Data driven estimates for mixtures

Data with asymmetric heavy tails can arise from mixture of data from multiple populations or processes. We propose a computer intensive procedure to fit by quasi-maximum likelihood a mixture model to a robustly standardized data set. The robust standardization of the data set results in well defined tails which are modeled using extreme value theory. The data are assumed to be a mixture of a normal distribution contaminated by a distribution with heavy tails. This procedure provides an analytical expression for the mixture distribution of the data, which may be used in simulations and construction of scenarios, while providing an accurate estimation of quantiles associated with probabilities close to zero or one. The performance of the proposed data driven procedure is assessed by simulation experiments and also by its application to real data.