• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.77-87
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• 2001

Some asymptotic results on the local likelihood density estimator of Copas(1995) are derived when the locally parametric model has several parameters. It turns out that it has the same asymptotic mean squared error as that of Hjort and Jones(1996).

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.147-158
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• 2004

Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation on the modulus of continuity. This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.12.1-12
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• 2003

Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation On the modulus of continuity This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.

• 한국연소학회:학술대회논문집
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• 2004.11a
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• pp.62-69
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• 2004

Zone conditional formulations for the Reynolds average reaction progress variable are used to derive an asymptotic expression for turbulent burning velocity. New DNS runs are performed for validation in a statistically one dimensional steady state configuration. Parametric study is performed with respect to turbulent intensity, integral length scale, density ratio and laminar flame speed. Results show good agreement between DNS results and the asymptotic expression in terms of measured maximum flame surface density and estimated turbulent diffusivity in unburned gas.

• Journal of the Korean Society of Combustion
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• v.9 no.4
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• pp.1-8
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• 2004

Zone conditional formulation for the Reynolds average reaction progress variable is used to derive an asymptotic expression for turbulent burning velocity. New DNS runs are performed for validation in a statistically one dimensional steady state configuration. Parametric study is performed with respect to turbulent intensity, integral length scale, density ratio and laminar flame speed. Results show good agreement between DNS results and the asymptotic expression in terms of measured maximum flame surface density and estimated turbulent diffusivity in unburned gas.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.679-698
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• 2018

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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.7
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• pp.1217-1233
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• 2015

The paper studies characteristics of the minimum mean-square error symmetric scalar quantizers for the generalized gamma, Bucklew-Gallagher and Hui-Neuhoff probability density functions. Toward this goal, asymptotic formulas for the inner- and outermost thresholds, and distortion are derived herein for nonuniform quantizers for the Bucklew-Gallagher and Hui-Neuhoff densities, parallelling the previous studies for the generalized gamma density, and optimal uniform and nonuniform quantizers are designed numerically and their characteristics tabulated for integer rates up to 20 and 16 bits, respectively, except for the Hui-Neuhoff density. The assessed asymptotic formulas are found consistently more accurate as the rate increases, essentially making their asymptotic convergence to true values numerically acceptable at the studied bit range, except for the Hui-Neuhoff density, in which case they are still consistent and suggestive of convergence. Also investigated is the uniqueness problem of the differentiation method for finding optimal step sizes of uniform quantizers: it is observed that, for the commonly studied densities, the distortion has a unique local minimizer, hence showing that the differentiation method yields the optimal step size, but also observed that it leads to multiple solutions to numerous generalized gamma densities.

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.297-309
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• 1999

A sequential procedure of fixed-width confidence intervals for quantiles satisfying a condition of coverage probability is provided based on recursive density estimators. It is shown that the proposed sequential procedure is asymptotically efficient. In addition, the asymptotic normality for the proposed stopping time is derived.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.345-355
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• 2018

This paper looks into phase plane behavior of the solution near the positive steady-state for the system with prey density dependent response functions. The positive invariance and boundedness property of the solution to the objective model are proved. The existence result of a positive steady-state and asymptotic analysis near the positive constant equilibrium for the objective system are of interest. The results of phase plane analysis for the system are proved by observing the asymptotic properties of the solutions. Also some numerical analysis results for the behaviors of the solutions in time are provided.

• Journal of the Korean Statistical Society
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• v.29 no.2
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• pp.169-185
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• 2000

Given a random sample of size N (unknown) with density f(x│$\theta$), suppose that only n observations which lie outside a region r are recorded. On the basis of n observation, the Bayes estimators of $\theta$ and N are considered and their asymptotic expansions are developed to find the third order asymptotic properties with those of the maximum likelihood estimators and the Bayes modal estimators. The asymptotic m.s.e.'s of these estimators are expressed. An example is given to illustrate the results obtained.