• Journal of Korean Society of Transportation
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• v.25 no.4
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• pp.109-121
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• 2007

In this study, an imputation model using circular probability distribution was developed in order to overcome problems of missing data from a traffic survey. The existing ad-hoc or heuristic, model-based and algorithm-based imputation techniques were reviewed through previous studies, and then their limitations for imputing missing traffic volume data were revealed. The statistical computing language 'R' was employed for model construction, and a mixture of von Mises probability distribution, which is classified as symmetric, and unimodal circular probability were finally fitted on the basis of traffic volume data at survey stations in urban and rural areas, respectively. The circular probability distribution model largely proved to outperform a dummy variable regression model in regards to various evaluation conditions. It turned out that circular probability distribution models depict circularity of hourly volumes well and are very cost-effective and robust to changes in missing mechanisms.

• 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.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.166-175
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• 1995

When a neutral particle beam(NPB) aimed at the object and receive a small number of neutron signals at the detector without any errors, it obeys Poisson law. Under the two assumptions that neutral particle scattering distribution and aiming errors have a circular Gaussian distributions that neutral particle scattering distribution and aiming errors have a circular Gaussian distribution respectively, an exact probability distribution of neutral particles vecomes a Poisson-power function distribution. We study and prove some properties, such as limiting distribution, unimodality, stochastical ordering, computational recursion fornula, of this distribution. We also prove monotone likelihood ratio(MLR) property of this distribution. Its MLR property can be used to find a criteria for the hypothesis testing problem.

• Geomechanics and Engineering
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• v.38 no.1
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• pp.93-106
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• 2024

The present paper investigates the spatial variability effect of soil property on the three-dimensional probabilistic characteristics of the bearing capacity factor (i.e., mean and coefficient of variation) of a circular footing resting on clayey soil where both mean and standard deviation of undrained shear strength increases with depth, keeping the coefficient of variation constant. The mean trend of undrained shear strength is defined by introducing the dimensionless strength gradient parameter. The finite difference method along with the random field and Monte Carlo simulation technique, is used to execute the numerical analyses. The lognormal distribution is chosen to generate random fields of the undrained shear strength. In the study, the potential failure of the structure is represented through the failure probability. The influences of different vertical scales of fluctuation, dimensionless strength gradient parameters, and coefficient of variation of undrained shear strength on the probabilistic characteristics of the bearing capacity factor and failure probability of the footing, along with the probability and cumulative density functions, are explored in this study. The variations of failure probability for different factors of safety corresponding to different parameters are also illustrated. The results are presented in non-dimensional form as they might be helpful to the practicing engineers dealing with this type of problem.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.4
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• pp.824-831
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• 2009

This paper proposes an obstacle avoidance algorithm for an autonomous mobile robot. The proposed method based on the circular navigation with probability distribution finds local-paths to avoid collisions. Futhermore, it makes mobile robots to achieve obstacle avoidance and optimal path planning due to the accurate decision of the final goal. Simulation results are included to show the feasibility of the proposed method.

• Research in Mathematical Education
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• v.6 no.1
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• pp.97-106
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• 2002

Educators have found that the concept of randomness is often misunderstood by students. Chance recently pointed out that students should be introduced to the concept of randomness through the use of simulations. In this article, we studied various aspects of the probability distribution off linear random path in a circle and introduce some related simulations to guide student exploration and discovery. Consider a random line segment that crosses a circle with a certain radius. Perhaps it can be considered to be a path that an airplane shows up and flies into a random direction in a monitor. What is the expected amount of flying distance through the monitor, and the expected variation\ulcorner Are we monitoring what we see scientifically\ulcorner This article studies the probability distribution and some related aspects of a linear random path within a circular monitor. Some simulative activity is also introduced which can be used in a statistics or probability classes.

• Journal of Powder Materials
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• v.10 no.3
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• pp.201-208
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• 2003

Distributions of diamond particles protruding on the surface of worn diamond segments in circular saw has been investigated. Scanning electron microscope was used to examine the worn ,surface and radial saw blade wear and grinding ratio was measured. The number of protruded diamond particle was approximately 50% of the total number of particles, and that was independent of diamond particle concentration and table speed. It was also noted that the inter-particle distance did not follow a symmetric function like Gaussian distribution function, instead it fitted well with a probability density function based on gamma function. The distribution of inter-particle spacing, therefore, was analyzed using a gamma function model.

• Proceedings of the KOR-KST Conference
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• 2007.05a
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• pp.610-619
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• 2007

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.243-255
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• 1996

The number of neutron signals from a neutral particle beam(NPB) at the detector, without any errors, obeys Poisson distribution, Under two assumptions that NPB scattering distribution and aiming errors have a circular Gaussian distribution respectively, an exact probability distribution of signals becomes a Poisson-power function distribution. In this paper, we show that the error rate in simple hypothesis testing for the limiting Poisson-power function distribution is not zero. That is, the limit of ${\alpha}+{\beta}$ is zero when Poisson parameter$\kappa\rightarro\infty$, but this limit is not zero (i.e., $\rho\ell$>0)for the Poisson-power function distribution. We also give optimal decision algorithms for a specified error rate.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.967-973
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• 1995

A neutral particle beam(NPB) aimed at the object and receive a small number of neutron signals at the detector to estimate the mass of an object Since there is uncertainty about the location of the axis of the beam relative to the object, we could have aiming errors which may lead to incorrect information about the object. Under the two assumptions that neutral particle scattering distribution and aiming errors have a circular normal distribution respectively, we have derived an exact probability distribution of neutral particles. It becomes a Poison-power function distribution., We proved monotone likelihood ratio property of tlis distribution. This property can be used to find a criteria for the hypothesis testing problem.