• Honam Mathematical Journal
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• v.31 no.4
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• pp.505-513
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• 2009

Let {$X_k;k{\in}N^d$} be centered and identically distributed random field which is asymptotically negative dependent in a certain case. In this note we prove that for $p{\alpha}$ > 1 and ${\alpha}$ > ${\frac{1}{2}}$ $E{\mid}X_1{\mid}^p(log^+{\mid}X_1{\mid}^{d-1})$ < ${\infty}$ if and only if ${\sum}_n{\mid}n{\mid}^{p{\alpha}-2}P$($max_{1{\leq}k{\leq}n{\mid}S_k{\mid}}$ > ${\epsilon}{\mid}n{\mid}$) < ${\infty}$ for all ${\epsilon}$ > 0, where log$^+$x = max{1,log x}.

• East Asian mathematical journal
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• v.24 no.3
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• pp.251-261
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• 2008

Let {${\xi}_j;j\;{\geq}\;1$} be a centered strictly stationary random sequence defined by $S_0\;=\;0$, $S_n\;=\;\Sigma^n_{j=1}\;{\xi}_j$ and $\sigma(n)\;=\;33\sqrt {ES^2_n}$ where $\sigma(t),\;t\;>\;0$, is a nondecreasing continuous regularly varying function. Suppose that there exists $n_0\;{\geq}\;1$ such that, for any $n\;{\geq}\;n_0$ and $0\;{\leq}\;{\varepsilon}\;<\;1$, there exist positive constants $c_1$ and $c_2$ such that $c_1e^{-(1+{\varepsilon})x^2/2}\;{\leq}\;P\{\frac{{\mid}S_n{\mid}}{\sigma(n)}\;{\geq}\;x\}\;{\leq}\;c_2e^{-(1-{\varepsilon})x^2/2$, $x\;{\geq}\;1$ Under some additional conditions, we investigate some limsup results for the increments of partial sum processes of the sequence {${\xi}_j;j\;{\geq}\;1$}.

• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.337-346
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• 2019

This paper discusses a method for obtaining nonnegative estimates for variance components in a random effects model. A variance component should be positive by definition. Nevertheless, estimates of variance components are sometimes given as negative values, which is not desirable. The proposed method is based on two basic ideas. One is the identification of the orthogonal vector subspaces according to factors and the other is to ascertain the projection in each orthogonal vector subspace. Hence, an observation vector can be denoted by the sum of projections. The method suggested here always produces nonnegative estimates using projections. Hartley's synthesis is used for the calculation of expected values of quadratic forms. It also discusses how to set up a residual model for each projection.

• KIISE Transactions on Computing Practices
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• v.21 no.7
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• pp.476-481
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• 2015

We have parallelized the cumulative sum (CUSUM) test of NIST's statistical random number test suite in a CUDA environment. Storing random walks in an array instead of in scalar variables eliminates data dependence. The change in data structure makes it possible to apply parallel scans, scatters, and reductions at each stage of the test. In addition, serial data exchanges between CPU and GPU are removed by migrating CPU's tasks to GPU. Finally we have optimized global memory accesses. The overall speedup is 23 times over the sequential version. Our results contribute to improving security of random numbers for cryptographic keys as well as reducing the time for evaluation of randomness.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.257-266
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• 2016

Random Coefficient Autoregressive models (RCA) have attracted increased interest due to the wide range of applications in biology, economics, meteorology and finance. We consider an RCA as an appropriate model for non-linear properties and better than an AR model for linear properties. We study the methods of RCA parameter estimation. Especially we proposed the special case that an random coefficient ${\phi}(t)$ has the initial value ${\phi}(0)$ in the RCA model. In practical study, we estimated the parameters and compared Prediction Error Sum of Squares (PRESS) criterion between AR and RCA using Korean Mumps data.

