• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.275-283
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• 1999

In order to estimate a parameter $(\alpha,\beta^r), r\epsilonN$, in a distribution belonging to a location-scale family we usually use best invariant estimator (BIE) and best unbiased estimator (BUE). But in some conditions Ryu (1996) showed that BIE is better than BUE. In this paper we calculate risks of BIE and BUE in a normal and an exponential distribution respectively and calculate a percentage risk improvement exponential distribution respectively and calculate a percentage risk improvement (PRI). We find the sample size n which make no significant differences between BIE and BUE in a normal distribution. And we show that BIE is always significantly better than BUE in an exponential distribution. Also simulation in a normal distribution is given to convince us of our result.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.4
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• pp.398-402
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• 2014

A generalized trigonometric fuzzy set is a generalization of a trigonometric fuzzy number. Zadeh([7]) defines the probability of the fuzzy event using the probability. We define the normal and exponential fuzzy probability on $\mathbb{R}$ using the normal and exponential distribution, respectively, and we calculate the normal and exponential fuzzy probability for generalized trigonometric fuzzy sets.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.101-113
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• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• Journal of Korean Society of Transportation
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• v.4 no.2
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• pp.3-14
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• 1986

This study was undertaken to develop the gap acceptance model of left-turn drivers on the major road at intersections. Typical unsignalized intersections on the two-lane and four-lane streets in Masan City were selected for the study intersection. For the gap distribution model, the lognormal, negative exponential, shifted negative exponential, and Gamma distributions were tested using the x2 and K-S tests. Based on the results for both streets, it was concluded that among the distributions tested the lognormal distribution represented the gap distribution best, followed by the shifted negative exponential distribution. Stochastic models of the gap-acceptance behavior of left-turn drivers on the major road at unsignalized intersections were programmed using SLAM Ⅱ, a simulation computer language. A stochastic model was selected for the gap-acceptance behavior to compare the results of the simulation with the observed data. The model assumes that a fixed critical acceptance gap is assigned to each left-turn driver based on a normal distribution and the gap distribution of the opposing traffic stream follows the shifted negative exponential distribution.

• International Journal of Reliability and Applications
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• v.4 no.3
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• pp.97-111
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• 2003

By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.581-589
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• 2005

The purpose of this thesis is to develop and introduce Add-in program which we can systematically, visually and dynamically study discrete probability distribution of binomial distribution, poisson distribution and hypergeometric distribution, and continuous probability distribution of normal distribution, exponential distribution, and the definition and characteristics of t distribution, F distribution and ${\chi}^2$ distribution to be driven from normal distribution, and graphs, the computation process of probability by using VBA which is the device of Excel.

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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• pp.159-160
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• 1996

Recent high resolution CO observations of normal and starburst galaxies at Owens Valley Millimeter Array are summarized. While normal disk galaxies generally show exponential distribution which follows the optical blue light, starburst galaxies are often characterized by a compact ($\~$1 kpc) nuclear complex whose surface gas mass density is strongly correlated with the observed large infrared luminosity and thus the ongoing massive star formation.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1039-1047
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• 2014

An autoregressive model with normal errors is a natural model that attempts to fit time series data. More flexible models that include normal distribution as a special case are necessary because they can cover normality to non-normality models. The skewed exponential power distribution is a possible candidate for autoregressive models errors that may have tails lighter(platykurtic) or heavier(leptokurtic) than normal and skewness; in addition, the use of skewed exponential power distribution can reduce the influence of outliers and consequently increases the robustness of the analysis. We use SIR algorithm and grid method for an efficient Bayesian estimation.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.531-542
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• 2015

In this survey, we use the normal linear model to demonstrate the use of the linear Bayes method. The superiorities of linear Bayes estimator (LBE) over the classical UMVUE and MLE are established in terms of the mean squared error matrix (MSEM) criterion. Compared with the usual Bayes estimator (obtained by the MCMC method) the proposed LBE is simple and easy to use with numerical results presented to illustrate its performance. We also examine the applications of linear Bayes method to some other distributions including two-parameter exponential family, uniform distribution and inverse Gaussian distribution, and finally make some remarks.

• Journal of the Korean Data and Information Science Society
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• v.26 no.2
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• pp.487-493
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• 2015

Time series data sometimes show violation of normal assumptions. For cases where the assumption of normality is untenable, more exible models can be adopted to accommodate heavy tails. The exponential power distribution (EPD) is considered as possible candidate for errors of time series model that may show violation of normal assumption. Besides, the use of exible models for errors like EPD might be able to conduct the robust analysis. In this paper, we especially consider EPD as the exible distribution for errors of autoregressive models. Also, we represent this distribution as scale mixture of uniform and this form enables efficient Bayesian estimation via Markov chain Monte Carlo (MCMC) methods.