• The Journal of the Acoustical Society of Korea
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• v.30 no.6
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• pp.308-314
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• 2011

This paper presents techniques for estimating directions of multiple sound sources ranging from $0^{\circ}$ to $360^{\circ}$ using circular probability distributions having a periodic property. Phase differences containing direction information of sources can be modeled as mixtures of multiple probability distributions and source directions can be estimated by maximizing log-likelihood functions. Although the von Mises distribution is widely used for analyzing this kind of periodic data, we define a new class of circular probability distributions from Gaussian and Laplacian distributions by adopting a modulo operation to have $2{\pi}$-periodicity. Direction estimation with these circular probability distributions is done by implementing corresponding EM (Expectation-Maximization) algorithms. Simulation results in various reverberant environments confirm that Laplacian distribution provides better performance than von Mises and Gaussian distributions.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.35-58
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• 2004

For fixed positive integers and $\textit{k}\;(n\;{\geq}\;{\textit{k}}\;+\;2)$, the exact probability distributions of non-overlapping and overlapping patterns of two failures separated by (i) exactly $textsc{k}$ successes, (ii) at least $\textit{k}$ successes and (iii) at most $\textit{k}$ successes have been obtained for Bernoulli independent and Markov dependent trials by using combinatorial technique. The waiting time distributions for the first occurrence and the $r^{th}$ (r > 1) occurrence of the patterns have also been obtained.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.317-328
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• 2002

We first derive group ordering reference priors in a two-way mixed-effects analysis of variance (ANOVA) model. We show that posterior distributions are proper and provide marginal posterior distributions under reference priors. We also examine whether the reference priors satisfy the probability matching criterion. Finally, the reference prior satisfying the probability matching criterion is shown to be good in the sense of frequentist coverage probability of the posterior quantile.

• Journal of The Korean Society of Agricultural Engineers
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• v.51 no.3
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• pp.53-62
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• 2009

This study was carried out to select optimal probability distribution based on design accumulated monthly mean inflow from the viewpoint of drought by Gamma (GAM), Generalized extreme value (GEV), Generalized logistic (GLO), Generalized normal (GNO), Generalized pareto (GPA), Gumbel (GUM), Normal (NOR), Pearson type 3 (PT3), Wakeby (WAK) and Kappa (KAP) distributions for the observed accumulative monthly mean inflow of Chungjudam. L-moment ratio was calculated using observed accumulative monthly mean inflow. Parameters of 10 probability distributions were estimated by the method of L-moments with the observed accumulated monthly mean inflow. Design accumulated monthly mean inflows obtained by the method of L-moments using different methods for plotting positions formulas in the 10 probability distributions were compared by relative mean error (RME) and relative absolute error (RAE) respectively. It has shown that the design accumulative monthly mean inflow derived by the method of L-moments using Weibull plotting position formula in WAK and KAP distributions were much closer to those of the observed accumulative monthly mean inflow in comparison with those obtained by the method of L-moment with the different formulas for plotting positions in other distributions from the viewpoint of RME and RAE.

• Journal of The Korean Society of Agricultural Engineers
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• v.55 no.3
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• pp.105-111
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• 2013

Probability distribution of microbes in wastewater is a crucial factor to be determined for microbial risk assessment associated with its reuse. The objective of this study was to investigate probability distribution of an indicator microorganism in wastewater. Daily total coliform counts measured from nationwide wastewater treatment plants in 2010 by the Ministry of Environment were used for statistical analysis. Basic statistics and probability distributions were estimated in the three different spatial scales using the MS Excel software and FARD2006 model. Overall, wastewater from manure and livestock treatment plants demonstrated greater median coliform counts than from sewage and village treatment plants. Generalized logistic (GLO) and 2-parameter Weibull (WBU2) appeared to be the two probability distributions that fitted best for total coliform numbers in wastewater. The study results of microbial statistics and probability distributions would provide useful data for quantitative assessment of microbial risk from agricultural wastewater reuse.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.22 no.4
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• pp.35-47
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• 2023

Various single probability distributions have been used to represent time headway distributions. However, it has often been difficult to explain the time headway distribution as a single probability distribution on site. This study used the EM algorithm, which is one of the maximum likelihood estimations, for the parameters of combined mixture distributions with a certain relationship between two normal distributions for the time headway of vehicles. The time headway distribution of vehicle arrival is difficult to represent well with previously known single probability distributions. But as a result of this analysis, it can be represented by estimating the parameters of the mixture probability distribution using the EM algorithm. The result of a goodness-of-fit test was statistically significant at a significance level of 1%, which proves the reliability of parameter estimation of the mixture probability distribution using the EM algorithm.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.2
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• pp.64-72
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• 2000

Surface roughness is one of the most important characteristics in machining processes. This study presents probabilistic models to estimate surface roughness experimentally in multi-pass horizontal surface grinding operations from three independent distributions such as the initial surface roughness distributions of workpiece, the distributions of the wheel radius, and the distributions of distances between major active grains. To specify the model characteristics from surface roughness measurements, either the probability satisfying a given surface roughness or the range of surface roughness satisfying a given probability have been estimated while grinding conditions are fixed. Finally, the relationship between grinding conditions satisfying surface roughness range under a given probability can be established.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.595-598
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• 2004

This research seeks to derive the design rainfalls through the L-moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall at 38 rainfall stations in Korea. To select the appropriate distribution of annual maximum daily rainfall data by the rainfall stations, Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO) and Pearson Type 3 (PT3) probability distributions were applied and their aptness were judged using an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test. Parameters of appropriate distributions were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were finally derived by GEV distribution, which was proved to be more appropriate than the other distributions.

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.3
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• pp.31-42
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• 2004

This research seeks to derive the design rainfalls through the L-moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall at 38 rainfall stations in Korea. To select the appropriate distribution of annual maximum daily rainfall data by the rainfall stations, Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO) and Pearson Type 3 (PT3) probability distributions were applied and their aptness were judged using an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test. Parameters of appropriate distributions were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were finally derived by GEV distribution, which was proved to be more appropriate than the other distributions.

• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.129-142
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• 2017

In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.