Metrika

, Volume 63, Issue 2, pp 215–221 | Cite as

A new condition for identifiability of finite mixture distributions

  • N. Atienza
  • J. Garcia-Heras
  • J. M. Muñoz-Pichardo
Original Article

Abstract

In this paper a sufficient condition for the identifiability of finite mixtures is given. This condition is less restrictive than Teicher’s condition Teicher H, Ann Math Stat 34:1265–1269 (1963) and therefore it can be applied to a wider range of families of mixtures. In particular, it applies to the classes of all finite mixtures of Log-gamma and of reversed Log-gamma distributions. These families have been already studied by Henna J Jpn Stat Soc 24:193–200 (1994) using another condition, different from Teicher’s, but more difficult to check in many cases. Furthermore, the result given in this paper is very appropiated for the case of mixtures of the union of different distribution families. To illustrate this an application to the class of all finite mixtures generated by the union of Lognormal, Gamma and Weibull distributions is given, where Teicher’s and Henna’s conditions are not applicable

Keywords

Identifiability Finite mixture Log-normal distributions Gamma distributions Weibull distributions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Atienza N (2003) Mixturas de distribuciones: Modelización de experiencias con asimetría en los datos. Ph. D. Thesis. University of Seville, SpainGoogle Scholar
  2. Ashton WD (1971) Distribution for gaps in road traffic. J Inst Math Appl 7:37–46CrossRefMATHGoogle Scholar
  3. Barndorff-Nielsen O (1965) Identifiability of mixtures of exponential families. J Math Anal Appl 12:115–121CrossRefMathSciNetMATHGoogle Scholar
  4. Böhning D (2000) Computer-assisted analysis of mixtures and applications: Meta-analysis, disease mapping and others. Chapman and Hall, BocaRaton, LondonMATHGoogle Scholar
  5. Chandra S (1977) On the mixtures of probability distributions. Scand J Stat 4:105–112MATHGoogle Scholar
  6. Cohen AC (1965) Estimation in mixtures of discrete distributions. In: Patil GP (ed) Classical and contagious discrete distributions. Pergamon, New York, pp 373–378Google Scholar
  7. Henna J (1994) Examples of identifiable mixture. J Jpn Stat Soc 24:193–200MathSciNetMATHGoogle Scholar
  8. Khalaf EA (1988) Identifiability of finite mixtures using a new transform. Ann Inst Stat Math 40:261–265CrossRefMATHGoogle Scholar
  9. Lindsay BG (1995) Mixture models: theory, geometry and applications. Institute of Mathematical Statistics, HaywardGoogle Scholar
  10. Marazzi A, Paccaud F, Ruffieux C, Beguin C (1998) Fitting the distributions of length of stay by parametric models. Medical-Care 36(6):915–927CrossRefPubMedGoogle Scholar
  11. McLachlan GJ, Basford KE (1988) Mixture models. Marcel Dekker, New YorkMATHGoogle Scholar
  12. McLachlan GJ, Peel D (2000) Finite mixture models. Wiley, New YorkMATHGoogle Scholar
  13. Teicher H (1963) Identifiability of finite mixtures. Ann Math Stat 34:1265–1269CrossRefMathSciNetMATHGoogle Scholar
  14. Titterington DM, Smith AFM, Makov UE (1985) Statistical analysis of finite mixture distributions. Wiley, New YorkMATHGoogle Scholar

Copyright information

© Springer Verlag 2005

Authors and Affiliations

  • N. Atienza
    • 1
  • J. Garcia-Heras
    • 2
  • J. M. Muñoz-Pichardo
    • 2
  1. 1.Departamento Matemática Aplicada I, Escuela Técnica Superior de Ingeniería InformáticaUniversidad de SevillaS.N SevillaSpain
  2. 2.Departamento Estadística e I.O., Facultad de MatemáticasUniversidad de SevillaS.N. SevillaSpain

Personalised recommendations