• Bulletin of the Korean Mathematical Society
• /
• v.45 no.1
• /
• pp.75-93
• /
• 2008

The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.

• Journal of the Korean Mathematical Society
• /
• v.37 no.6
• /
• pp.885-899
• /
• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• Communications for Statistical Applications and Methods
• /
• v.6 no.1
• /
• pp.319-326
• /
• 1999

We shall derive several estimators for the minimum and maximum of two generalized uniform scale parameters with a common known shape parameter when the order of the scales is unknown and sample sizes are equal. Also we shall obtain the biases and mean squared errors for the proposed several estimators and compare numerically performances for the preposed several estimators.

• Journal of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.223-233
• /
• 2012

In this paper we establish some limsup results and a generalized uniform law of the iterated logarithm (LIL) for the increments of partial sums of a strictly stationary and linearly positive quadrant dependent (LPQD) sequence of random variables.

• Kyungpook Mathematical Journal
• /
• v.9 no.1_2
• /
• pp.41-42
• /
• 1969

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

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.37 no.5A
• /
• pp.279-289
• /
• 2012

Characteristics, such as the support limit and distortions, of minimum mean-squared error (MSE) N-level uniform and nonuniform scalar quantizers are studied for the family of the generalized gamma density functions as N increases. For the study, MSE-optimal scalar quantizers are designed at integer rates from 1 to 16 bits/sample, and their characteristics are compared with corresponding asymptotic formulas. The results show that the support limit formulas are generally accurate. They also show that the distortion of nonuniform quantizers is observed to converge to the Panter-Dite asymptotic constant, whereas the distortion of uniform quantizers exhibits slow or even stagnant convergence to its corresponding Hui-Neuhoff asymptotic constant at the studied rate range, though it may stay at a close proximity to the asymptotic constant for the Rayleigh and Laplacian pdfs. Additional terms in the asymptote result in quite considerable accuracy improvement, making the formulas useful especially when rate is 8 or greater.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1573-1581
• /
• 2010

we investigate the n-fold convolution of the uniform distributions. First, we are concerned with the explicit distribution function of the partial sum ${\zeta}_n$ when the random variables are independent and has identically uniform distribution, next, we determine the n-fold convolution distribution of ${\zeta}_n$ when the identically distributed condition is not satisfied.

• Journal of KSNVE
• /
• v.9 no.1
• /
• pp.103-112
• /
• 1999

A new modeling and analysis technique for one-dimensional distributed parameter systems is presented. First. discretized equations of motion in Laplace domain are derived by applying discretization methods for partial differential equations of a one-dimensional structure with respect to spatial coordinate. Secondly. the z and inverse z transformations are applied to the discretized equations of motion for obtaining a dynamic matrix for a uniform element. Four different discretization methods are tested with an example. Finally, taking infinite on the number of step for a uniform element leads to an exact dynamic matrix for the uniform element. A generalized modal analysis procedure for eigenvalue analysis and modal expansion is also presented. The resulting element dynamic matrix is tested with a numerical example. Another application example is provided to demonstrate the applicability of the proposed method.

• Korean Management Science Review
• /
• v.14 no.1
• /
• pp.31-52
• /
• 1997

The Generalized Assignment Problem(GAP) determines the minimum assignment of n tasks to m workstations such that each task is assigned to exactly one workstation, subject to the capacity of a workstation. In this paper, we presented a new heuristic search algorithm for GAPs. then we tested it on 4 different benchmark sample sets of random problems generated according to uniform distribution on a microcomputer.