415 – General Methodology
An Introduction to M-Distributions
David Vaughan
Wilfrid Laurier University
A highly flexible class of distributions, called mixed tail or M-distributions, is introduced, and fundamental properties discussed. M-distributions allow not only a vast array of combinations of skewness and kurtosis, but also permit very different tail behaviours. For example, one tail can be (essentially) normal and the other Cauchy; or one tail can be exponential and the other Student's t. The densities are explicit functions, and have as many moments as the thickest tail distribution. Because the centre of these distributions is smooth, maximum likelihood can be used in parameter estimation. In this talk, motivation for such distributions as models is presented, as are some of the fundamental model fitting methods for M-distributions.
