• The Korean Journal of Applied Statistics
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• v.30 no.4
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• pp.579-590
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• 2017

The multivariate empirical distribution function could be defined when its distribution function can be estimated. It is known that bivariate empirical distribution functions could be visualized by using Step plot and Quantile plot. In this paper, the multivariate empirical distribution plot is proposed to represent the multivariate empirical distribution function on the unit square. Based on many kinds of empirical distribution plots corresponding to various multivariate normal distributions and other specific distributions, it is found that the empirical distribution plot also depends sensitively on its distribution function and correlation coefficients. Hence, we could suggest five goodness-of-fit test statistics. These critical values are obtained by Monte Carlo simulation. We explore that these critical values are not much different from those in text books. Therefore, we may conclude that the proposed test statistics in this work would be used with known critical values with ease.

• Journal of Korean Society for Quality Management
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• v.44 no.1
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• pp.167-180
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• 2016

Purpose: The problem for the traditional control chart is that it is unable to monitor the very small fraction of nonconforming and the underlying distribution is the normal distribution. $Z_p$ control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the $Z_p$ control chart in order to use under non-normal process. Methods: $Z_p$ is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal $Z_p$ control chart is designed based on ${\alpha}$-risk calculated by cumulative distribution function of Burr distribution. ${\beta}$-risk, which is for performance evaluation, obtains in the Burr distribution's cumulative distribution function and control limit. Results: The control limit for non-normal $Z_p$ control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal $Z_p$ control chart is able to control not only the very small fraction of nonconforming, but it is also useful when $Z_p$ distribution is non-normal distribution.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.747-757
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• 2005

A physical variable is customarily thought of as a function. Another way of describing a physical variable is to specify it as a functional, whose special type is called a distribution. It turns out that the distribution concept provide a better mechanism for analyzing certain physical phenomena than does the function concept. By using wavelets with high regularity we give a resolution of functions with slow growth.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.113-118
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• 2003

In this paper, We assume that strengths of two components system follow a bivariate pareto distribution. And these two components are subjected to a common stress which is independent of the strength of the components. We obtain maximum likelihood estimator(MLE) for the system reliability from stress-strength relationship. Also we derive asymptotic properties of the MLE and present a numerical study.

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1213-1223
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• 2009

In this paper, we develop noninformative priors for two parameter Pareto distribution. Specially, we derive Jereys' prior, probability matching prior and reference prior for the parameter of interest. In our case, the probability matching prior is only a first order matching prior and there does not exist a second order matching prior. Some simulation reveals that the matching prior performs better to achieve the coverage probability. A real example is also considered.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.171-189
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• 2005

In this paper, we first establish some characterization of tightness for a sequence of random elements taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in $R^P$. As a result, we give some sufficient conditions for a sequence of fuzzy random sets to converge in distribution.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.843-854
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• 2020

The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.595-600
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• 1999

We present a simple geometric approach which uses polar transformation and elementary trigonometry to evaluating an orthant probability in a bivariate normal distribution. Figures are provided to illustrate the situation for varying correlation coefficient. We derive the distribution of the sample correlation coefficient from a bivariate normal distribution when the sample size is 2 as an application.

• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.323-327
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• 2004

In this paper, we investigate the limiting distribution of the Ljung-Box test statistic in the unit root AR models with ARCH errors. We show that the limiting distribution is approximately chi-square distribution with the degrees of freedom only depending on the number of autocorrelation lags appearing in the test. Some simulation results are provided for illustration.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.837-845
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• 1998

We shall propose several estimators and confidence intervals for the scale parameter in a uniform distribution with the presence of a unidentified outlier and obtain biases and mean squared errors for their proposed estimators. And we shall numerically compare the performances for the proposed several estimators of the sclae parameter. Also, we shall compare lengths of confidence intervals of the scale parameter in a uniform distribution through Monte Carlo methods.