• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } for n $\geq$ 1. We say $X_{j}$ is an upper record value of { $X_{n}$ , n$\geq$1} if $Y_{j}$ > $Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, n$\geq$1, where u(n) = min{j｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• Proceedings of the KSRS Conference
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• 2008.03a
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• pp.195-200
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• 2008

The accuracy of classifying pixels in HIRIS images is usually degraded by noisy bands since noisy bands may deform the typical shape of spectral reflectance. Proposed in this paper is a statistical method for noisy band removal which mainly makes use of the correlation coefficients between bands. Considering each band as a random variable, the correlation coefficient measures the strength and direction of a linear relationship between two random variables. While the correlation between two signal bands is high, existence of a noisy band will produce a low correlation due to ill-correlativeness and undirectedness. The application of the correlation coefficient as a measure for detecting noisy bands is under a two-pass screening scheme. This method is independent of the prior knowledge of the sensor or the cause resulted in the noise. The classification in this experiment uses the unsupervised k-nearest neighbor algorithm in accordance with the well-accepted Euclidean distance measure and the spectral angle mapper measure. This paper also proposes a hierarchical combination of these measures for spectral matching. Finally, a separability assessment based on the between-class and within-class scatter matrices is followed to evaluate the performance.

• Structural Engineering and Mechanics
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• v.27 no.2
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• pp.199-222
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• 2007

Composite laminated structures supported on elastic foundations are being increasingly used in a great variety of engineering applications. Composites exhibit larger dispersion in their material properties compared to the conventional materials due to large number of parameters associated with their manufacturing and fabrication processes. And also the dispersion in elastic foundation stiffness parameter is inherent due to inaccurate modeling and determination of elastic foundation properties in practice. For a better modeling of the material properties and foundation, these are treated as random variables. This paper deals with effects of randomness in material properties and foundation stiffness parameters on the free vibration response of laminated composite plate resting on an elastic foundation. A $C^0$ finite element method has been used for arriving at an eigen value problem. Higher order shear deformation theory has been used to model the displacement field. A mean centered first order perturbation technique has been employed to handle randomness in system properties for obtaining the stochastic characteristic of frequency response. It is observed that small amount of variations in random material properties and foundation stiffness parameters significantly affect the free vibration response of the laminated composite plate. The results have been compared with those available in the literature and an independent Monte Carlo simulation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.156-156
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• 2022

Explicitly spatially distributed and reliable data on industrial water demand is very much important for both policy makers and researchers in order to carry a region-specific analysis of water resources management. However, such type of data remains scarce particularly in underdeveloped and developing countries. Current research is limited in using different spatially available socio-economic, climate data and geographical data from different sources in accordance to predict industrial water demand at finer resolution. This study proposes a random forest regression (RFR) model to predict the industrial water demand at 0.50× 0.50 spatial resolution by combining various features extracted from multiple data sources. The dataset used here include National Polar-orbiting Partnership (NPP)/Visible Infrared Imaging Radiometer Suite (VIIRS) night-time light (NTL), Global Power Plant database, AQUASTAT country-wise industrial water use data, Elevation data, Gross Domestic Product (GDP), Road density, Crop land, Population, Precipitation, Temperature, and Aridity. Compared with traditional regression algorithms, RF shows the advantages of high prediction accuracy, not requiring assumptions of a prior probability distribution, and the capacity to analyses variable importance. The final RF model was fitted using the parameter settings of ntree = 300 and mtry = 2. As a result, determinate coefficients value of 0.547 is achieved. The variable importance of the independent variables e.g. night light data, elevation data, GDP and population data used in the training purpose of RF model plays the major role in predicting the industrial water demand.

