We introduce logarithmic generalized Maxwell distribution 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 independent and identically distributed 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 tending to the extreme limit.
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