Parameter estimates of alpha-stable distribution and Hurst coefficients

Abstract

This paper presents a comparison of six different methods of estimating parameters for alpha-stable distributions on simulated and real data. Subsequently, the paper numerically investigates the relationship between estimated Hurst coefficients of the data used to fit alpha-stable distributions and the parameters of the distribution. Alpha-stable distributions are important since many real-life data cannot be represented by traditional distributions and the numerical investigation relating to the Hurst coefficient is motivated by the fact that many of such real-life data are rich in multifractality. The real data used for this study relate to rainfall and streamflow data, which are known to have a strong multifractal signature, and a traditional distribution usually fails to fit such data. The authors show that a connection between parameter estimates of alpha-stable distributions fitted to data rich in multifractality with their Hurst coefficient may exist. Based on the simulation study, it has been noted that out of the six parameter estimation approaches, the maximum-likelihood-based parameter estimation and the empirical-characteristic-function-based parameter estimation approaches are superior in obtaining a better estimate of the four alpha-stable parameters, which leads to reduced error in quantile estimation.