• Journal of the Society of Disaster Information
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• v.20 no.1
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• pp.156-168
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• 2024

Purpose: The trend of highway traffic accidents shows a repeating pattern of increase and decrease, with the fatality rate being highest on highways among all road types. Therefore, there is a need to establish improvement measures that reflect the situation within the country. Method: We conducted accident severity analysis using Random Forest on data from accidents occurring on 10 specific routes with high accident rates among national highways from 2019 to 2021. Factors influencing accident severity were identified. Result: The analysis, conducted using the SHAP package to determine the top 10 variable importance, revealed that among highway traffic accidents, the variables with a significant impact on accident severity are the age of the perpetrator being between 20 and less than 39 years, the time period being daytime (06:00-18:00), occurrence on weekends (Sat-Sun), seasons being summer and winter, violation of traffic regulations (failure to comply with safe driving), road type being a tunnel, geometric structure having a high number of lanes and a high speed limit. We identified a total of 10 independent variables that showed a positive correlation with highway traffic accident severity. Conclusion: As accidents on highways occur due to the complex interaction of various factors, predicting accidents poses significant challenges. However, utilizing the results obtained from this study, there is a need for in-depth analysis of the factors influencing the severity of highway traffic accidents. Efforts should be made to establish efficient and rational response measures based on the findings of this research.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• Journal of the Korea Society of Computer and Information
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• v.27 no.6
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• pp.167-174
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• 2022

In this paper we investigate the permutation test for the equality of correlation coefficients in several independent populations. Permutation test is a non-parametric testing methodology based upon the exchangeability of observations. Exchangeability is a generalization of the concept of independent, identically distributed random variables. Using permutation method, we may construct asymptotically exact test. This method is asymptotically as powerful as standard parametric tests and is a valuable tool when the sample sizes are small and normality assumption cannot be met. We first review existing parametric approaches to test the equality of correlation coefficients and compare them with the permutation test. At the end, all the approaches are illustrated using Iris data example.

• Journal of the Korea Concrete Institute
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• v.26 no.3
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• pp.343-350
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• 2014

A probabilistic construction stage analysis using the Monte Carlo Simulation was performed to address the effects of uncertainty regarding the material properties, environmental factors, and applied forces. In the previous research, creep and shrinkage were assumed to be completely independent random variables. However, because of the common influencing factors in the material models for the creep and shrinkage estimation, strong correlation between creep and shrinkage can be presumed. In this paper, an Monte Carlo Simulation using CEB-FIB creep and shrinkage equations were performed to actually evaluate the correlation coefficient between two phenomena, and then another Monte Carlo Simulation to evaluate the statistical properties of axial strain affected by partially correlated random variables including the material properties, environmental factors, and applied forces. The results of Monte Carlo Simulation were compared with measured strains of a column on a first story in a 58-story building. Comparison indicated that the variation due to the uncertainty related with the material properties were most severe. And measured strains was within the range of mean+standard deviation.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.47 no.1
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• pp.41-50
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• 2024

Korea is facing a significant problem with historically low fertility rates, which is becoming a major social issue affecting the economy, labor force, and national security. This study analyzes the factors contributing to the regional gap in fertility rates and derives policy implications. The government and local authorities are implementing a range of policies to address the issue of low fertility. To establish an effective strategy, it is essential to identify the primary factors that contribute to regional disparities. This study identifies these factors and explores policy implications through machine learning and explainable artificial intelligence. The study also examines the influence of media and public opinion on childbirth in Korea by incorporating news and online community sentiment, as well as sentiment fear indices, as independent variables. To establish the relationship between regional fertility rates and factors, the study employs four machine learning models: multiple linear regression, XGBoost, Random Forest, and Support Vector Regression. Support Vector Regression, XGBoost, and Random Forest significantly outperform linear regression, highlighting the importance of machine learning models in explaining non-linear relationships with numerous variables. A factor analysis using SHAP is then conducted. The unemployment rate, Regional Gross Domestic Product per Capita, Women's Participation in Economic Activities, Number of Crimes Committed, Average Age of First Marriage, and Private Education Expenses significantly impact regional fertility rates. However, the degree of impact of the factors affecting fertility may vary by region, suggesting the need for policies tailored to the characteristics of each region, not just an overall ranking of factors.