• Journal of Radiation Protection and Research
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• v.41 no.2
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• pp.149-154
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• 2016

Background: Any real application of Bayesian inference must acknowledge that both prior distribution and likelihood function have only been specified as more or less convenient approximations to whatever the analyzer's true belief might be. If the inferences from the Bayesian analysis are to be trusted, it is important to determine that they are robust to such variations of prior and likelihood as might also be consistent with the analyzer's stated beliefs. Materials and Methods: The robust Bayesian inference was applied to atmospheric dispersion assessment using Gaussian plume model. The scopes of contaminations were specified as the uncertainties of distribution type and parametric variability. The probabilistic distribution of model parameters was assumed to be contaminated as the symmetric unimodal and unimodal distributions. The distribution of the sector-averaged relative concentrations was then calculated by applying the contaminated priors to the model parameters. Results and Discussion: The sector-averaged concentrations for stability class were compared by applying the symmetric unimodal and unimodal priors, respectively, as the contaminated one based on the class of ${\varepsilon}$-contamination. Though ${\varepsilon}$ was assumed as 10%, the medians reflecting the symmetric unimodal priors were nearly approximated within 10% compared with ones reflecting the plausible ones. However, the medians reflecting the unimodal priors were approximated within 20% for a few downwind distances compared with ones reflecting the plausible ones. Conclusion: The robustness has been answered by estimating how the results of the Bayesian inferences are robust to reasonable variations of the plausible priors. From these robust inferences, it is reasonable to apply the symmetric unimodal priors for analyzing the robustness of the Bayesian inferences.

• The Korean Journal of Applied Statistics
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• v.8 no.1
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• pp.159-167
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• 1995

Considering special discrete distribution of exponential family as a sequence with respect to the points of support, the squence is unimodal in some sense. In this paper, we study under what condition the mixture of that discrete distribution with respect to a parameter is unimodal. We derive the maximal interval of the parameter in which each mixture of the discrete distribution such as Binomial and Poisson is always unimodal.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.201-212
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• 2014

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1335-1352
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• 2019

In this article, a new family of lifetime distributions by adding two additional parameters is introduced. The new family is called, the logarithmic Kumaraswamy family of distributions. For the proposed family, explicit expressions for some mathematical properties are derived. Maximum likelihood estimates of the model parameters are also obtained. This method is applied to develop a new lifetime model, called the logarithmic Kumaraswamy Weibull distribution. The proposed model is very flexible and capable of modeling data with increasing, decreasing, unimodal or modified unimodal shaped hazard rates. To access the behavior of the model parameters, a simulation study has been carried out. Finally, the potentiality of the new method is proved via analyzing two real data sets.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.513-518
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• 2004

The well-known mode-mean-median inequality for the unimodal population distribution does not always hold for the frequency distribution. But many elementary statistics text books just mention that the relative location of the mean and median can be used to determine whether a distribution is positively or negatively skewed. In this paper we introduce the method generating data that is positively skewed but mean

• Journal of the Korea Institute of Military Science and Technology
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• v.15 no.5
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• pp.601-614
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• 2012

Since the optimized use of sonar systems available for detection is a very practical problem for a given ocean environment, the measure of mission achievability is needed for operating the sonar system efficiently. In this paper, a theory on Measure Of Effectiveness(MOE) for specific mission such as detection is described as the measure of mission achievability, and a recursive Cumulative Detection Probability(CDP) algorithm is found to be most efficient from comparing three CDP algorithms for discrete glimpses search to reduce computation time and memory for complicated scenarios. The three CDPs which are MOE for sonar-maneuver pattern are calculated as time evolves for comparison, based on three different formula depending on the assumptions as follows; dependent or independent glimpses, unimodal or non-unimodal distribution of Probability of Detection(PD) as a function of observation time interval for detection. The proposed CDP algorithm which is made from unimodal formula is verified and applied to OASPP(Optimal Acoustic Search Path Planning) with complicated scenarios.

• Geomechanics and Engineering
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• v.36 no.4
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• pp.343-353
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• 2024

The hydraulic anisotropic behavior of unsaturated soil has not been fully explored in relation to the grain-size distribution. The present study conducted laboratory assessments to examine the hydraulic anisotropy condition of statically compacted specimens in various initial states. The investigation incorporated the concept of hydraulic anisotropy by employing two discrete forms of soil stratification: horizontal-layering (HL) and vertical-layering (VL). The examined soils comprised sandy silt and silty sand, exhibiting either unimodal or bimodal soil-water characteristic curve (SWCC). This study aimed to investigate the potential correlation between the hydraulic anisotropy ratio and soil properties. The present study established a correlation between the hydraulic anisotropy ratio and several soil parameters, including fine content, dry density, plastic limit, and liquid limit. The study results indicate a non-linear relationship between the percentage of fine and dry density in soils with unimodal and bimodal soil-water characteristic curve (SWCC) and hydraulic anisotropy ratio.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.517-530
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• 2007

We studied a modelling process for unimodal and multimodal circular data by using von Mises and its mixture distribution. In particular we suggested EM algorithm to find ML estimates of the mixture model. Simulation results showed the suggested methods are very accurate. Applications to two kinds of real data sets are also included.

• Analytical Science and Technology
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• v.10 no.3
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• pp.203-208
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• 1997

Barium titanyl oxalate(BTO) was precipatated by utilizing the thermal decomposition of dimethyl oxalate in acidic aqueous solution having $BaCl_2$ and $TiCl_4$. Particle morphology of BTO was influeneced by the various experimental factors. i.e.. the faster rate to nucleation with higher temperature and the higher ratio of [DMO]/[$Ba^{2+}+Ti^{4+}$] was found to correspond to the faster rate of transformation of particle size distribution from unimodal to broad unimodal through bimodal. The BT powder obtained by calcination at $900^{\circ}C$ in air consists of larger particles than BT generated by general coprecipitation method and shows tetragonal symmetry. The stirring during reaction was also found to have much effect upon characteristics of BTO and BT.

• Journal of Korea Multimedia Society
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• v.15 no.11
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• pp.1305-1318
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• 2012

Image segmentation is one of the difficult research problems in machine vision and pattern recognition field. A commonly used segmentation method is the Otsu method. It is simpler and easier to implement but it fails if the histogram is unimodal or similar to unimodal. And if some target area is smaller than background object, then its histogram has the distribution close to unimodal. In this paper, we proposed an improved image segmentation method based on 1D Otsu method for a small target detection. To overcome drawbacks by unimodal histogram effect, we depressed the background histogram using a logarithm function. And to improve a signal to noise ratio, we used a local average value by the neighbor window for thresholding using 1D Otsu method. The experimental results show that our proposed algorithm performs better segmentation result than a traditional 1D Otsu method, and needs much less computational time than that of the 2D Otsu method.