Computational Statistics

, Volume 34, Issue 1, pp 173–199 | Cite as

Modified beta modified-Weibull distribution

  • Abdus Saboor
  • Muhammad Nauman KhanEmail author
  • Gauss M. Cordeiro
  • Marcelino A. R. Pascoa
  • Juliano Bortolini
  • Shahid Mubeen
Original Paper


We introduce a flexible modified beta modified-Weibull model, which can accommodate both monotonic and non-monotonic hazard rates such as a useful long bathtub shaped hazard rate in the middle. Several distributions can be obtained as special cases of the new model. We demonstrate that the new density function is a linear combination of modified-Weibull densities. We obtain the ordinary and central moments, generating function, conditional moments and mean deviations, residual life functions, reliability measures and mean and variance (reversed) residual life. The method of maximum likelihood and a Bayesian procedure are used for estimating the model parameters. We compare the fits of the new distribution and other competitive models to two real data sets. We prove empirically that the new distribution gives the best fit among these distributions based on several goodness-of-fit statistics.


Bayesian analysis Modified beta distribution Moments Simulation study 



The research of Abdus Saboor has been supported in part by the Higher Education Commission of Pakistan (Grant No. 3104).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsKohat University of Science and TechnologyKohatPakistan
  2. 2.Departamento de EstatísticaUniversidade Federal de PernambucoRecifeBrazil
  3. 3.Departamento de EstatísticaUniversidade Federal de Mato GrossoCuiabáBrazil
  4. 4.Department of MathematicsSargodha UniversitySargodhaPakistan

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