Asymptotic properties of MLE's of parameters of exponentiated exponential lifetime distributions. Issue 22 (21st September 2021)

• Record Type: Journal Article
• Authors: Gleaton, James U.; Sa, Ping; Hamid, Sami
• Is Part Of: Communications in statistics. Volume 51:Issue 22(2022)
• Page Start: 7856
• Page End: 7870
• Publication Date: 2021-09-21
• Subjects: Exponentiated exponential distributions -- asymptotic behavior of MLE's -- simulation results; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2021.1882495
• Languages: English
• ISSNs: 0361-0926

Abstract

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.