• Communications for Statistical Applications and Methods
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• 제16권2호
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• pp.389-396
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• 2009

Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.

• Journal of Korean Society for Quality Management
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• 제27권1호
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• pp.46-58
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• 1999

The exact distributions of the sample variance $(S^2_n)$ and the estimator ($\hat{C}_p$) of the process capability index are not easily obtained in general. In this paper, the approximations using saddlepoint techniques to the distributions of these statistics are suggested and compared with the other approximation methods. For comparisons, the exact values obtained by extensive Monte-Carlo (simulation) studies are also given. As a result, the suggested approximation methods are very accurate even in moderate or small sample sizes and are easy to use. Also, the suggested methods can be adapted to approximate the distributions of more complicated statistics, including $\hat{C}_pk$ ,$\hat{C}_pm$, etc.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.539-546
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• 2014

This paper introduces the approximation and a proposed method to deal the optimum location network selection problem such that the total cost is minimized. For the proposed method, we derived a feasible solution and the variance. To compare the performances of the approximation and the proposed method, computer simulation is also implemented. The result showed the solutions being optimum with 74% for the proposed method and 57% for the approximation. When the solutions is not optimum, maximum and average deviations are below 4% and 2% respectively. The results indicate a slightly better performance of the proposed method in a certain case.

• The Korean Journal of Applied Statistics
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• 제11권2호
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• pp.287-302
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• 1998

Saddlepoint approximation to the distribution function of sample mean(Daniels, 1987) is extended to the case of general statistic in this paper. The suggested approximation methods are applied to derive the approximations to the distributions of some statistics, including sample valiance and studentized mean. Some comparisons with other methods show that the suggested approximations are very accurate for moderate or small sample sizes. Even in extreme tail the accuracies are also maintained.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.907-912
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• 2013

This paper focuses on the situation of optimizing the total cost with m given messages and n network nodes. Associated with each network node, a fixed cost is incurred to the receiver if at least one message is received. The mean and variance of the total costs are obtained. Normal approximation is used. Empirical results showed that the derived method reduces research work substantially.

• The Korean Journal of Applied Statistics
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• 제22권6호
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• pp.1131-1142
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• 2009

We suggest a fast and accurate algorithm to compute ARLs of CUSUM chart for controling process variance. The algorithm solves the characteristic integral equations of CUSUM chart (for controling variance). The algorithm is directly applicable for the cases of odd sample sizes. When the sample size is even, by using well-known approximation algorithm combinedly with the new algorithm for neighboring odd sample sizes, we can also evaluate the ARLs of CUSUM charts efficiently and accurately. Based on the new algorithm we consider the optimal design of upward and downward CUSUM charts for controling process variance.

• Journal of the Korean Data and Information Science Society
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• 제22권6호
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• pp.1217-1222
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• 2011

In this paper, we show that any circular density can be closely approximated by an exponential family of distributions. Therefore we propose an exponential family of distributions as a new family of circular distributions, which is absolutely suitable to model any shape of circular distributions. In this family of circular distributions, the trigonometric moments are found to be the uniformly minimum variance unbiased estimators (UMVUEs) of the parameters of distribution. Simulation result and goodness of fit test using an asymmetric real data set show usefulness of the novel circular distribution.

• The Journal of the Acoustical Society of Korea
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• 제24권1호
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• pp.1-10
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• 2005

This paper presents a wideband LPA (local polynomial approximation) beamforming algorithm that is appropriate for wideband moving sources. The Proposed wideband LPA algorithm adopts STMV (steered minimum variance) method that utilizes a steered covariance matrix obtained from multiple frequency components in one data snapshot, instead of multiple data snapshots in one frequency bin. The wideband LPA cost function is formed using STMV weight vector. The Proposed algorithm searches for the instantaneous DOA and angular velocity that maximize the wideband LPA cost function. resulting in a higher resolution performance than that of a DS LPA beamforming algorithm. Several simulations using artificial data and sea trial data are used to demonstrate the performance of the Proposed algorithm.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제30권11C호
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• pp.1116-1124
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• 2005

We investigated the mean and variance of the MSE and the MI-based image registration methods that have been widely applied for image registration. By using the first order Taylor series expansion, we have approximated the mean and the variance for one-dimensional image registration. The asymptotic results show that the MSE based method is unbiased and efficient for the same image registration problem while the MI-based method shows larger variance. However, for the different modality image registration problem, the MSE based method is largely biased while the MI based method still achieves registration. The results imply that the MI based method achieves robustness to the different image modalities at the cost of inefficiency. The analytical results are supported by simulation results.

• Journal of the Korean Mathematical Society
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• 제57권5호
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• pp.1167-1186
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• 2020

This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among the state variables. This full correlation structure possesses the limitation to have fully analytical pricing formula for hybrid models of variance swaps, due to the non-affinity property embedded in the model itself. We address this issue by obtaining an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions. Subsequently, we implement numerical experiments to evaluate the accuracy of our pricing formula. Our findings confirm that the impact of the correlation between the underlying and the interest rate is significant for pricing discretely-sampled variance swaps.