A link between two-sided power and asymmetric Laplace distributions: with applications to mean and variance approximations

Motivated by our investigations of refinements of the project evaluation and review technique (PERT), we have developed a reparameterization of the asymmetric Laplace distribution and found it to be a useful tool for extending and improving various three-point approximations of continuous distributions (pioneered by Pearson and Tukey (Biometrika 52(3/4) (1965) 533)) by specifying the values of two quantiles and the mode.