• Journal of the Korean Statistical Society
• /
• v.33 no.3
• /
• pp.303-312
• /
• 2004

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter. This is the peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose non parametric maximum likelihood estimators of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.135-152
• /
• 2000

For a linear operator Q from $R^{d}\; into\; R^{d},\; {\alpha}\;>0\; and\ 0-semi-stability and the operater semi-stability of probability measures on $R^{d}$ are defined. Characterization of $(Q,b,{\alpha})$-semi-stable Gaussian distribution is obtained and the relationship between the class of $(Q,b,{\alpha})$-semi-stable non-Gaussian distributions and that of operator semistable distributions is discussed.

• Communications of the Korean Mathematical Society
• /
• v.25 no.3
• /
• pp.485-489
• /
• 2010

A family of continuous probability distribution has been characterized through the difference of two conditional expectations, conditioned on a non-adjacent record statistic. Also, a result based on the unconditional expectation and a conditional expectation is used to characterize a family of distributions. Further, some of its deductions are also discussed.

• Journal of applied mathematics & informatics
• /
• v.37 no.3_4
• /
• pp.245-249
• /
• 2019

In this paper we obtain characterizations of a family of continuous probability distribution by independence property of upper record values. Also, we introduce some examples of the characterizations of distributions from these general classes of continuous distributions.

• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.765-800
• /
• 2022

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

• Journal of Korean Institute of Industrial Engineers
• /
• v.42 no.1
• /
• pp.38-49
• /
• 2016

This paper proposes a mathematical model-based solution for sourcing decisions with an objective of minimizing the manufacturer's total cost in the two-echelon supply chain with supply capacity risk. The risk impact is represented by uniform, beta, and triangular distributions. For the mathematical model, the probability vector of normal, risk, and recovery statuses are developed by using the status transition probability matrix and the equations for estimating the supply capacity under risk and recovery statuses are derived for each of the three probability distributions. Those formulas derived are validated using the sampling method. The results of the simulation study on the test problem show that the sourcing decisions using the proposed solution reduce the total cost by 1.6~3.7%, compared with the ones without a consideration of supply capacity risk. The total cost reduction increases approximately in a linear fashion as the probability of risk occurrence or reduction rate of supply capacity due to risk events is increased.

• Proceedings of the Korean Society for Bioinformatics Conference
• /
• 2003.10a
• /
• pp.7-16
• /
• 2003

In this paper, we propose a probabilistic framework to predict the interaction probability of proteins. The notion of domain combination and domain combination pair is newly introduced and the prediction model in the framework takes domain combination pair as a basic unit of protein interactions to overcome the limitations of the conventional domain pair based prediction systems. The framework largely consists of prediction preparation and service stages. In the prediction preparation stage, two appearance pro-bability matrices, which hold information on appearance frequencies of domain combination pairs in the interacting and non-interacting sets of protein pairs, are constructed. Based on the appearance probability matrix, a probability equation is devised. The equation maps a protein pair to a real number in the range of 0 to 1. Two distributions of interacting and non-interacting set of protein pairs are obtained using the equation. In the prediction service stage, the interaction probability of a protein pair is predicted using the distributions and the equation. The validity of the prediction model is evaluated fur the interacting set of protein pairs in Yeast organism and artificially generated non-interacting set of protein pairs. When 80% of the set of interacting protein pairs in DIP database are used as foaming set of interacting protein pairs, very high sensitivity(86%) and specificity(56%) are achieved within our framework.

• Earthquakes and Structures
• /
• v.22 no.2
• /
• pp.157-168
• /
• 2022

A moment-independent importance measure analysis approach was introduced to quantify the effects of structural uncertainty parameters on probabilistic seismic demands of simply supported girder bridges. Based on the probability distributions of main uncertainty parameters in bridges, conditional and unconditional bridge samples were constructed with Monte-Carlo sampling and analyzed in the OpenSees platform with a series of real seismic ground motion records. Conditional and unconditional probability density functions were developed using kernel density estimation with the results of nonlinear time history analysis of the bridge samples. Moment-independent importance measures of these uncertainty parameters were derived by numerical integrations with the conditional and unconditional probability density functions, and the uncertainty parameters were ranked in descending order of their importance. Different from Tornado diagram approach, the impacts of uncertainty parameters on the whole probability distributions of bridge seismic demands and the interactions of uncertainty parameters were considered simultaneously in the importance measure analysis approach. Results show that the interaction of uncertainty parameters had significant impacts on the seismic demand of components, and in some cases, it changed the most significant parameters for piers, bearings and abutments.

• Journal of Environmental Science International
• /
• v.17 no.1
• /
• pp.57-66
• /
• 2008

The frequency analysis and the probability plot were applied to heavy metal contents of soils collected from the Goseong Cu mine area as a statistic method for the determination of the threshold value which was able to partition a population comprising largely dispersed heavy metal contents into the background and the anomalous populations. Almost all the heavy metal contents of soil showed a positively skewed distributions and their cumulative percentage frequencies plotted as a curved lines on logarithmic probability plot which represent a mixture of two or more overlapping populations. Total Cu, Pb and Cd data and extractable Cu and Pb data could be partitioned into background and anomalous populations by using the inflection in each curve. The others showed a normally distributed population or an largely overlapped populations. The threshold values obtained from replotted frequency distributions with the partitioned populations were Cu 400 mg/kg, Pb 450 mg/kg and Cd 3.5 mg/kg in total contents and Cu 40 mg/kg and Pb 12 mg/kg in extractable contents, respectively. The thresholds for total contents are much higher than the tolerable level of soil pollution proposed by Kloke(Cu 100 mg/kg, Pb 100 mg/kg, Cd 3 mg/kg), but those for extractable contents are not exceeded the worrying level of soil pollution proposed by Ministry of Environment(Cu 50 mg/kg, Pb 100 mg/kg). When the threshold values were used as the criteria of soil pollution in the study area, $9{\sim}19%$ of investigated soil population was in polluted level. The spatial distributions of heavy metal contents greater than threshold values showed that polluted soils with heavy metals are restricted within the mountain soils in the vicinity of abandoned mines.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.33-36
• /
• 2008

We introduce some properties for fuzzy binomial distributions with fuzzy valued probability. First we define fuzzy type I error and type II error for fuzzy relative frequency and agreement index. And we show that an fuzzy power function and fuzzy binomial frequency function for binomial proportion test.