An estimation procedure for the Linnik distribution

TL;DR

This paper introduces a new, computationally simple estimation method for the parameters of the Linnik distribution, based on moments of log-transformed data, and validates it through simulations.

Contribution

It presents a novel, asymptotically unbiased estimation procedure for Linnik distribution parameters using log-moments, with improved simplicity and fewer restrictions.

Findings

Estimators are asymptotically unbiased.

The method performs well on simulated data.

Estimation algorithm is computationally efficient.

Abstract

We propose estimators for the parameters of the Linnik L$(\alpha,\gamma)$ distribution. The estimators are derived from the moments of the log-transformed Linnik distributed random variable, and are shown to be asymptotically unbiased. The estimation algorithm is computationally simple and less restrictive. Our procedure is also tested using simulated data.