Book
The shifted-scaled Dirichlet Distribution in the Simplex
| Τίτλος: | The shifted-scaled Dirichlet Distribution in the Simplex |
|---|---|
| Συγγραφείς: | Monti, G.S., Mateu Figueras, G., Pawlowsky Glahn, Vera, Egozcue Rubí, Juan José |
| Συνεισφορές: | Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada |
| Πηγή: | © International Workshop on Compositional Data Analysis (4th: 2011: Sant Feliu de GuÍxols, Girona). CODAWORK 2011: International Workshop on Compositional Data Analysis, hold on May 9-13rd. 2011, Sant Feliu de Guíxols, Girona Llibres / Capítols de LLibre (D-IMAE) DUGiDocs – Universitat de Girona instname UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya |
| Στοιχεία εκδότη: | Universitat Politècnica de Catalunya. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), 2011. |
| Έτος έκδοσης: | 2011 |
| Θεματικοί όροι: | Quantitative research, Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica, Investigació quantitativa, Matemàtiques i estadística::Estadística matemàtica [Àrees temàtiques de la UPC], Estadística matemàtica -- Congressos, Data analytics, Anàlisi multivariable -- Congressos, Distribució (Teoria de la probabilitat) -- Congressos, Distribution (Probability theory) -- Congresses, Mathematical statistics -- Congresses, compositional data, aitchison geometry, Multivariate analysis -- Congresses |
| Περιγραφή: | Perturbation and powering are two operations in the simplex that define a vector-space structure. Perturbation and powering in the simplex play the same role as the sum and product by scalars in real space. A standard Dirichlet random composition can be shifted by perturbation, and scaled powering by a real scalar. The obtained random composition has a shifted-scaled Dirichlet distribution. The procedure is analogous to standardization of real random variables. The derived distribution is a generalization of the Dirichlet one, and it is studied from a probabilistic point of view. In the simplex, considered as an Euclidean space, the Aitchison measure is the natural (Lebesgue type) measure, which is compatible with its operations and metrics. Therefore, a natural way of describing the generalized (shifted-scaled) Dirichlet probability distributions is using probability densities with respect to the Aitchison measure. This density representation is compared with the traditional probability density with respect to the Lebesgue measure. In particular, the center and variability for both representations are compared |
| Τύπος εγγράφου: | Part of book or chapter of book Conference object |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Σύνδεσμος πρόσβασης: | http://hdl.handle.net/10256/13637 http://hdl.handle.net/2117/366723 https://hdl.handle.net/2117/366723 https://hdl.handle.net/10281/22158 https://hdl.handle.net/2072/319416 |
| Αριθμός Καταχώρησης: | edsair.dedup.wf.002..8f09537a31bd6595c8537eeb28c68942 |
| Βάση Δεδομένων: | OpenAIRE |
| Η περιγραφή δεν είναι διαθέσιμη |