• Communications of Mathematical Education
• /
• v.24 no.1
• /
• pp.177-193
• /
• 2010

The purpose of this study is to explore normal distribution in probability distributions of the area of statistics in high school mathematics. To do this these contents such as approximation of normal distribution from binomial distribution, investigation of normal distribution curve and the area under its curve through the method of Monte Carlo, linear transformations of normal distribution curve, and various types of normal distribution curves are explored with CAS calculator. It will not be ablt to be attained for the objectives suggested the area of probability distribution in a paper-and-pencil classroom environment from the perspectives of tools of CAS calculator such as trivialization, experimentation, visualization, and concentration. Thus, this study is to explore various properties of normal distribution curve with CAS calculator and derive from pedagogical implications of teaching and learning normal distribution curve.

• Journal of the Korea Society of Computer and Information
• /
• v.25 no.6
• /
• pp.119-129
• /
• 2020

Software development activities are influenced by stochastic theory rather than deterministic one due to having process variability. Stochastic methods factor in the uncertainties associated with project activities and provides insight into the expected project outputs as probability distributions rather than as deterministic approximations. Thus, successful software projects systematically manage and balance five objectives based on historical probability: scope, size, cost, effort, schedule, and quality. Although software size estimation having much uncertainty in initial development has traditionally performed using deterministic methods: LOC(Lines Of Code), COCOMO(COnsructive COst MOdel), FP(Function Point), SLIM(Software LIfecycle Management). This research aims to present a function point method based on stochastic distribution and a case study based on Monte Carlo Simulation applying on an automotive electrical and electronics system software development. It is expected that the result of this paper is used as guidance for establishing of function point method in organizations and tools for helping project managers make decisions correctly.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.32 no.2
• /
• pp.391-404
• /
• 2022

Aron Gohr proposed a cryptanalysis method based on deep learning technology for the lightweight block cipher Speck. This is a method that enables a chosen plaintext attack with higher accuracy than the classical differential cryptanalysis. In this paper, by using the probability distribution, we analyze the mechanism of such deep learning based cryptanalysis and propose the results applied to the lightweight block cipher Simon. In addition, we examine that the probability distributions of the predicted values of the neural networks within the cryptanalysis working processes are different depending upon the characteristics of round functions of Speck and Simon, and suggest a direction to improve the efficiency of the neural distinguisher which is the core technology of Aron Gohr's cryptanalysis.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.17 no.11
• /
• pp.2945-2965
• /
• 2023

The laser inertial measurement unit is a precision device widely used in rocket navigation system and other equipment, and its quality is directly related to navigation accuracy. In the quality evaluation of laser inertial measurement unit, there is inevitably uncertainty in the index input information. First, the input numerical information is in interval form. Second, the index input grade and the quality evaluation result grade are given according to different national standards. So, it is a key step to transform the interval information input by the index into the data form consistent with the evaluation result grade. In the case of uncertain input, this paper puts forward a method based on probability distribution to solve the problem of asymmetry between the reference grade given by the index and the evaluation result grade when evaluating the quality of laser inertial measurement unit. By mapping the numerical relationship between the designated reference level and the evaluation reference level of the index information under different distributions, the index evidence symmetrical with the evaluation reference level is given. After the uncertain input information is transformed into evidence of interval degree distribution by this method, the information fusion of interval degree distribution evidence is carried out by interval evidential reasoning algorithm, and the evaluation result is obtained by projection covariance matrix adaptive evolution strategy optimization. Taking a five-meter redundant laser inertial measurement unit as an example, the applicability and effectiveness of this method are verified.

• Communications for Statistical Applications and Methods
• /
• v.31 no.1
• /
• pp.1-35
• /
• 2024

The assumption of homoscedasticity is one of the most crucial assumptions for many parametric tests used in the biological sciences. The aim of this paper is to compare the empirical probability of type I error and the power of ten parametric and two non-parametric tests for homoscedasticity with simulations under different types of distributions, number of groups, number of samples per group, variance ratio and significance levels, as well as through empirical data from an agricultural experiment. According to the findings of the simulation study, when there is no violation of the assumption of normality and the groups have equal variances and equal number of samples, the Bhandary-Dai, Cochran's C, Hartley's Fmax, Levene (trimmed mean) and Bartlett tests are considered robust. The Levene (absolute and square deviations) tests show a high probability of type I error in a small number of samples, which increases as the number of groups rises. When data groups display a nonnormal distribution, researchers should utilize the Levene (trimmed mean), O'Brien and Brown-Forsythe tests. On the other hand, if the assumption of normality is not violated but diagnostic plots indicate unequal variances between groups, researchers are advised to use the Bartlett, Z-variance, Bhandary-Dai and Levene (trimmed mean) tests. Assessing the tests being considered, the test that stands out as the most well-rounded choice is the Levene's test (trimmed mean), which provides satisfactory type I error control and relatively high power. According to the findings of the study and for the scenarios considered, the two non-parametric tests are not recommended. In conclusion, it is suggested to initially check for normality and consider the number of samples per group before choosing the most appropriate test for homoscedasticity.

