• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.563-568
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• 1995

It is well-known that the sample mean and the sample variance are jointly sufficient under normality assumption. In this paper a proof of the joint sufficiency is given without using the factorization criterion. It is related to a finite Sanov-type conditional theorem, i.e., the conditional probability density of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are independently and identically distributed (i.i.d.) normal random variables with mean m and variance $\delta^2$, equals that of $Y_1$ given sample mean $\mu$ and sample variance $\sigma^2$, where $Y_1, Y_2, \cdots, Y_n$ are i.i.d. normal random variables with mean $\mu$ and variance $\sigma^2$.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.863-875
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• 2010

In this paper we apply the martingale approach, which has been widely used in mathematical finance, to investigate the optimal investment problem for an insurer under the criterion of mean-variance. When the risk and security assets are described by the L$\acute{e}$vy processes, the closed form solutions to the maximization problem are obtained. The mean-variance efficient strategies and frontier are also given.

• Journal of the Korean Statistical Society
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• v.18 no.2
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• pp.118-124
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• 1989

In the one-way random effect model, we often estimate the variance components by the ANOVA method and then estimate the population mean. Whe there are only two distint group sizes, the conventional mean estimator is represented as a weighted average of two normal means with weights being the function of variance component estimators. In this paper, we will study a method which can compute the exact variance of the mean estimator when we set the negative variance component estimate to zero.

• 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.

• Journal of the Korean Society of Industry Convergence
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• v.12 no.1
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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.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.249-259
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• 2002

In order to estimate the mean and variance for a Normal distribution which is truncated at both right and left sides, maximum likelihood estimators based on the entire sample from the original distribution are compared with the sample mean and variance of the censored sample which is the data remaining after truncation using simulation. We found that, surprisingly, the mean squared error of the mean based on the censored data Is smaller than that of the full sample estimators.

• Communications for Statistical Applications and Methods
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• v.23 no.1
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• pp.33-45
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• 2016

Variance components should be estimated based on mean change when the mean of the observations drift gradually over time. Consistent estimators for the variance components are studied for a particular modeling situation with some underlying functions or drift. We propose a new variance estimator with Fourier estimation of variations. The consistency of the proposed estimator is proved asymptotically. The proposed procedures are studied and compared empirically with the variance estimators removing trends. The result shows that our variance estimator has a smaller mean square error and depends on drift patterns. We estimate and apply the variance to Nile River flow data and resting state fMRI data.

• East Asian mathematical journal
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• v.5 no.1
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• pp.95-110
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• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.511-521
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• 2010

In this paper, we define the one-sided fuzzy set and we calculate the mean value and variance, defined by C. Carlsson and R. $Full{\acute{e}}r$, of this fuzzy set. And we obtain a result that, in some special case, the mean of the product of two fuzzy sets is the product of means of each fuzzy sets. This result can be considered as the similar result which is well-known in the independence of events in probability theory.

• Earthquakes and Structures
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• v.23 no.2
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• pp.115-128
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• 2022

One common method to select input ground motions to predict dynamic behavior of structures subjected to seismic excitation requires spectral acceleration (S_a) match target mean response spectrum. However, dispersion of ground motions, which explicitly affects the structural response, is rarely discussed in this method. Generally, selecting ground motions matching target mean and variance has been utilized as an appropriate method to predict reliable seismic response. The goal of this paper is to investigate the impact of target spectra variance of ground motions on structural seismic response. Two sets of ground motions with different target variances (zero variance and minimum variance larger than inherent variance of the target spectrum) are selected as input to two different structures. Structural responses at different heights are compared, in terms of peak, mean and dispersion. Results show that increase of target spectra variance tends to increase peak floor acceleration, peak deformation and dispersions of response of interest remarkably. To short-period structures, dispersion increase ratios of seismic response are close to that of S_a of input ground motions at the first period. To long-period structures, dispersions of floor acceleration and floor response spectra increase more significantly at the bottom, while dispersion increase ratios of IDR and deformation are close to that of S_a of input ground motions at the first period. This study could further provide useful information on selecting appropriate ground motion to predict seismic behavior of different types of structures.