• Journal of applied mathematics & informatics
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• 제26권5_6호
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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.

• Asian-Australasian Journal of Animal Sciences
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• 제13권3호
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• pp.413-422
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• 2000

In the class of models which include random effects, the variance component estimates are important to obtain accurate predictors and estimators. Variance component estimation is straightforward for balanced data but not for unbalanced data. Since orthogonality among factors is absent in unbalanced data, various methods for variance component estimation are available. REML estimation is the most widely used method in animal breeding because of its attractive statistical properties. Recently, Bayesian approach became feasible through Markov Chain Monte Carlo methods with increasingly powerful computers. Furthermore, advances in variance component estimation with complicated models such as generalized linear mixed models enabled animal breeders to analyze non-normal data.

• Communications for Statistical Applications and Methods
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• 제20권4호
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• pp.247-257
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• 2013

A variety of practical problems can be addressed in the framework of rotation (successive) sampling. The present work presents a sample rotation pattern where sampling units are drawn on two successive occasions. The problem of estimation of population variance on current (second) occasion in two - occasion successive (rotation) sampling has been considered. A class of estimators has been proposed for population variance that includes many estimators as a particular case. Asymptotic properties of the proposed class of estimators are discussed. The proposed class of estimators is compared with the sample variance estimator when there is no matching from the previous occasion. Optimum replacement policy is discussed. Results are supported with the empirical means of comparison.

• 제어로봇시스템학회논문지
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• 제8권3호
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• pp.275-280
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• 2002

A new algorithm for gradual scene change detection in MPEG based frame sequences is proposed in this paper. The proposed algorithm is based on the fact that most of gradual curves can be characterized by variance distributions of edge information in the frame sequences. Average edge frame sequences are obtained by performing "sober" edge detection. Features are extracted by comparing variances with those of local blocks in the average edge frames. Those features are further processed by the opening operation to obtain smoothing variance curves. The lowest variance in the local frame sequences is chosen as a gradual detection point. Experimental results show that the proposed method provides 85% precision and 86% recall rate fur gradual scene changes.

• Communications for Statistical Applications and Methods
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• 제13권1호
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• pp.61-72
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• 2006

When using the well-known variance estimator of Sen (1953) and Yates and Grundy (1953) in inclusion probability proportional to size sampling, we often encounter the problems due to the calculation of the joint probabilities. Sarndal (1996) and Knottnerus (2003) proposed alternative strategies for variance estimation to avoid those problems in the traditional method. We discuss some of practical issues that arise when they are used. Also, we describe the traditional strategy using a sampling procedure available in a statistical software. It would be one of the attractive choices for design-based variance estimation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권2호
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• pp.123-135
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• 2016

This article deals with the pricing of Asian options under a constant elasticity of variance (CEV) model as well as a stochastic elasticity of variance (SEV) model. The CEV and SEV models are underlying asset price models proposed to overcome shortcomings of the constant volatility model. In particular, the SEV model is attractive because it can characterize the feature of volatility in risky situation such as the global financial crisis both quantitatively and qualitatively. We use an asymptotic expansion method to approximate the no-arbitrage price of an arithmetic average Asian option under both CEV and SEV models. Subsequently, the zero and non-zero constant leverage effects as well as stochastic leverage effects are compared with each other. Lastly, we investigate the SEV correction effects to the CEV model for the price of Asian options.

• Communications for Statistical Applications and Methods
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• 제25권3호
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• pp.275-282
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• 2018

This paper discusses the use of projections for the sums of squares in the analyses of variance for two-way nested design data. The model for this data is assumed to only have random effects. Two different sizes of experimental units are required for a given experimental situation, since nesting is assumed to occur both in the treatment structure and in the design structure. So, variance components are coming from the sources of random effects of treatment factors and error terms in different sizes of experimental units. The model for this type of experimental situation is a random effects model with more than one error terms and therefore estimation of variance components are concerned. A projection method is used for the calculation of sums of squares due to random components. Squared distances of projections instead of using the usual reductions in sums of squares that show how to use projections to estimate the variance components associated with the random components in the assumed model. Expectations of quadratic forms are obtained by the Hartley's synthesis as a means of calculation.

• 한국산업융합학회 논문집
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• 제12권1호
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• pp.35-42
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• 2009

In Taguchi's quadratic expected loss function used as robustness metric of performance characteristics, the mean and variance contributions are confounded. The consolidation of the mean and variance in the expected loss function may not always be the ideal approach. This paper presents a procedure for multi-attributes design optimization, where the mean and variance of performance characteristics are considered as separate attributes having designer's relative preferences for them and Technique for Order Preference by Similarity to Ideal Solution(TOPSIS) is introduced to attain robust optimal design. The effectiveness of proposed approach is shown with an example of a weld line minimization problem in the injection molding process.

• Journal of the Korean Data and Information Science Society
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• 제16권2호
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• pp.173-183
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• 2005

This paper studies quick detection of variance change point for iid data. For development of sensitive and adaptive variance change point detector, moving variance ratio is employed as a variance ratio estimator. It is shown that selection of tuning parameters of detector, (i.e., information and lag tuning parameters) is critical for detector to achieve desirable sensitivity and adaptiveness. Interestingly our simulation result reveals limitations of the commonly used change ratio against the previous day. Our results will provide useful insight when the detector is applied to time series data.

• Journal of the Korean Data and Information Science Society
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• 제28권2호
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• pp.443-449
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• 2017

Estimation of population proportion like the distribution rate of LED TV and the prevalence of a disease are often estimated based on survey sample data. Population proportion is generally considered as a special form of population mean. In complex sampling like stratified multistage sampling with unequal probability sampling, the denominator of mean may be random variable and it is estimated like ratio estimator. In this research, we examined the estimation of distribution rate based on stratified multistage sampling, and determined some numerical outcomes using stratified random sample data with about 25% of missing observations. In the data used for this research, the survey weight was determined by deterministic way. So, the weights are not random variable, and the population distribution rate and its variance estimator can be estimated like population mean estimation. When the weights are not random variable, if one estimates the variance of proportion estimator using ratio method, then the variances may be inflated. Therefore, in estimating variance for population proportion, we need to examine the structure of data and survey design before making any decision for estimation methods.