Tail properties and approximate distribution and expansion for extreme of LGMD

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• 作者：Jianwen Huang ; Jianjun Wang ; Guowang Luo…
• 关键词：limit distribution ; logarithmic generalized Maxwell distribution ; Mills’ ratio ; maximum ; tail properties
• 刊名：Journal of Inequalities and Applications
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：2017
• 期：1
• 全文大小：1368KB
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X
• 卷排序：2017

文摘

We introduce logarithmic generalized Maxwell distribution motivated by Vodă (Math. Rep. 11:171-179, 2009), which is an extension of the generalized Maxwell distribution. Some interesting properties of this distribution are studied and the asymptotic distribution of the partial maximum of an i.i.d. sequence from the logarithmic generalized Maxwell distribution is gained. The expansion of the limit distribution from the normalized maxima is established under the optimal norming constants, which shows the rate of convergence of the distribution for normalized maximum to the extreme limit.