Goodness-of-fit tests for the power-generalized weibull probability distribution

Vassilly Voinov, Natalya Pya, Niyaz Shapakov, Yevgeniy Voinov

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


The power-generalized Weibull probability distribution is very often used in survival analysis mainly because different values of its parameters allow for various shapes of hazard rate such as monotone increasing/decreasing, ∩-shaped, ∪-shaped, or constant. Modified chi-squared tests based on maximum likelihood estimators of parameters that are shown to be -consistent are proposed. Power of these tests against exponentiated Weibull, three-parameter Weibull, and generalized Weibull distributions is studied using Monte Carlo simulations. It is proposed to use the left-tailed rejection region because these tests are biased with respect to the above alternatives if one will use the right-tailed rejection region. It is also shown that power of the McCulloch test investigated can be two or three times higher than that of Nikulin-Rao-Robson test with respect to the alternatives considered if expected cell frequencies are about 5.

Original languageEnglish
Pages (from-to)1003-1012
Number of pages10
JournalCommunications in Statistics: Simulation and Computation
Issue number5
Publication statusPublished - May 1 2013


  • Accelerated life testing
  • Modified chi-squared goodness-of-fit tests
  • Power-generalized Weibull distribution
  • Survival analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation

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