On asymptotic of extremes from generalized Maxwell distribution
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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.
Abstract
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.
참고문헌 (16)
- F. Al-Bender, "The generalized Maxwell-slip model: a novel model for friction simulation and compensation", Trans. Automat. Control, 50(11), pp.1883~1887 (2005)[DOI]
- P. Asinari, "Generalized maxwell state and h theorem for computing fluid flows using the lattice boltzmann method", Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 79, pp.461~475 (2009)
- P. Hall, "On the rate of convergence of normal extremes", J. Appl. Probab., 16(2), pp.433~439 (1979)[DOI]
- J. Huang, "Tail behavior of the generalized Maxwell distribution", Comm. Statist. Theory Methods, 45(14), pp.4230~4236 (2016)[DOI]
- Kapteijn, "The generalized maxwell-stefan model for diffusion in zeolites: sorbate molecules with different saturation loadings", Chem. Eng. Sci., 55, pp.2923~2930 (2000)[DOI]
- S. Kumar, "Sequential test for the parameter of generalized Maxwell distribution", National J. Syst. Inf. Technol., 4, pp.1~10 (2011)
- V. Lampaert, "A generalized Maxwell-slip friction model appropriate for control purposes", Proceedings of the 2003 International Conference on Physics and Control, 4, pp.1170~1177 (2003)
- Fuming Lin, "Convergence rate of extremes for the generalized short-tailed symmetric distribution", 대한수학회보, 53(5), pp.1549~1566 (2016), 대한수학회
- C. Liu, "Convergence rate of extremes from Maxwell sample", J. Inequal. Appl., 2013(477), pp.11~ (2013)[DOI]
- K. A. Nair, "Asymptotic distribution and moments of normal extremes", Ann. Probab., 9(1), pp.150~153 (1981)[DOI]
- E. Omey, "Rates of convergence for densities in extreme value theory", Ann. Probab., 16(2), pp.479~486 (1988)[DOI]
- Zuoxiang Peng, "CONVERGENCE RATES FOR THE MOMENTS OF EXTREMES", 대한수학회보, 49(3), pp.495~510 (2012), 대한수학회
- Z. Peng, "Convergence rate of extremes for the general error distribution", J. Appl. Probab., 47(3), pp.668~679 (2010)[DOI]
- A. Plucinska, "On orthogonality properties of generalized Maxwell distribution", J. Appl. Statist. Sci., 7(1), pp.1~6 (1998)
- S. I. Resnick, "Extreme Values, Regular Variation, and Point Processes, Applied Probability. A Series of the Applied Probability Trust, 4" (1987), Springer-Verlag
- V. Gh. Voda, "A modified Weibull hazard rate as generator of a generalized Maxwell distribution", Math. Rep. (Bucur.), 11(2), pp.171~179 (2009)