• Journal of Korean Society for Quality Management
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• v.23 no.3
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• pp.102-112
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• 1995

Estimation of each of mean response, difference between mean responses and derivatives of the response function is a possible objective of a response surface design. These objectives are to be achieved simultaneously when an experiment is designed to improve mean response. For the situations where departure from the assumed model is suspected, first and second order designs for improving mean response are obtained by combining minimum bias designs for the individual design objectives. D- and A-optimalities are used for selecting specific second order designs. The results are applied to central composite designs.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.157-173
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• 2007

In this article it is considered that how the slope-rotatability property of a second order design for response surface model is affected by block effects and how the design points are assigned into the blocks so that the blocked design may have the property of slope-rotatability. If an unblocked design is blocked properly, it could be a slope-rotatable design with block effects and this property is named as block slope-rotatability. We approach this problem from the moment matrix of the blocked design, which plays an important role to get the variances of the estimates, and suggest conditions of block slope-rotatability.

• Communications of Mathematical Education
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• v.16
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• pp.139-147
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• 2003

While the statistical concept 'order statistics' has a great number of applications in our society ranging from industry to military analysis, it is not necessarily an easy concept to understand for many people. Adding some interesting simulation activities of this concept to the probability or statistics curriculum, however, can enhance the learning curve greatly. A hands-on and a graphic calculator based activities of a missile simulation were introduced by Kim(2003) in the context of order statistics. This article revisits the two activities in his paper and point out a dilemma that occurs from the violation of an assumption on two deviation parameters associated with the missile simulation. A third activity is introduced to resolve the dilemma in the terms of a kernel density estimation which is a nonparametric approach.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.79-89
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• 2018

In this paper, we study the maximal property of the volume of the convex hull of d-dimensional independent random vectors. We show that the volume of the random convex hull from a multivariate location-scale family indexed by ${\Sigma}$ is stochastically maximized in simple stochastic order when ${\Sigma}$ is diagonal. The claim can be applied to a broad class of multivariate distributions that include skewed/unskewed multivariate t-distributions. We numerically investigate the proven stochastic relationship between the dependent and independent random convex hulls with the Gaussian random convex hull. The numerical results confirm our theoretical findings and the maximal property of the volume of the independent random convex hull.

• Journal of Korea Water Resources Association
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• v.31 no.2
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• pp.145-153
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• 1998

In this paper the first- and second order statistics of soil moisture are derived using the Washita '92 data. Also the possible correlations among the soil texture, the brightness temperature, the NDVI and the soil moisture are investigated based in the linear regression study. Only the correlation between the soil moisture and the brightness temperature shows significant values. The soil moisture decay coefficients in time were estimated for each soil type and cross-checked by calculating the last rainfall time before the observation to be about 20days in all different soil types. The second-order statistics of soil moisture based on the correlogram and the spectrum was analyzed to derive the data characteristics and compared with those of the NDVI and the soil texture. This analysis shows that the soil moisture within the highly correlated soil texture field is affected much by the relatively less correlated vegetation field in the Washita area, where the effect of topography is known to be small. The soil moisture media was derived and its parameters were estimated successfully using the first - and sedcond -order statistics.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.211-223
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• 1997

We introduce the linear estimators based on order statistics in the three-parameter Weibull distribution and compare the small sample performances of proposed linear estimators in the three- parameter Weibull distribution with an unidentified outlier.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.111-127
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• 2007

The logistic distribution is generalized using the Marshall-Olkin scheme and its generalization. Some properties are studied. First order autoregressive time series model with Marshall-Olkin semi-logistic distribution as marginal is developed and studied.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.243-250
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• 1999

We consider $Y=X{\lambda}Z,\;{\lambda}>0$, where X and Z are independent random variables, and Y is the length biased distribution or the equilibrium distribution of X. The purpose of this paper is to consider the distribution of X or Y when the distribution of Z is given and the distribution of Z when the distribution of X or Y is given, In particular, we obtain that the necessary and sufficient conditions for X to be $X^{2}({\upsilon})\;is\;Z{\sim}X^{2}(2)\;and\;for\;Z\;to\;be\;X^{2}(1)\;is\;X{\sim}IG({\mu},\;{\mu}^{2}/{\lambda})$, where $IG({\mu},\;{\mu}^{2}/{\lambda})$ is two-parameter inverse Gaussian distribution. Also we show that X is smaller than Y in the reverse Laplace transform ratio order if and only if $X_{e}$ is smaller than $Y_{e}$ in the Laplace transform ratio order. Finally, we can get the results that if X is smaller than Y in the Laplace transform ratio order, then $Y_{L}$ is smaller than $X_{L}$ in the Laplace transform order, and that if X is smaller than Y in the reverse Laplace transform ratio order, then $_{\mu}X_{L}$ is smaller than $_{\nu}Y_{L}$ in the Laplace transform order.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.91-103
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• 2006

Yun (2005) introduced an estimator of the second order parameter characterizing the tail behavior of probability distributions and proved its consistency. In this paper we prove its asymptotic normality under a third order condition.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.135-144
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• 2005

In this paper, we develop the noninformative priors for the exponential models when the parameter of interest is the difference of two means. We develop the first and second order matching priors. We reveal that the second order matching priors do not exist. It turns out that Jeffreys' prior does not satisfy a first order matching criterion. The Bayesian credible intervals based on the first order matching meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior.