Discriminating between generalized exponential, geometric extreme exponential and Weibull distributions

Abstract

Generalized exponential, geometric extreme exponential and Weibull distributions are three non-negative skewed distributions that are suitable for analysing lifetime data. We present diagnostic tools based on the likelihood ratio test (LRT) and the minimum Kolmogorov distance (KD) method to discriminate between these models. Probability of correct selection has been calculated for each model and for several combinations of shape parameters and sample sizes using Monte Carlo simulation. Application of LRT and KD discrimination methods to some real data sets has also been studied.

Keywords:

• generalized exponential distribution
• geometric extreme exponential distribution
• Weibull distribution
• Kolmogorov distance
• likelihood ratio
• probability of correct selection

Acknowledgements

The author would like to thank the anonymous referee for his/her helpful comments that greatly improved the earlier version of this paper.