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In this paper, with optimal normalized constants, the asymptotic expansions of the distribution and density of the normalized maxima from generalized Maxwell distribution are derived. For the distributional expansion, it shows that the convergence rate of the normalized maxima to the Gumbel extreme value distribution is proportional to $1/\log n.$ For the density expansion, on the one hand, the main result is applied to establish the convergence rate of the density of extreme to its limit. On the other hand, the main result is applied to obtain the asymptotic expansion of the moment of maximum.
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참고문헌 (16)
참고문헌 신청
F. Al-Bender / 2005 / The generalized Maxwell-slip model: a novel model for friction simulation and compensation / Trans. Automat. Control 50(11):1883~1887
P. Asinari / 2009 / Generalized maxwell state and h theorem for computing fluid flows using the lattice boltzmann method / Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79:461~475
P. Hall / 1979 / On the rate of convergence of normal extremes / J. Appl. Probab. 16(2):433~439
J. Huang / 2016 / Tail behavior of the generalized Maxwell distribution / Comm. Statist. Theory Methods 45(14):4230~4236
Kapteijn / 2000 / The generalized maxwell-stefan model for diffusion in zeolites: sorbate molecules with different saturation loadings / Chem. Eng. Sci. 55:2923~2930
P. Asinari / 2009 / Generalized maxwell state and h theorem for computing fluid flows using the lattice boltzmann method / Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79:461~475
P. Hall / 1979 / On the rate of convergence of normal extremes / J. Appl. Probab. 16(2):433~439
J. Huang / 2016 / Tail behavior of the generalized Maxwell distribution / Comm. Statist. Theory Methods 45(14):4230~4236
Kapteijn / 2000 / The generalized maxwell-stefan model for diffusion in zeolites: sorbate molecules with different saturation loadings / Chem. Eng. Sci. 55:2923~2930
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