Compositional data consist of proportions and are therefore subject to a unit-sum constraint. Such data originate, for example, when analyzing rock compositions, household budgets, pollution or biological components and arise naturally in a great variety of disciplines.
In this seminar, a new parametric family of distributions for compositional data is proposed and investigated. Such family, called flexible Dirichlet, is obtained by normalizing a correlated basis and is a particular Dirichlet mixture. The Dirichlet distribution is included as an inner point. The flexible Dirichlet is shown to exhibit a rich dependence pattern, capable of discriminating among many of the independence concepts relevant for compositional data. At the same time it can model multi-modality. A number of stochastic representations are presented, disclosing its remarkable tractability. In particular, it is closed under marginalization, conditioning, subcomposition, amalgamation and permutation. An illustrative application to real data is shown. Finally, possible uses of the flexible Dirichlet within the Bayesian approach are touched upon.
Le attività di ricerca svolte dai docenti e ricercatori del Dipartimento di Scienze statistiche si articolano in vari filoni di indirizzo probabilistico, statistico - matematico (teorico ed applicato), economico e demografico.