title: Tail properties and approximate distribution and expansion for extreme of LGMD.
abstract: 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.
authors.affiliation: School of Mathematics and Statistics, Southwest University, Chongqing, 400715 China.
authors.forename: Jianwen
authors.initials: J
authors.lastname: Huang
authors.affiliation: School of Mathematics and Statistics, Southwest University, Chongqing, 400715 China.
authors.forename: Jianjun
authors.initials: J
authors.lastname: Wang
authors.affiliation: School of Mathematics and Computational Science, Zunyi Normal College, Zunyi, 563002 China.
authors.forename: Guowang
authors.initials: G
authors.lastname: Luo
authors.affiliation: School of Mathematics and Computational Science, Zunyi Normal College, Zunyi, 563002 China.
authors.forename: Jun
authors.initials: J
authors.lastname: He
keywords: Mills’ ratio; limit distribution; logarithmic generalized Maxwell distribution; maximum; tail properties