, Volume 63, Issue 2, pp 215–221

A new condition for identifiability of finite mixture distributions


    • Departamento Matemática Aplicada I, Escuela Técnica Superior de Ingeniería InformáticaUniversidad de Sevilla
  • J. Garcia-Heras
    • Departamento Estadística e I.O., Facultad de MatemáticasUniversidad de Sevilla
  • J. M. Muñoz-Pichardo
    • Departamento Estadística e I.O., Facultad de MatemáticasUniversidad de Sevilla
Original Article

DOI: 10.1007/s00184-005-0013-z

Cite this article as:
Atienza, N., Garcia-Heras, J. & Muñoz-Pichardo, J.M. Metrika (2006) 63: 215. doi:10.1007/s00184-005-0013-z


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


IdentifiabilityFinite mixtureLog-normal distributionsGamma distributionsWeibull distributions

Copyright information

© Springer Verlag 2005