• Journal of the Chungcheong Mathematical Society
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• 제26권3호
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• pp.615-623
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• 2013

In this paper we establish a central limit theorem for weighted sums of $Y_n={\sum_{i=1}^{n}}a_n,_iX_i$, where $\{a_{n,i},\;n{\in}N,\;1{\leq}i{\leq}n\}$ is an array of nonnegative numbers such that ${\sup}_{n{\geq}1}{\sum_{i=1}^{n}}a_{n,i}^2$ < ${\infty}$, ${\max}_{1{\leq}i{\leq}n}a_{n,i}{\rightarrow}0$ and $\{X_i,\;i{\in}N\}$ is a sequence of linear negatively quadrant dependent random variables with $EX_i=0$ and $EX_i^2$ < ${\infty}$. Using this result we will obtain a central limit theorem for partial sums of linear processes.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제28권10C호
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• pp.936-941
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• 2003

Density evolution was developed as a method for computing the capacity of low-density parity-check(LDPC) codes under the sum-product algorithm [1]. Based on the assumption that the passed messages on the belief propagation model can be approximated well by Gaussian random variables, a modified and simplified version of density evolution technique was introduced in [2]. Recently, the min-sum algorithm was applied to the density evolution of LDPC codes as an alternative decoding algorithm in [3]. Next question is how the min-sum algorithm is combined with a Gaussian approximation. In this paper, the capacity of various rate LDPC codes is obtained using the min-sum algorithm combined with the Gaussian approximation, which gives a simplest way of LDPC code analysis. Unlike the sum-product algorithm, the symmetry condition [4] is not maintained in the min-sum algorithm. Therefore, the variance as well as the mean of Gaussian distribution are recursively computed in this analysis. It is also shown that the min-sum threshold under a gaussian approximation is well matched to the simulation results.

• International Journal of Contents
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• 제2권2호
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• pp.17-24
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• 2006

The work presented in this paper is divided into two parts. The first part presents finite urn problems which generate truncated negative binomial random variables. Some combinatorial identities that arose from the negative binomial sampling and truncated negative binomial sampling are established. These identities are constructed and serve important roles when we deal with these distributions and their characteristics. Other important results including cumulants and moments of the distributions are given in somewhat simple forms. Second, the distributions of the maximum of two chi-square variables and the distributions of the maximum correlated F-variables are then derived within the negative binomial sampling scheme. Although multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information and deeper insight regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of these distributions. We supplement our findings with exact simple computational methods where no interpolations are involved.

• Transactions of the Korean Society of Mechanical Engineers A
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• 제29권11호
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• pp.1472-1479
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• 2005

Multiple surface crack distributed randomly along a weld toe influences strongly on the fatigue crack propagation life of welded joint. It is investigated by using statistical approaches based on series of systematic experiments. From the statistical results, initial crack numbers and its locations follow the normal distribution, and the probability of initial crack depths and lengths can be described well by tile Weibull distribution. These characteristics are used to calculate the fatigue crack propagation life, in which the mechanisms of mutual interaction and coalescence of the multiple cracks are considered as well as the Mk-factors obtained from a parametric study on the crack depths and lengths. The automatic calculation is achieved by the NESUSS, where the parameters such as the number, location and size of the cracks are all treated as random variables. The random variables are dealt through the Monte-Carlo simulation with sampling random numbers of 2,000. The simulation results show that the multiple cracks lead to much shorter crack propagation life compared with those in single crack situation. The sum of the simulation and tile fatigue crack initiation life derived by the notch strain approach agrees well with the experiments.

• Journal of Communications and Networks
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• 제12권3호
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• pp.222-230
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• 2010

In this paper, we present a closed-form approximation of the average sum rate of zero-forcing (ZF) beamforming (BF) with semi-orthogonal user selection (SUS). We first derive the survival probability associated with the SUS that absolute square of the channel correlation between two users is less than the orthogonalization level threshold (OLT).With this result, each distribution for the number of surviving users at each iteration of the SUS and the number of streams for transmission is calculated. Secondly, the received signal power of ZF-BF is represented as a function of the elements of the upper triangular matrix from QR decomposition of the channel matrix. Thirdly, we approximate the received signal power of ZF-BF with the SUS as the maximum of scaled chisquare random variables where the scaling factor is approximated as a function of both OLT and the number of users in the system. Putting all the above derivations and order statistics together, the approximated ergodic sum rate of ZF-BF with the SUS is shown in a closed form. The simulation results verify that the approximation tightly matches with the sample average for any OLT and even for a small number of users.

• Journal of the Korean Statistical Society
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• 제28권4호
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• pp.523-533
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• 1999

We consider the M/G/1 queueing model with D-policy. The server is turned off at the end of each busy period and is activated again only when the sum of the service times of all waiting customers exceeds a fixed value D. We obtain the distribution of unfinished work and show that the unfinished work decomposes into two random variables, one of which is the unfinished work of ordinary M/G/1 queue. We also derive the distribution of queue waiting time.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1573-1581
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• 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.

• Bulletin of the Korean Mathematical Society
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• 제43권1호
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• pp.169-178
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• 2006

For double arrays of constants ${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$ and sequences ${X_n,\;n{\geq}1}$ of asymptotically almost negatively associated (AANA) random variables the almost sure convergence of $\sum\limits{_{i=1}}{^{k_n}}\;a_{ni}X_i$ is derived.

• Journal of the Chungcheong Mathematical Society
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• 제26권3호
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• pp.491-499
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• 2013

In this paper, we prove the weak law of large numbers for weighted sums of noncommutative random variables in noncommutative Lorentz space under weaker conditions than the conditions in [7].

• Journal of the Korean Statistical Society
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• 제32권1호
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• pp.21-24
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• 2003

In the recent papers by Harris and Park (1994) and by Hui and Park (2000), a family of lattice distributions derived from a sum of independent identically distributed random variables is examined. In this paper we generalize a result of Hui and Park (2000) on lattice distributions on the torus using the Poisson summation formula.