Brazilian Journal of Probability and Statistics

The beta generalized logistic distribution

Alice L. Morais, Gauss M. Cordeiro, and Audrey H. M. A. Cysneiros

Full-text: Open access


For the first time, a four-parameter beta generalized logistic distribution is obtained by compounding the beta and generalized logistic distributions. The new model extends some well-known distributions and its shape is quite flexible, specially the skewness and the tail weights, due to the extra shape parameters. We obtain general expansions for the moment generating and quantile functions. The estimation of the parameters is investigated by maximum likelihood. An application to a real data set is given to show the flexibility and potentiality of our distribution.

Article information

Braz. J. Probab. Stat., Volume 27, Number 2 (2013), 185-200.

First available in Project Euclid: 21 February 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Beta distribution generalized logistic distribution maximum likelihood order statistic


Morais, Alice L.; Cordeiro, Gauss M.; Cysneiros, Audrey H. M. A. The beta generalized logistic distribution. Braz. J. Probab. Stat. 27 (2013), no. 2, 185--200. doi:10.1214/11-BJPS166.

Export citation


  • Barreto-Souza, W., Cordeiro, G. M. and Simas, A. B. (2011). Some results for beta Fréchet distribution. Communications in Statistics. Theory and Methods 40, 798–811.
  • Barreto-Souza, W., Santos, A. and Cordeiro, G. M. (2010). The beta generalized exponential distribution. Journal of Statistical Computation and Simulation 80, 159–172.
  • Eugene, N., Lee, C. and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics. Theory and Methods 31, 497–512.
  • Famoye, F., Lee, C. and Olumolade, O. (2005). The beta–Weibull distribution. Journal of Statistical Theory and Applications 4, 121–136.
  • Gradshteyn, I. S. and Ryzhik, I. M. (2007). Table of Integrals, Series, and Products, 7nd ed. Amsterdam: Elsevier.
  • Kong, L., Lee, C. and Sepanski, J. H. (2007). On the properties of beta–gamma distribution. Journal of Modern Applied Statistical Methods 6, 187–211.
  • Lee, C., Famoye, F. and Olumolade, O. (2007). Beta–Weibull distribution: Some properties and applications to censored data. Journal of Modern Applied Statistical Methods 6, 173–186.
  • Nadarajah, S. and Gupta, A. K. (2004). The beta Fréchet distribution. Far East Journal of Theoretical Statistics 14, 15–24.
  • Nadarajah, S. and Kotz S. (2004). The beta Gumbel distribution. Mathematical Problems in Engineering 4, 323–332.
  • Nadarajah, S. and Kotz S. (2006). The beta exponential distribution. Reliability Engineering and System Safety 91, 689–697.
  • Prentice, R. L. (1976). A generalization of the probit and logit models for dose response curves. Biometrics 32, 761–768.