Asymptotic properties of MLE’s of parameters of exponentiated exponential lifetime distributions

Abstract

The properties of exponential distributions are well-known, including asymptotic properties of MLE’s. We consider distributions generated from exponential lifetime distributions by taking positive real powers of the exponential c.d.f. We then consider the asymptotic behavior of the MLE’s for the parameters of these distributions. It was found that the regularity conditions are satisfied provided that the power parameter, α, is at least 1.5. Simulation results were examined for several values of the power parameter. Simulation results indicated that asymptotic efficiency holds for α > 0.5. For α = 0.25, MLE’s could not be obtained.

Keywords:

• Exponentiated exponential distributions
• asymptotic behavior of MLE’s
• simulation results

Acknowledgments

The authors wish to thank the referees for their time and consideration in reviewing this paper.