Bayesian Statistics with the Zipf-Polylog distribution

V. Peña Pizarro, A. Duarte-López, M. Pérez Casany

The Zipf-Polylog is a discrete probability distribution that contains the Zipf, the Log-series and the Geometric distributions as particular cases. It is well known that the Zipf distribution is linear in log-log scale while real data are usually only linear in the tail. In log-log scale, the Zipf-Polylog shows a log-concave pattern, as most of the real datasets do, while maintaining the linearity in the tail. This makes it very attractive from a practical point of view.
In this work the Zipf-Polylog distribution is studied from a Bayesian point of view. Given that the distribution is an exponential family, it has a conjugate prior distribution that will be determined. The parameter interpretation of the conjugate prior and posterior distributions will be also analyzed. Finally, by means of a mixture of the posterior distribution defined in the interior of the parameter space and in the boundary, it will be possible to test the Zipf against the Zipf-Polylog distribution.

Keywords: Zipf, Power law, Bayesian statistics, discrete distributions

Non Parametric Statistics I
June 12, 2025  3:30 PM
Sala de prensa (MR 13)

A. Baíllo Moreno, J. Cárcamo Urtiaga

P. De La Lama, J. A. Martin Fernandez, M. Comas Cufi

Á. Herce Postigo, M. J. Salvador Figueras

A. García Nogales