Annals of the Institute of Statistical Mathematics

, Volume 54, Issue 3, pp 585–594

Likelihood Ratio Statistic for Exponential Mixtures

  • Gabriela Ciuperca

DOI: 10.1023/A:1022415228062

Cite this article as:
Ciuperca, G. Annals of the Institute of Statistical Mathematics (2002) 54: 585. doi:10.1023/A:1022415228062


Let f0(x) be the exponential density and fγ(x) the translation model. Let (Xi)i=1,n be i.i.d. random variables, with density g. We test that g is f0 against g is a simple mixture, using the LRT statistic. We prove that the LRT diverges to infinity with probability 1/2 and it is equal to 0 with probability 1/2. Therefore, the classical likelihood limiting theory does not hold.

Mixture modelslikelihood testexponential distribution

Copyright information

© The Institute of Statistical Mathematics 2002

Authors and Affiliations

  • Gabriela Ciuperca
    • 1
  1. 1.Laboratoire de Probabilités, Combinatoire et Statistique, Domaine de Gerland, Bât. Recherche BUniv. Lyon 1Lyon cedex 07France