Estimation for Strictly Positive Stable Laws

Abstract—Positive stable laws have become a standard tool in modelling heavy tailed data in such diverse areas as finance, engineering and survival analysis. Due to the non–existence of closed–form expression for the corresponding densities, standard procedures for estimation of the parameters of positive stable distributions appear to be computationally expensive. In this note we show that the first two moments of negative order provide a straightforward estimation procedure, in which the solution of the resulting equations exists, and leads to unique moment estimates for the parameters involved. Simulations and application of this method on real data are also included. Keywords: stable distribution, moment estimation, heavy tails, skewness

• Type: Conference
• Year: 2007
• Where: WCE
• Authors: Simos G. Meintanis
• Keywords: Abstract—Positive Stable Laws, Positive Stable Distributions, Stable Distribution, WCE 2007, WCE 2008