Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Advances in Data Analysis and Classification
Erschienen in: Advances in Data Analysis and Classification 3/2013

01.09.2013 | Regular Article

On mixtures of skew normal and skew \(t\)-distributions

verfasst von: Sharon X. Lee, Geoffrey J. McLachlan

Erschienen in: Advances in Data Analysis and Classification | Ausgabe 3/2013

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Finite mixtures of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the connection between them and their relative performance becomes rather unclear. This paper aims to provide a concise overview of these developments by presenting a systematic classification of the existing skew symmetric distributions into four types, thereby clarifying their close relationships. This also aids in understanding the link between some of the proposed expectation-maximization based algorithms for the computation of the maximum likelihood estimates of the parameters of the models. The final part of this paper presents an illustration of the performance of these mixture models in clustering a real dataset, relative to other non-elliptically contoured clustering methods and associated algorithms for their implementation.
Vorheriger Artikel Special issue on “Model-based clustering and classification”
Nächster Artikel A Monte Carlo evaluation of three methods to detect local dependence in binary data latent class models

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
Arellano-Valle RB, Genton MG (2010) Multivariate extended skew-\(t\) distributions and related families. METRON 68:201–234MathSciNetCrossRef
Arellano-Valle RB, Branco MD, Genton MG (2006) A unified view on skewed distributions arising from selections. Can J Stat 34:581–601
Arellano-Valle RB, Castro LM, Genton MG, Gómez HW (2008) Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis. Bayesian Anal 3:513–540
Arnold BC, Beaver RJ, Meeker WQ (1993) The nontruncated marginal of a truncated bivariate normal distribution. Psychometrika 58:471–478MathSciNetMATHCrossRef
Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Stat 12:171–178MathSciNetMATH
Azzalini A, Capitanio A (1999) Statistical applications of the multivariate skew-normal distribution. J R Stat Soc Ser B 61(3):579–602MathSciNetMATHCrossRef
Azzalini A, Capitanio A (2003) Distribution generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J R Stat Soc Ser B 65(2):367–389MathSciNetMATHCrossRef
Basso RM, Lachos VH, Cabral CRB, Ghosh P (2010) Robust mixture modeling based on scale mixtures of skew-normal distributions. Comput Stat Data Anal 54:2926–2941MathSciNetCrossRef
Cabral CRB, Lachos VH, Prates MO (2012) Multivariate mixture modeling using skew-normal independent distributions. Comput Stat Data Anal 56:126–142MathSciNetMATHCrossRef
Contreras-Reyes JE, Arellano-Valle RB (2012) Growth curve based on scale mixtures of skew-normal distributions to model the age-length relationship of cardinalfish (epigonus crassicaudus). arXiv:12125180 [statAP]
Franczak BC, Browne RP, McNicholas PD (2012) Mixtures of shifted asymmetric laplace distributions. arXiv:12071727 [statME]
Frühwirth-Schnatter S, Pyne S (2010) Bayesian inference for finite mixtures of univariate and multivariate skew-normal and skew-\(t\) distributions. Biostatistics 11:317–336CrossRef
Genton MG (ed) (2004) Skew-elliptical Distributions and their Applications: a Journey beyond Normality. Chapman & Hall/CRC, Boca Raton/Florida
Genton MG, Loperfido N (2005) Generalized skew-elliptical distributions and their quadratic forms. Ann Inst Stat Math 57:389–401MathSciNetCrossRef
González-Farás G, Domínguez-Molinz JA, Gupta AK (2004) Additive properties of skew normal random vectors. J Stat Plan Inference 126:521–534CrossRef
Gupta AK, González-Faríaz G, Domínguez-Molina JA (2004) A multivariate skew normal distribution. J Multivar Anal 89:181–190
