## Abstract

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 language | English |
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Pages (from-to) | 1003-1012 |

Number of pages | 10 |

Journal | Communications in Statistics: Simulation and Computation |

Volume | 42 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1 2013 |

## Keywords

- 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