arXiv subjects

Carlo Orsi

Publications and source records attributed to Carlo Orsi.

4 recordsLinked to original sources

arXiv2021

A Novel Approach to Handling the Non-Central Dirichlet Distribution

In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its definition by as many non-central ones. Specifically, a novel approach to tackling the analysis of this model is introduced based on a simple conditional density together with a suitable transposition into the non-central framework of a characterizing property of independent Chi-Squared random variables. This approach thus enables to remedy the undeniable mathematical complexity of the joint density function of such distribution by paving the way towards achieving a new attractive stochastic representation as well as a surprisingly simple closed-form expression for its mixed raw moments.

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arXiv2021

A New Class of Non-Central Dirichlet Distributions

In the present paper new light is shed on the non-central extensions of the Dirichlet distribution. Due to several probabilistic and inferential properties and to the easiness of parameter interpretation, the Dirichlet distribution proves the most well-known and widespread model on the unitary simplex. However, despite its many good features, such distribution is inadequate for modeling the data portions next to the vertices of the support due to the strictness of the limiting values of its joint density. To replace this gap, a new class of distributions, called Conditional Non-central Dirichlet, is presented herein. This new model stands out for being a more easily tractable version of the existing Non-central Dirichlet distribution which maintains the ability of this latter to capture the tails of the data by allowing its own density to have arbitrary positive and finite limits.

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arXiv2021

New Developments on the Non-Central Chi-Squared and Beta Distributions

New formulas for the moments about zero of the Non-central Chi-Squared and the Non-central Beta distributions are achieved by means of novel approaches. The mixture representation of the former model and a new expansion of the ascending factorial of a binomial are the main ingredients of the first approach, whereas the second one hinges on an interesting relationship of conditional independence and a simple conditional density of the latter model. Then, a simulation study is carried out in order to pursue a twofold purpose: providing numerical validations of the derived moment formulas on one side and discussing the advantages of the new formulas over the existing ones on the other.

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arXiv2017

New insights into non-central beta distributions

The beta family owes its privileged status within unit interval distributions to several relevant features such as, for example, easyness of interpretation and versatility in modeling different types of data. However, its flexibility at the unit interval endpoints is poor enough to prevent from properly modeling the portions of data having values next to zero and one. Such a drawback can be overcome by resorting to the class of the non-central beta distributions. Indeed, the latter allows the density to take on arbitrary positive and finite limits which have a really simple form. That said, new insights into such class are provided in this paper. In particular, new representations and moments expressions are derived. Moreover, its potential with respect to alternative models is highlighted through applications to real data.

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