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Limiting behaviour of the stationary search cost distribution driven by a generalized gamma process

Kume, Alfred, Leisen, Fabrizio, Lijoi, Antonio (2018) Limiting behaviour of the stationary search cost distribution driven by a generalized gamma process. Electronic Communications in Probability, 23 . Article Number 11. ISSN 1083-589X. (doi:10.1214/18-ECP111) (KAR id:66122)


Consider a list of labeled objects that are organized in a heap. At each time, object j is selected with probability pj and moved to the top of the heap. This procedure defines a Markov chain on the set of permutations which is referred to in the literature as Move-to-Front rule. The present contribution focuses on the stationary search cost, namely the position of the requested item in the heap when the Markov chain is in equilibrium. We consider the scenario where the number of objects is infinite and the probabilities pj's are defined as the normalization of the increments of a subordinator. In this setting, we provide an exact formula for the moments of any order of the stationary search cost distribution. We illustrate the new findings in the case of a generalized gamma subordinator and deal with an extension to the two-parameter Poisson-Dirichlet process, also known as Pitman-Yor process.

Item Type: Article
DOI/Identification number: 10.1214/18-ECP111
Uncontrolled keywords: γ–stable process, Generalized gamma process, Heaps, Move-to-front rule, Search cost distribution, Subordinator, Two–parameter Poisson–Dirichlet process
Subjects: Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Fabrizio Leisen
Date Deposited: 23 Feb 2018 07:13 UTC
Last Modified: 04 Jul 2023 11:23 UTC
Resource URI: (The current URI for this page, for reference purposes)

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