Parameter estimation of alpha-stable distributions based on MCMC

The^α -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 of^α -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 of^α -stable distribution at every iteration. The simulation results show that our estimation method is capable of estimating all the parameters accurately.