• Journal of the Korean Data and Information Science Society
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• 제20권1호
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• pp.191-202
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• 2009

In this study, we drive the one dimensional marginal transform function, probability density function and probability distribution function for the random variables $T_{{\xi}N}$ (Time taken by the servers during the vacations), ${\xi}_N$(Number of vacations taken by the servers) and ${\eta}_N$(Number of customers or units arrive in the system) by controlling the variability of two random variables simultaneously.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2000년도 추계학술대회
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• pp.411-411
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• 2000

Consider the problem of estimating the reliability of a multicomponent stress-strength system which functions if at least r of the k identical components simultaneously function. All stresses and strengths are assumed to be independent random variables with two parameter Weibull distributions. First, we derive reference priors and probability matching priors which are noninformative priors. We next investigate sufficient conditions for propriety of posteriors under reference priors and probability matching priors. Finally, we provide, using these priors, some numerical results for Bayes estimates of the reliability by applying Gibbs sampling technique.

• Journal of the Korean Statistical Society
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• 제32권4호
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• pp.373-384
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• 2003

In this paper, we formulate multivariate one-sided alternatives and propose a class of nonparametric tests for possibly right censored data. We obtain the asymptotic tail probability (or p-value) by showing that our proposed test statistics have asymptotically multivariate normal distributions. Also, we illustrate our procedure with an example and compare it with other procedures in terms of empirical powers for the bivariate case. Finally, we discuss some properties of our test.

• Journal of the Korean Statistical Society
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• 제27권2호
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• pp.205-220
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• 1998

Dependence concepts for ordered two-way contingency tables have been of considerable interest. We consider a dependence concept which is less restrictive than likelihood ratio dependence and more restrictive than regression dependence. Maximum likelihood estimation of cell probability under this dependence restriction is studied. The likelihood ratio statistics for and against this dependence are proposed and their large sample distributions are derived. A real data is analyzed to illustrate the estimation and testing procedures.

• East Asian mathematical journal
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• 제39권5호
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• pp.537-547
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• 2023

In this paper, we introduce the optimal approximation by a Gaussian function for a probability density function. We show that the approximation can be obtained by solving a non-linear system of parameters of Gaussian function. Then, to understand the non-normality of the empirical distributions observed in financial markets, we consider the nearly Gaussian function that consists of an optimally approximated Gaussian function and a small periodically oscillating density function. We show that, depending on the parameters of the oscillation, the nearly Gaussian functions can have fairly thick heavy tails.

• Journal of Electrical Engineering and information Science
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• 제1권1호
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• pp.151-155
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• 1996

This paper derives the two-dimensional probability distribution and density functions of morphological dilation and erosion of a one-dimensional memoryless source and reports numerical results for a uniform source, thus providing methodology for joint distributions for other morphological operations. The joint density functions expressed in closed forms contain the Dirac delta functions due to the joint discontinuity within the dilation and erosion. They also exhibit symmetry between these two morphological density functions of dilated and/or eroded sources, in the computation of other higher moments thereof, and in multidimensional quantization.

• 아태비즈니스연구
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• 제11권4호
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• pp.37-48
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• 2020

Purpose - This study empirically investigates whether the risk property included in fat-tails of return distributions is systematic or unsystematic based on the devised statistical methods. Design/methodology/approach - This study devised empirical designs based on two traditional methods: principal component analysis (PCA) and the testing method of portfolio diversification effect. The fatness of the tails in return distributions is quantitatively measured by statistical probability. Findings - According to the results, the risk property in the fat-tails of return distributions has the economic meanings of eigenvalues having a value greater than 1 through PCA, and also systematic risk that cannot be removed through portfolio diversification. In other words, the fat-tails of return distributions have the properties of the common factors, which may explain the changes of stock returns. Meanwhile, the fatness of the tails in the portfolio return distributions shows the asymmetric relationship of common factors on the tails of return distributions. The negative tail in the portfolio return distribution has a much closer relation with the property of common factors, compared to the positive tail. Research implications or Originality - This empirical evidence may complement the existing studies related to tail risk which is utilized in pricing models as a common factor.

• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.121-130
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• 1993

불균형 일원 변량모형에서 AOV추정량과 사전값이 0, 1, ${\infty}$인 MINQUE에 국한하여 정규분포를 가정할 때 분산성분의 추정량이 음이 될 이론적 확률을 구하고, 비정규분포에 대해서는 모의실험을 통해 추정량이 음이 될 확률을 구하였다. 이 때 정차분포에서의 이론적 확률과 모의실험에 의해 계산된 확률간에 유의한 차이가 없고 표본수, 수준수 그리고 ${\rho}$가 커지면 각 추정량은 음이 될 확률이 작아지며, 고려된 추정량 중에서 AOV추정량이 대부분의 경우에 음이 될 확률이 가장 작게 나타났다.

• 대한기계학회논문집B
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• 제22권5호
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• pp.607-617
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• 1998

Comparisons of joint probability density distribution obtained from the raw data of measured droplet sizes and velocities in a transient diesel fuel spray with computed joint probability density function were made. Simultaneous droplet sizes and velocities were obtained using PDPA. Mathematical probability density functions which can fit the experimental distributions were extracted using the principle of maximum likelihood. Through the statistical process of functions, mean droplet diameters, non-dimensional mass, momentum and kinetic energy were estimated and compared with the experimental ones. A joint log-hyperbolic density function presents quite well the experimental joint density distribution which were extracted from experimental data.

• Communications for Statistical Applications and Methods
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• 제14권2호
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• pp.431-442
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• 2007

In this paper, we develop the noninformative priors when the parameter of interest is the difference between quantiles of two exponential distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that Jeffreys' prior does not satisfy the first order matching criterion. The Bayesian credible intervals based on the first order probability matching prior meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior. Some simulation and real example will be given.