On the Distributional Expansions of Powered Extremes from Maxwell Distribution

In this paper, asymptotic expansions of the distributions and densities of powered extremes for Maxwell samples are considered. The results show that the convergence speeds of normalized partial maxima relies on the powered index. Additionally, compared with previous result, the convergence rate of the distribution of powered extreme from Maxwell samples is faster than that of its extreme. Finally, numerical analysis is conducted to illustrate our findings.