Ho HJ, Lin TI, Chen HY, Wang WL (2012) Some results on the truncated multivariate \(t\) distribution. J Stat Plan Inference 142:25–40MathSciNetMATHCrossRef
Iversen DH (2010) Closed-skew distributions: simulation, inversion and parameter estimation. Norwegian University of Science and Technology, Master’s thesis
Karlis D, Santourian A (2009) Model-based clustering with non-elliptically contoured distributions. Stat Comput 19:73–83MathSciNetCrossRef
Lachos VH, Ghosh P, Arellano-Valle RB (2010) Likelihood based inference for skew normal independent linear mixed models. Stat Sin 20:303–322MathSciNetMATH
Lee SX, McLachlan GJ (2011) On the fitting of mixtures of multivariate skew t-distributions via the EM algorithm. arXiv:11094706 [statME]
Lee SX, McLachlan GJ (2013) Finite mixtures of multivariate skew \(t\)-distributions: some recent and new results. Stat Comput
Lin TI (2009) Maximum likelihood estimation for multivariate skew normal mixture models. J Multivar Anal 100:257–265MATHCrossRef
Lin TI, Lee JC, Hsieh WJ (2007a) Robust mixture modeling using the skew-\(t\) distribution. Stat Comput 17:81–92MathSciNetCrossRef
Lin TI, Lee JC, Yen SY (2007b) Finite mixture modelling using the skew normal distribution. Stat Sin 17:909–927MathSciNetMATH
Liseo B, Loperfido N (2003) A Bayesian interpretation of the multivariate skew-normal distribution. Stat Probab Lett 61:395–401MathSciNetMATHCrossRef
Ma Y, Genton MG (2004) A flexible class of skew-symmetric distributions. Scand J Stat 31:459–468
Pyne S, Hu X, Wang K, Rossin E, Lin TI, Maier LM, Baecher-Allan C, McLachlan GJ, Tamayo P, Hafler DA, De Jager PL, Mesirow JP (2009) Automated high-dimensional flow cytometric data analysis. Proc Natl Acad Sci USA 106:8519–8524CrossRef
Riggi S, Ingrassia S (2013) Modeling high energy cosmic rays mass composition data via mixtures of multivariate skew-\(t\) distributions. arXiv:13011178 [astro-phHE]
Sahu SK, Dey DK, Branco MD (2003) A new class of multivariate skew distributions with applications to Bayesian regression models. Can J Stat 31:129–150MathSciNetMATHCrossRef
Soltyk S, Gupta R (2011) Application of the multivariate skew normal mixture model with the EM algorithm to value-at-risk. MODSIM 2011—19th international congress on modelling and simulation, Perth
Vrbik I, McNicholas PD (2012) Analytic calculations for the EM algorithm for multivariate skew \(t\)-mixture models. Stat Probab Lett 82:1169–1174MathSciNetMATHCrossRef
Vrbik I, McNicholas PD (2013) Parsimonious skew mixture models for model-based clustering and classification. arXiv:13022373 [statCO]
Wang K, Ng SK, McLachlan GJ (2009) Multivariate skew \(t\) mixture models: applications to fluorescence-activated cell sorting data. In: Shi H, Zhang Y, Bottema MJ, Lovell BC, Maeder AJ (eds) DICTA 2009 (conference of digital image computing: techniques and applications, Melbourne). IEEE Computer Society, Los Alamitos, pp 526–531
Metadaten
Titel
On mixtures of skew normal and skew -distributions
verfasst von
Sharon X. Lee
Geoffrey J. McLachlan
Publikationsdatum
01.09.2013
Verlag
Springer Berlin Heidelberg
Erschienen in
Advances in Data Analysis and Classification / Ausgabe 3/2013
Print ISSN: 1862-5347
Elektronische ISSN: 1862-5355
DOI
https://doi.org/10.1007/s11634-013-0132-8

Weitere Artikel der Ausgabe 3/2013

Advances in Data Analysis and Classification 3/2013 Zur Ausgabe

Regular Article

Dimension reduction for model-based clustering via mixtures of multivariate -distributions

Regular Article

Clustering student skill set profiles in a unit hypercube using mixtures of multivariate betas

Regular Article

A Monte Carlo evaluation of three methods to detect local dependence in binary data latent class models

Regular Article

Model-based clustering of probability density functions

Regular Article

Model-based clustering of high-dimensional data streams with online mixture of probabilistic PCA

Editorial

Special issue on “Model-based clustering and classification”