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
Scheduled
Non Parametric Statistics I
June 12, 2025 3:30 PM
Auditorio 1. Ricard Vinyes