A useful method for defining models for compositional data, i.e. data representing proportions, is via normalisation of a vector (basis) of positive random variables. The well known Dirichlet distribution is obtained from a basis of independent Gamma variables. Despite its many good properties, such a distribution is inadequate for modeling compositional data, as it implies a poor and always negative dependence structure. In this work a new basis is proposed which includes the Dirichlet one and allows for fairly rich dependence patterns. Its main properties are explored. The generated compositional data distribution is derived and shown, in particular, to be capable of modeling positive dependence too.

Ongaro, A., Migliorati, S., Monti, G. (2011). A new multivariate distribution as a basis for compositional data. In Proceedings Asmda 2011. roma : Ets.

A new multivariate distribution as a basis for compositional data

ONGARO, ANDREA;MIGLIORATI, SONIA;MONTI, GIANNA SERAFINA
2011

Abstract

A useful method for defining models for compositional data, i.e. data representing proportions, is via normalisation of a vector (basis) of positive random variables. The well known Dirichlet distribution is obtained from a basis of independent Gamma variables. Despite its many good properties, such a distribution is inadequate for modeling compositional data, as it implies a poor and always negative dependence structure. In this work a new basis is proposed which includes the Dirichlet one and allows for fairly rich dependence patterns. Its main properties are explored. The generated compositional data distribution is derived and shown, in particular, to be capable of modeling positive dependence too.
No
paper
Gamma distribution, Dirichlet distribution, mixture, simplex
English
Applied Stochastic Models and Data Analysis Conference
97888467-3045-9
Ongaro, A., Migliorati, S., Monti, G. (2011). A new multivariate distribution as a basis for compositional data. In Proceedings Asmda 2011. roma : Ets.
Ongaro, A; Migliorati, S; Monti, G
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/23214
Citazioni
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
Social impact