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Statistical Papers

, Volume 60, Issue 1, pp 223–237 | Cite as

On the unimodality of the likelihood ratio with applications

  • Félix BelzunceEmail author
  • Carolina Martínez-Riquelme
Regular Article

Abstract

Along this paper, we study the relationship between the unimodality of the likelihood ratio and the behaviour of the ratio of two survival functions. The results provide sufficient conditions for both the hazard rated order when the likelihood ratio order does not hold and the mean residual life order when the hazard rate order does not hold. Examples where these results can be applied are also given.

Keywords

Likelihood ratio order Hazard rate order Mean residual life order Unimodality 

Mathematics Subject Classification

60E15 

Notes

Acknowledgments

The authors want to acknowledge the comments by two anonymous referees that have greatly improved the presentation and the contents of this paper. The authors also want to acknowledge the support received from the Ministerio de Economía y Competitividad under Grant MTM2012-34023-FEDER.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Dpto. Estadística e Investigación Operativa, Facultad de MatemáticasUniversidad de MurciaMurciaSpain

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