Goodness-of-Fit Tests for the Power-Generalized Weibull Probability Distribution

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.

Keywords:

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

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62F10
• 62N86

Acknowledgments

The authors are grateful to Professor Nikulin, who encouraged us to conduct this research, and to referees for their valuable comments and suggestions that helped us much in improving the presentation.