A parsimonious dynamic mixture for heavy-tailed distributions

Abstract

Dynamic mixture distributions are convenient models for highly skewed and heavy-tailed data. However, estimation has proved to be challenging and computationally expensive. To address this issue, we develop a more parsimonious model, based on a one-parameter weight function given by the exponential cumulative distribution function. Parameter estimation is carried out via maximum likelihood, approximate maximum likelihood and noisy cross-entropy. Simulation experiments and real-data analyses suggest that approximate maximum likelihood is the best method in terms of RMSE, albeit at a high computational cost. With respect to the version of the dynamic mixture with weight equal to the two-parameter Cauchy cumulative distribution function, the reduced flexibility of the present model is more than compensated by better statistical and computational properties.