Laplace-Weibull Mixtures for Modeling Price Changes

B. Mandelbrot and E. Fama in the sixties, and W. Ziemba in the seventies, suggested stable laws for modeling stock returns and commodity prices. Geometric stable distributions, with Laplace distribution playing the role of a "normal" law, have been found to give better fit to such data. We study the "stability" properties of Laplace and a mixture of Laplace and Weibull and discuss the statistical inference for such mixture models. Application of the mixture distribution to modeling price changes in real estate prices in France is given.