood. To show the performance of this model, a Monte Carlo simulation was performed.