• Journal of Korean Society for Quality Management
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• v.7 no.2
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• pp.7-10
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• 1979

In this paper the Rao-Blackwell and Lehmann-$Scheff{\acute{e}}$ Theorem are used to drive the minimum variance unbiased estimators of system reliability for a number of distributions when a system consists of n Components whose random life times are assumed to be independent and identically distributed. For the case of a negative exponential life time, we obtain the maximum likelihood estimator of the system reliability and compair it with minimum variance unbiased estimator of the system reliability.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.902-904
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• 1988

For a generalized minimum variance controller algorithm the weighting polynomials are are calculated in a way to assign the closed loop poles of the system and to specify the controller gain at a frequency. As a result the oscillations in the control signal may be reduced without changing the deterministic behaviour of the system.

• Journal of the Korean Data and Information Science Society
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• v.22 no.4
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• pp.811-817
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• 2011

We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the introduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ${\leq}$ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability ar compared each other.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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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.

• Journal of Korean Society for Quality Management
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• v.15 no.2
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• pp.27-37
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• 1987

In life testing problem, many authors obtained the minimum variance unbiased estimator of $P_r$[X>Y] for the exponential family generally and conceptually. In this paper, we study the maximum likelihood estimator and minimum variance unbiased estimator of $P_r$[X>Y] in exponential X and normal Y.

• International Journal of Contents
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• v.3 no.1
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• pp.1-8
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• 2007

The distributions of the minimum correlated F-variable arises in many applied statistical problems including simultaneous analysis of variance (SANOVA), equality of variance, selection and ranking populations, and reliability analysis. In this paper, negative binomial sampling technique is employed to derive the distributions of the minimum of chi-square variables and hence the distributions of the minimum correlated F-variables. The work presented in this paper is divided in two parts. The first part is devoted to develop some combinatorial identities arised from the negative binomial sampling. These identities are constructed and justified to serve important purpose, when we deal with these distributions or their characteristics. Other important results including cumulants and moments of these distributions are also given in somewhat simple forms. Second, the distributions of minimum, chisquare variable and hence the distribution of the minimum correlated F-variables are then derived within the negative binomial sampling framework. 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 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 the distributions. The computation methods we adopted are exact and no interpolations are involved.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.229-241
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• 1997

We consider discrimination curve and minimum dwell time for Poisson distribution and Poisson-power function distribution. Let the random variable X has Poisson distribution with mean .lambda.. For the hypothesis testing H$\_$0/:.lambda. = t vs. H$\_$1/:.lambda. = d (d$\_$0/ if X.leq.c. Since a critical value c can not be determined to satisfy both types of errors .alpha. and .beta., we considered discrimination curve that gives the maximum d such that it can be discriminated from t for a given .alpha. and .beta.. We also considered an algorithm to compute the minimum dwell time which is needed to discriminate at the given .alpha. and .beta. for the Poisson counts and proved its convergence property. For the Poisson-power function distribution, we reject H$\_$0/ if X.leq..'{c}.. Since a critical value .'{c}. can not be determined to satisfy both .alpha. and .beta., similar to the Poisson case we considered discrimination curve and computation algorithm to find the minimum dwell time for the Poisson-power function distribution. We prosent this algorithm and an example of computation. It is found that the minimum dwell time algorithm fails for the Poisson-power function distribution if the aiming error variance .sigma.$\^$2/$\_$2/ is too large relative to the variance .sigma.$\^$2/$\_$1/ of the Gaussian distribution of intensity. In other words, if .ell. is too small, we can not find the minimum dwell time for a given .alpha. and .beta..

• Korean Journal of Hydrosciences
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• v.6
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• pp.13-22
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• 1995

The augmenting hydrologic data using a correlation procedure has been used to improve the estimates of the mean and variance at the site of interest with short record when one or more near by sites with longer records are available. The variance of the unbiased maximum likelihood estimator of $ derived by Moran based on the multivariate normal distribytion is modified into the form of Matalas and Jacobs for the biveriate normal distribution to get the critical minimum values of the multiple correlation coefficient which give the improvement for estimating the variance at the site of interest. Those values are tabulated for various lengths of short records and the number of sites.

• Korean Management Science Review
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• v.28 no.1
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• pp.159-167
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• 2011

The theory of random utility maximization (RUM) defines the probability of an alternative being chosen as the probability of its utility being perceived as higher than those of all the other competing alternatives in the choice set (Marschak 1960). According to this theory, consumers perceive the utility of an alternative not as a constant but as a probability distribution. Over the last two decades, there have been an increasing number of studies on the effect of utility variance on choice probability. The common result of the previous studies is that as the utility variance increases, the effect of the mean value of the utility (the deterministic component of the utility) on choice probability is reduced. This study provides a theoretical investigation on the effect of utility variance on choice probability without any assumptions on the specific forms of probability distributions. This study suggests that without assumptions of the probability distribution functions, firms cannot apply the marketing strategy of maximizing choice probability (or market share), but can only adopt the strategy of maximizing the minimum or maximum value of the expected choice probability. This study applies the Chebyshef inequality and shows how the changes in utility variances affect the maximum of minimum of choice probabilities and provides managerial implications.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.4
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• pp.137-152
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• 2014

In this paper, I suggest several techniques to estimate covariance matrix and compare the performance of the global minimum variance portfolio (GMVP) in terms of out of sample mean standard deviation and return. As a result, the return differences among the GMVPs are insignificant. The mean standard deviation of the GMVP using historical covariance is sensitive to the estimation window and the number of assets in the portfolio. Among the model covariance, the GMVP using constant systematic risk ratio model or using short sale restriction shows the best performance. The performance difference between the GMVPs using historical covariance and model covariance becomes insignificant as the historical covariance is estimated with longer estimation window. Lastly, the implied volatilities from ELW prices do not lead to superior performance to the historical variance.