On von Mises type conditions for p-max stable laws, rates of convergence and generalized log Pareto distributions

In this article we obtain an alternative formulation of the von Mises type conditions for p-max stable laws in terms of generalized log Pareto distributions (glogPds). Relationship between the rate of convergence of extremes and the remainder terms in the von Mises type conditions is investigated. It is shown that the rate of convergence in the von Mises type conditions for p-max stable laws determines the distance of the underlying distribution function from a glogPd.