On asymmetric generalization of the Weibull distribution by scale-location mixing of normal laws

Two approaches are suggested to the definition of asymmetric generalized Weibull distribution. These approaches are based on the representation of the two-sided Weibull distributions as variance-mean normal mixtures or more general scale-location mixtures of the normal laws. Since both of these mixtures can be limit laws in limit theorems for random sums of independent random variables, these approaches can provide additional arguments in favor of asymmetric two-sided Weibull-type models of statistical regularities observed in some problems related to stopped random walks, in particular, in problems of modeling the evolution of financial markets.