• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.515-521
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• 2010

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_n\;=\;\frac{1}{N}Y_nY_n^TT_n$ where $Y_n\;=\;[Y_{ij}]_{n\;{\times}\;N}$ is with independent, identically distributed entries and $T_n$ is an $n\;{\times}\;n$ symmetric non-negative definite random matrix independent of the $Y_{ij}$'s. In the present paper, using the inversion formula of the Stieltjes transform, we will find that the limiting distribution of $B_n$ has a continuous density function away from zero.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.57
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• pp.123-129
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• 2000

The Bootstrap method proposed by Efron is non-parametric method which doesn't depend on the estimation of prior distribution refer to population. A typical statistical process control chart which is generally used is developed under the assumption that observations follow mutually independent and identically distributed within a sample and between samples. However, autocorrelation greatly affect the developed control chart under the assumption that observations are mutually independent. Many researchers showed that the result which was analyzed by using a typical control chart for the observations which has the correlation violated to the independence assumption can not be true. Therefore, we compared the standard method with bootstrap method and then evaluated them for x control chart and EWMA control chart by using bootstrap method which was proposed by Efron in the AR(1) model when the observations have correlation.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.519-524
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• 2009

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_{n}\;=\;\frac{1}{n}Y_{m}^{T}T_{m}Y_{m}$ where $Ym\;=\;[Y_{ij}]_{m{\times}n}$ is with independent, identically distributed entries and $T_m$ is an $m{\times}m$ symmetric nonnegative definite random matrix independent of the $Y_{ij}{^{\prime}}s$. In the present paper, using the inversion formula of the Stieltjes transform, we will find the density function of the limiting distribution of $B_n$ away from zero.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.493-502
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• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

• Journal of the Korea Society for Simulation
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• v.13 no.2
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• pp.23-34
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• 2004

Regenerative simulation (RS) is a method of stochastic steady-state simulation in which output data are collected and analysed within regenerative cycles (RCs). Since data collected during consecutive RCs are independent and identically distributed, there is no problem with the initial transient period in simulated processes, which is a perennial issue of concern in all other types of steady-state simulation. In this paper, we address the issue of experimental analysis of the quality of sequential regenerative simulation in the sense of the coverage of the final confidence intervals of mean values. The ultimate purpose of this study is to determine the best version of RS to be implemented in Akaroa2 [1], a fully automated controller of distributed stochastic simulation in LAN environments.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.2
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• pp.134-140
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• 2011

Recent work in compressed sensing theory shows that $M{\times}N$ independent and identically distributed sensing matrix whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal with high probability even if $M{\ll}N$. In particular, it is well understood that the $L_1$-minimization algorithm is able to recover sparse signals from incomplete measurements. In this paper, we propose a novel sparse signal reconstruction method that is based on the reweighted $L_1$-minimization via support detection.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.497-503
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• 2005

This paper presents characterizations on the independence of the exponential and Pareto distributions by record values. Let ${X_{n},\;n {\ge1}$ be a sequence of independent and identically distributed(i.i.d) random variables with a continuous cumulative distribution function(cdf) F(x) and probability density function(pdf) f(x). $Let{\;}Y_{n} = max{X_1, X_2, \ldots, X_n}$ for n \ge 1. We say $X_{j}$ is an upper record value of ${X_{n},{\;}n\ge 1}, if Y_{j} > Y_{j-1}, j > 1$. The indices at which the upper record values occur are given by the record times {u(n)}, n \ge 1, where u(n) = $min{j|j > u(n-1), X_{j} > X_{u(n-1)}, n \ge 2}$ and u(l) = 1. Then F(x) = $1 - e^{-\frac{x}{a}}$, x > 0, ${\sigma} > 0$ if and only if $\frac {X_u(_n)}{X_u(_{n+1})} and X_u(_{n+1}), n \ge 1$, are independent. Also F(x) = $1 - x^{-\theta}, x > 1, {\theta} > 0$ if and only if $\frac {X_u(_{n+1})}{X_u(_n)}{\;}and{\;} X_{u(n)},{\;} n {\ge} 1$, are independent.

• Journal of Korean Society of Transportation
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• v.21 no.4
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• pp.57-66
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• 2003

Because the Logit model easily calculates probabilities for choice alternatives and estimates parameters for explanatory variables, it is widely used as a traffic mode choice model. However, this model includes an assumption which is independently and identically distributed to the error component distribution of the mode choice utility function. This paper is a study on the estimation of the Heteroscedastic Logit Model. which mitigates this assumption. The purpose of this paper is to estimate a Logit model that more accurately reflects the mode choice behavior of passengers by resolving the homoscedasticity of the model choice utility error component. In order to do this, we introduced a scale factor that is directly related to the error component distribution of the model. This scale factor was defined so as to take into account the heteroscedasticity in the difference in travel time between using public transport and driving a car, and was used to estimate the travel time parameter. The results of the Logit Model estimation developed in this study show that Heteroscedastic Logit Models can realistically reflect the mode choice behavior of passengers, even if the difference in travel time between public and private transport remains the same as passenger travel time increases, by identifying the difference in mode choice probability of passengers for public transportation.

• Journal of Internet Computing and Services
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• v.24 no.6
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• pp.1-11
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• 2023

Federated learning (FL) is a ground breaking machine learning paradigm that allow smultiple participants to collaboratively train models in a cloud environment, all while maintaining the privacy of their raw data. This approach is in valuable in applications involving sensitive or geographically distributed data. However, one of the challenges in FL is dealing with heterogeneous and non-independent and identically distributed (non-IID) data across participants, which can result in suboptimal model performance compared to traditionalmachine learning methods. To tackle this, we introduce FedGCD, a novel FL algorithm that employs Graph Neural Network (GNN)-based community detection to enhance model convergence in federated settings. In our experiments, FedGCD consistently outperformed existing FL algorithms in various scenarios: for instance, in a non-IID environment, it achieved an accuracy of 0.9113, a precision of 0.8798,and an F1-Score of 0.8972. In a semi-IID setting, it demonstrated the highest accuracy at 0.9315 and an impressive F1-Score of 0.9312. We also introduce a new metric, nonIIDness, to quantitatively measure the degree of data heterogeneity. Our results indicate that FedGCD not only addresses the challenges of data heterogeneity and non-IIDness but also sets new benchmarks for FL algorithms. The community detection approach adopted in FedGCD has broader implications, suggesting that it could be adapted for other distributed machine learning scenarios, thereby improving model performance and convergence across a range of applications.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.55-60
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• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.