• International Journal of Aeronautical and Space Sciences
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• v.5 no.2
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• pp.1-8
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• 2004

Real-Time Kinematic GPS positioning is widely used for many applications.Resolving ambiguities is the key to precise positioning. Integer ambiguity resolution isthe process of resolving the unknown cycle ambiguities of double difference carrierphase data as integers. Two important issues of resolving are efficiency andreliability. In the conventional search techniques, we generally used chi-squarerandom variables for decision variables. Mathematically, a chi-square random variableis the sum of mutually independent, squared zero-mean unit-variance normal(Gaussian) random variables. With this base knowledge, we can separate decisionvariables to several normal random variables. We showed it with related equationsand conceptual diagrams. With this separation, we can improve the computationalefficiency of the process without losing the needed performance. If we averageseparated normal random variables sequentially, averaged values are also normalrandom variables. So we can use them as decision variables, which prevent from asudden increase of some decision variable. With the method using averaged decisionvalues, we can get the solution more quicklv and more reliably.To verify the performance of our proposed algorithm, we conducted simulations.We used some visual diagrams that are useful for intuitional approach. We analyzedthe performance of the proposed algorithm and compared it to the conventionalmethods.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.2A
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• pp.105-111
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• 2010

Random unitary beamforming (RUB) is a very low complexity and practical transmission scheme for multiuser MIMO broadcast channel. In this paper, we propose the scheme that obtains the spatial multiplexing gain on the extension of the conventional RUB, that is, the receiver with two antennas is compared to that with one antenna in a conventional RUB, which results in the increased capacity. So, we propose the new codebook and the minimum mean square error successive interference cancellation (MMSE-SIC) receiver filter. We show the simulation result that the sum-rate of proposed system is increased.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.507-513
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• 2010

Let {$X_i,-{\infty}$ < 1 < $\infty$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$a_i,\;-{\infty}$ < i < ${\infty}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n={\sum}_{i=-\infty}^{\infty}a_{i+n}X_i$, n $\geq$ 1 and $S_n=Y_1+{\cdots}+Y_n$. In this paper we prove that E|$X_1$|$^rh$($|X_1|^p$) < $\infty$ implies ${\sum}_{n=1}^{\infty}n^{r/p-2-q/p}h(n)E{max_{1{\leq}k{\leq}n}|S_k|-{\epsilon}n^{1/p}}{_+^q}<{\infty}$ and ${\sum}_{n=1}^{\infty}n^{r/p-2}h(n)E{sup_{k{\leq}n}|k^{-1/p}S_k|-{\epsilon}}{_+^q}<{\infty}$ for all ${\epsilon}$ > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 ${\leq}$ p < 2 and r > 1 + p/2.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.4
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• pp.324-333
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• 2013

The purpose of this paper is to improve the efficiency of multi-objective topology optimization using a genetic algorithm (GA) with bar-system representation. We proposed a new GA using an elite initial population obtained from a Solid Isotropic Material with Penalization (SIMP) using a weighted sum method. SIMP with a weighted sum method is one of the most established methods using sensitivity analysis. Although the implementation of the SIMP method is straightforward and computationally effective, it may be difficult to find a complete Pareto-optimal set in a multi-objective optimization problem. In this study, to build a more convergent and diverse global Pareto-optimal set and reduce the GA computational cost, some individuals, with similar topology to the local optimum solution obtained from the SIMP using the weighted sum method, were introduced for the initial population of the GA. The proposed method was applied to a structural topology optimization example and the results of the proposed method were compared with those of the traditional method using standard random initialization for the initial population of the GA.

• International journal of advanced smart convergence
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• v.10 no.1
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• pp.75-81
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• 2021

As the number of connected smart devices and applications increases explosively, the existing orthogonal multiple access (OMA) techniques have become insufficient to accommodate mobile traffic, such as artificial intelligence (AI) and the internet of things (IoT). Fortunately, non-orthogonal multiple access (NOMA) in the fifth generation (5G) mobile networks has been regarded as a promising solution, owing to increased spectral efficiency and massive connectivity. In this paper, we investigate the achievable data rate for non-orthogonal multiple access (NOMA) with negatively-correlated information sources (CIS). For this, based on the linear transformation of independent random variables (RV), we derive the closed-form expressions for the achievable data rates of NOMA with negatively-CIS. Then it is shown that the achievable data rate of the negatively-CIS NOMA increases for the stronger channel user, whereas the achievable data rate of the negatively-CIS NOMA decreases for the weaker channel user, compared to that of the positively-CIS NOMA for the stronger or weaker channel users, respectively. We also show that the sum rate of the negatively-CIS NOMA is larger than that of the positively-CIS NOMA. As a result, the negatively-CIS could be more efficient than the positively-CIS, when we transmit CIS over 5G NOMA networks.