Parameter estimation of alpha-stable distributions based on MCMC
Yanling Hao, Zhi-ming Shan, Feng Chuan Shen, Dong-ze Lv · 2011
Theα-stable distribution is a very flexible tool to model NonGaussian data. Stable distributions can allow for modeling infinite variance, skewness and heavy tails, but gives rise to inferential problems related to the estimation of the stable distribution parameters. In this work, we study the estimation ofα-stable distributions using numerical Bayesian sampling techniques such as Markov chain Monte Carlo (MCMC), which can simultaneously estimate the four parameters of the model with good performance. Metropolis-Hastings algorithm is used to update the parameters ofα-stable distribution at every iteration. The simulation results show that our estimation method is capable of estimating all the parameters accurately.