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AMJCUB
Applied Mathematics-A Journal of Chinese Universities  2018, Vol. 33 Issue (2): 177-    DOI: 10.1007/s11766-018-3481-4
    
Higher order asymptotic behaviour of partial maxima of random sample from generalized Maxwell distribution under power normalization
HUANG Jian-wen$^1$ ,  WANG Jian-jun$^{1,2,*}$
$^1$ School of Mathematics and Statistics, Southwest University, Chongqing 400715, China. $^2$ Research Center for Artificial Intelligence \& Education Big Data, Southwest University, Chongqing 400715, China.
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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.



Key words： higher order expansion       extreme, generalized Maxwell distribution       nonlinear normalization     
Published: 16 July 2018
CLC:  60F15  
  60G70  
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Cite this article:

HUANG Jian-wen , WANG Jian-jun. Higher order asymptotic behaviour of partial maxima of random sample from generalized Maxwell distribution under power normalization. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(2): 177-.

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http://www.zjujournals.com/amjcub/10.1007/s11766-018-3481-4     OR     http://www.zjujournals.com/amjcub/Y2018/V33/I2/177


Higher order asymptotic behaviour of partial maxima of random sample from generalized Maxwell distribution under power normalization

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.

关键词： higher order expansion ,  extreme, generalized Maxwell distribution ,  nonlinear normalization 
[1] DENG Xin, TANG Xu-fei, WANG Shi-jie, WANG Xue-jun. On the strong convergence properties for weighted sums of negatively orthant dependent random variables[J]. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(1): 35-47.