On the Bimodal Gumbel Model with Application to Environmental Data


  • Cira Otiniano University of Brasilia
  • Roberto Vila University of Brasilia
  • Pedro Brom University of Brasilia
  • Marcelo Bourguignon Federal University of Rio Grande do Norte




The Gumbel model is a very popular statistical model due to its wide applicability for instance in the course of certain survival, environmental, financial or reliability studies. In this work, we have introduced a bimodal generalization of the Gumbel distribution that
can be an alternative to model bimodal data. We derive the analytical shapes of the corresponding probability density function and the
hazard rate function and provide graphical illustrations. Furthermore, We have discussed the properties of this density such as mode, bimodality, moment generating function and moments. Our results were verified using the Markov chain Monte Carlo simulation method. The maximum likelihood method is used for parameters estimation. Finally, we also carry out an application to real data that demonstrates the usefulness of the proposed distribution. 




How to Cite

Otiniano, C. ., Vila , R., Brom, P. ., & Bourguignon, M. . (2023). On the Bimodal Gumbel Model with Application to Environmental Data. Austrian Journal of Statistics, 52(2), 45–65. https://doi.org/10.17713/ajs.v52i2.1392