Gaussian-Laplacian mixture model for electricity market

This paper develops a statistical modeling and estimation approach combining robust regression and long tail estimation. The approach can be considered as a generalization of Huber regression in robust statistics. A mixture of asymmetric Laplace and Gaussian distributions is estimated using an EM algorithm. The approach estimates the regression model, distribution body, distribution tails, and boundaries between the body and the tails. As an application example, the model is estimated for historical power load data from an electrical utility. Practical usefulness of the model is illustrated by stochastic optimization of electricity order in day-ahead market. The computed optimal policy improves the cost compared to the baseline approach that relies on a normal distribution model.