Abstract
In this article, the higher order asymptotic expansions of cumulative distribution function and probability density function of extremes for generalized Maxwell distribution are established under nonlinear normalization. As corollaries, the convergence rates of the distribution and density of maximum are obtained under nonlinear normalization.
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The authors would like to thank the Editor and the referees for careful reading and for their comments which greatly improved the paper.
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Supported by the Natural Science Foundation of China (61673015, 61273020), the Fundamental Research Funds for the Central Universities (XDJK2015A007,SWU1809002), the Science Computing and Intelligent Information Processing of Guangxi Higher Education Key Laboratory (GXSCIIP201702), the Science and Technology Plan Project of Guizhou Province (LH[2015]7053, LH[2015]7055), Science and Technology Foundation of Guizhou Province (Qian Ke He Ji Chu[2016]1161), Guizhou Province Natural Science Foundation in China (Qian Jiao He KY[2016]255).
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Huang, Jw., Wang, Jj. Higher order asymptotic behaviour of partial maxima of random sample from generalized Maxwell distribution under power normalization. Appl. Math. J. Chin. Univ. 33, 177–187 (2018). https://doi.org/10.1007/s11766-018-3481-4
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DOI: https://doi.org/10.1007/s11766-018-3481-4