The Odd Log-Logistic Student t Distribution: Theory and Applications

  • Altemir da Silva Braga
  • Gauss M. Cordeiro
  • Edwin M. M. OrtegaEmail author
  • Giovana O. Silva


The normal distribution is most used in analysis of experiments. However, it is not suitable to apply in situations where the data have evidence of bimodality or heavier tails than the normal distribution. So, we propose a new four-parameter model called the odd log-logistic Student t distribution as an alternative to the normal and Student t distributions. The new distribution can be symmetric, platykurtic, mesokurtic or leptokurtic and may be unimodal or bimodal. Its various structural properties can be determined from the linear representation of its density function. The estimation of the model parameters is performed by maximum likelihood. The proposed distribution can be used as an alternative for randomized complete block design, thus providing analysis of real data more realistic than other special regression models. We perform a sensitivity analysis to detect influential or outlying observations, and construct generated envelopes from the residuals to select appropriate models. We illustrate the importance of the proposed model by means of three real data sets in analysis of experiments carried out in different regions of Brazil.


Log-logistic distribution Maximum likelihood estimation Moment Regression model Student t distribution 



We are very grateful to a referee and an associate editor for helpful comments that considerably improved the paper. We gratefully acknowledge financial support from CAPES, CNPq and FAPAC.


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Copyright information

© International Biometric Society 2017

Authors and Affiliations

  • Altemir da Silva Braga
    • 1
  • Gauss M. Cordeiro
    • 2
  • Edwin M. M. Ortega
    • 1
    Email author
  • Giovana O. Silva
    • 3
  1. 1.Departamento de Ciências ExatasUniversidade de São PauloPiracicabaBrazil
  2. 2.Departamento de EstatísticaUniversidade Federal de PernambucoRecifeBrazil
  3. 3.Departamento de EstatísticaUniversidade Federal da BahiaSalvadorBrazil

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