• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1169-1183
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• 2008

In this paper, a method to find the weighted possibilistic variance and moments about the mean value of fuzzy numbers via applying a difuzzification using minimizer of the weighted distance between two fuzzy numbers is introduced. In this way, we obtain the nearest weighted point with respect to a fuzzy number, this main result is a new and interesting alternative justification to define of weighted mean of a fuzzy number. Considering this point and the weighted distance quantity, we introduce the weighted possibilistic mean (WPM) value and the weighted possibilistic variance(WPV) of fuzzy numbers. This paper shows that WPM is the nearest weighted point to fuzzy number and the WPV of fuzzy number is preserved more properties of variance in probability theory so that it can simply introduce the possibilistic moments about the mean of fuzzy numbers without problem. The moments of fuzzy numbers play an important role to estimate of parameters, skewness, kurtosis in many of fuzzy times series models.

• The Korean Journal of Applied Statistics
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• v.30 no.4
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• pp.567-578
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• 2017

Grouped multivariate data can be tested for differences between two or more groups using multivariate analysis of variance (MANOVA). However, this method cannot be used if several assumptions of MANOVA are violated. In this case, multidimensional scaling (MDS) and analysis of distance (AOD) can be applied to grouped dissimilarities based on the various distances. A permutation test is a non-parametric method that can also be used to test differences between groups. MDS is used to calculate the coordinates of observations from dissimilarities and AOD is useful for finding group structure using the coordinates. In particular, AOD is mathematically associated with MANOVA if using the Euclidean distance when computing dissimilarities. In this paper, we study the between and within group structure by applying MDS and AOD to the grouped dissimilarities. In addition, we propose a new test statistic using the group structure for the permutation test. Finally, we investigate the relationship between AOD and MANOVA from dissimilarities based on the Euclidean distance.

• The Korean Journal of Applied Statistics
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• v.25 no.3
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• pp.485-501
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• 2012

This research is to find a design D that minimizes forecast variance in d dimensions over the candidate space ${\chi}$. We want a robust design since we may not know the specific covariance structure. We seek a design that minimizes a coverage criterion and hope that this design will provide a small forecast variance even if the covariance structure is unobservable. The details of an exchange or swapping algorithm and several properties of the parameters of coverage criterion with the unknown correlation structures are discussed.

• Journal of KIISE:Databases
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• v.31 no.2
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• pp.83-90
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• 2004

In this paper, we study the CCD(Clustering with Circular Distance) and the COD(Clustering with Obstructed Distance) problems to be considered when objects are being clustered in a circularly search space and a search space with the presence of obstacles. We also propose a now clustering algorithm for clustering efficiently objects that the insertion or the deletion is occurring frequently in multi-dimensional search space. The distance function for solving the CCD and COD Problems is defined in the Proposed clustering algorithm. This algorithm is included a clustering method to create clusters that have a high spatial locality by minimum computation time.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.7
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• pp.216-224
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• 2013

The within-class variance of Otsu's method is moderate but improper in expressing class statistical distributions. Otsu's method uses a variance to represent the distribution of each class. The variance utilizes a distance square from the mean to a data. This process is not proper in denoting a real class statistical distribution because of the distance square. In this paper, to express more exact class statistical distributions, the within-class standard deviation as a criterion for threshold selection is proposed and then the optimal threshold is determined by minimizing it. In order to have validity, it is shown through the experimental results that the proposed method was more superior to the counterparts.

• Korean Management Science Review
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• v.33 no.4
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• pp.51-64
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• 2016

The maximum weight of single stock in mutual fund is limited by regulations to enforce diversification. Under incomplete information with added constraints on portfolio weights, enhanced performance had been reported in previous researches. We analyze a weight vector to examine the effects of additional constraints on the portfolio's performance by computing the Euclidean distance from the in-sample tangency portfolio, as opposed to previous researches which analyzed ex-post return only. Empirical experiment was performed on Mean-variance and Minimum-variance model with Fama French's 30 industry portfolio and 10 industry portfolio for the last 1,000 months from August 1932 to November 2015. We find that diversification-constrained portfolios have 7% to 26% smaller Euclidean distances with the benchmark portfolio compared to those of unconstrained portfolios and 3% to 11% greater Sharpe Ratio.

• Imaging Science in Dentistry
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• v.34 no.3
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• pp.123-128
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• 2004

Purpose: To evaluate the reliability of measurements in spiral tomography through assessing the visibility of the alveolar crest and the measurements between the alveolar crest and other anatomic structures. Materials and Methods: 110 spiral tomograms of the jaws were taken by Scanora X-ray unit from the patients. The visibility of the alveolar crests was estimated by 3 observers and classified as clearly visible, questionable visibility, or not visible. 3 observers measured the distance between the alveolar crest and the reference points of anatomic structures. The measurements were repeated 2 weeks later. Results: 52.9% of alveolar crests on upper jaws and 61.5% of alveolar crests on lower jaws were visible. The interobserver and intraobserver agreements on the visibility were low. The mean ranges of the measurements were 1.39 mm (SD = 1.37 mm) on maxilla and 1.03 mm (SD = 1.01 mm) on mandible in the interobserver evaluation. The interobserver variance was greater than the intraobserver variance in the measurements of distance. Conclusion: Spiral tomography showed a relatively low reliability in the visibility and measurements of the alveolar crest.

• The Journal of the Acoustical Society of Korea
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• v.29 no.1E
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• pp.45-53
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• 2010

In this paper, we present the use of the Features Weighted Mahalanobis Distance (FWMD) in improving the performance of Likelihood Maximizing Beamforming (Limabeam) algorithm in speech recognition for microphone array. The proposed approach is based on the replacement of the traditional distance measure in a Gaussian classifier with adding weight for different features in the Mahalanobis distance according to their distances after the variance normalization. By using Features Weighted Mahalanobis Distance for Limabeam algorithm (FWMD-Limabeam), we obtained correct word recognition rate of 90.26% for calibrate Limabeam and 87.23% for unsupervised Limabeam, resulting in a higher rate of 3% and 6% respectively than those produced by the original Limabearn. By implementing a HM-Net speech recognition strategy alternatively, we could save memory and reduce computation complexity.

• Journal of Information Processing Systems
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• v.16 no.4
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• pp.832-844
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• 2020

The degree of dispersion of a random variable can be described by the variance, which reflects the distance of the random variable from its mean. However, the time complexity of the traditional variance calculation algorithm is O(n), which results from full calculation of all samples. When the number of samples increases or on the occasion of high speed signal processing, algorithms with O(n) time complexity will cost huge amount of time and that may results in performance degradation of the whole system. A novel multi-step recursive algorithm for variance calculation of the time-varying data series with O(1) time complexity (constant time) is proposed in this paper. Numerical simulation and experiments of the algorithm is presented and the results demonstrate that the proposed multi-step recursive algorithm can effectively decrease computing time and hence significantly improve the variance calculation efficiency for time-varying data, which demonstrates the potential value for time-consumption data analysis or high speed signal processing.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1281-1288
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• 2010

We consider Yut board game with four Yut sticks which are of the same shape and the same size so that they have the same probability of showing back when they are tossed. Since, in Yut board game, a player have to toss four sticks one more when sawi Mo or sawi Yut appears, the player may be interested in the distance which Mal can move in one's turn. Therefore, the probability mass function of the distance is obtained and probabilities with several values of back probability are summarized in a table. Also, the expectation, the variance, the skewness, and the kurtosis of the distribution are calculated and their values are also tablized for some values of back probability.