Objective Bayesian Analysis of the Yule-Simon Distribution with Applications

TL;DR

This paper develops objective Bayesian priors for the Yule-Simon distribution, a model for frequency data, and evaluates their performance through simulations and real data analysis.

Contribution

It introduces two new objective priors for the Yule-Simon distribution, filling a gap in Bayesian analysis of this distribution.

Findings

Jeffreys prior and loss-based prior perform well in simulations

The priors provide meaningful inference on real datasets

The approach enhances Bayesian methods for frequency data analysis

Abstract

The Yule-Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule-Simon distribution. In particular, we discuss the Jeffreys prior and a loss-based prior, which has recently appeared in the literature. We illustrate the performance of the derived priors through a simulation study and the analysis of real datasets.