• 한국음향학회지
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• 제30권6호
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• pp.308-314
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• 2011

본 논문에서는 주기성을 갖는 순환 확률분포를 이용하여 $0^{\circ}{\sim}360^{\circ}$ 범위의 다중 음원의 방향을 추정하는 기법을 제안한다. 음원의 방향 정보를 담고 있는 마이크로폰간의 위상차는 확률분포의 혼합물로 간주될 수 있으며, 음원 방향은 이 확률분포의 혼합물에 적용된 로그-우도함수 (log-likelihood function)를 최대화함으로써 추정된다. 주기성을 갖는 데이터의 분석에 von Mises 확률분포가 널리 활용된다는 사실은 잘 알려져 있지만, 본 논문에서는 기존의 Gaussian이나 Laplacian 확률분포에 $2{\pi}$ 모듈로 (modulo) 연산을 적용함으로써 $0^{\circ}{\sim}360^{\circ}$ 범위의 주기성을 갖는 순환 확률분포를 정의하고 이를 방향 추정에 활용한다. 순환 확률분포의 혼합물에 대한 로그-우도함수를 최대가 되게 하는 음원의 방향은 EM (Expectation-Maximization) 알고리즘을 이용하여 추정된다. 다양한 반향 환경에서의 실험 결과 Laplacian 확률분포가 von Mises나 Gaussian 확률분포보다 우수한 성능을 제공함을 확인할 수 있다.

• Journal of the Korean Statistical Society
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• 제33권1호
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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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• 제13권2호
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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.

• 한국농공학회논문집
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• 제51권3호
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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.

• 한국농공학회논문집
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• 제55권3호
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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.

• 한국ITS학회 논문지
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• 제22권4호
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• pp.35-47
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• 2023

그동안 차두시간분포를 나타내는 확률분포로 음지수분포, Erlang 분포, 정규분포 등 다양한 단일확률분포들이 사용되어져 왔다. 그러나, 실제 도로에서 차두시간분포의 조사결과는 단일확률분포로서 설명하기 어려운 경우가 있었다. 본 연구는 차량의 차두시간에 대해 두 개의 정규분포가 일정한 관련성을 가지고 결합된 복합확률분포의 파라메타에 대해 최우추정법 중 하나인 EM 알고리즘을 이용하여 추정하는 접근방법을 시도하였다. 이에 대한 분석결과 기존에 알려진 단일확률분포로서 잘 설명되기 어려웠던 차량도착 차두시간 분포를 EM 알고리즘을 이용하여 복합확률분포의 파라메타를 추정하여 설명하였다. χ² test 적합도 검정결과, 유의수준 1%에서 통계학적으로 유의성이 확보되어 EM 알고리즘을 이용한 복합확률분포의 파라메타 추정의 신뢰성이 입증되는 것으로 분석되었다.

• 한국정밀공학회지
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• 제17권2호
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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.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2004년도 학술발표회
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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.

• 한국농공학회논문집
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• 제46권3호
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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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• 제24권2호
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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.