• Journal of The Korean Society of Agricultural Engineers
• /
• v.46 no.5
• /
• pp.27-39
• /
• 2004

In the first part of this study, five homogeneous regions in view of topographical and geographically homogeneous aspects except Jeju and Ulreung islands in Korea were accomplished by K-means clustering method. A total of 57 rain gauges were used for the regional frequency analysis with minimum rainfall series for the consecutive durations. Generalized Extreme Value distribution was confirmed as an optimal one among applied distributions. Drought rainfalls following the return periods were estimated by at-site and regional frequency analysis using L-moments method. It was confirmed that the design drought rainfalls estimated by the regional frequency analysis were shown to be more appropriate than those by the at-site frequency analysis. In the second part of this study, LH-moment ratio diagram and the Kolmogorov-Smirnov test on the Gumbel (GUM), Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) distributions were accomplished to get optimal probability distribution. Design drought rainfalls were estimated by both at-site and regional frequency analysis using LH-moments and GEV distribution, which was confirmed as an optimal one among applied distributions. Design rainfalls were estimated by at-site and regional frequency analysis using LH-moments, the observed and simulated data resulted from Monte Carlotechniques. Design drought rainfalls derived by regional frequency analysis using L1, L2, L3 and L4-moments (LH-moments) method have shown higher reliability than those of at-site frequency analysis in view of RRMSE (Relative Root-Mean-Square Error), RBIAS (Relative Bias) and RR (Relative Reduction) for the estimated design drought rainfalls. Relative efficiency were calculated for the judgment of relative merits and demerits for the design drought rainfalls derived by regional frequency analysis using L-moments and L1, L2, L3 and L4-moments applied in the first report and second report of this study, respectively. Consequently, design drought rainfalls derived by regional frequency analysis using L-moments were shown as more reliable than those using LH-moments. Finally, design drought rainfalls for the classified five homogeneous regions following the various consecutive durations were derived by regional frequency analysis using L-moments, which was confirmed as a more reliable method through this study. Maps for the design drought rainfalls for the classified five homogeneous regions following the various consecutive durations were accomplished by the method of inverse distance weight and Arc-View, which is one of GIS techniques.

• The KIPS Transactions:PartB
• /
• v.13B no.7 s.110
• /
• pp.633-642
• /
• 2006

In the Internet environment many interactions between many users and unknown users take place and it is usually rare to have the trust information about others. Due to the lack of trust information, entities have to take some risks in transactions with others. In this perspective, it is crucial for the entities to be equipped with functionality to accumulate and manage the trust information on other entities in order to reduce risks and uncertainty in their transactions. This paper is concerned with a quantitative computational trust model which takes into account multiple evaluation criteria and uses the recommendation from others in order to get the trust for an entity. In the proposed trust model, the trust for an entity is defined as the expectation for the entity to yield satisfactory outcomes in the given situation. Once an interaction has been made with an entity, it is assumed that outcomes are observed with respect to evaluation criteria. When the trust information is needed, the satisfaction degree, which is the probability to generate satisfactory outcomes for each evaluation criterion, is computed based on the empirical outcome outcome distributions and the entity's preference degrees on the outcomes. Then, the satisfaction degrees for evaluation criteria are aggregated into a trust value. At that time, the reputation information is also incorporated into the trust value. This paper also shows that the model could help the entities effectively choose other entities for transactions with some experiments in e-commerce.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.2
• /
• pp.179-184
• /
• 2007

This paper deals with a context-aware application based on Bayesian network in the smart home. Bayesian network is a powerful graphical tool for learning casual dependencies between various context events and obtaining probability distributions. So we can recognize the resident's activities and home environment based on it. However as the sensors become various, learning the structure become difficult. We construct Bayesian network simple and efficient way with mutual information and evaluated the method in the virtual smart home.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.29 no.8C
• /
• pp.1055-1061
• /
• 2004

In this paper, we propose an efficient dynamic coding scheme by using multiple codewords in H.264/AVC entropy coding. The exponential Golomb (Exp-Golomb) codewords used in H.264/AVC do not reflect enough the symbol distributions of the combined syntax element in (7) due to their static probability distribution characteristics. However, the multiple codewords in this paper have different statistical characteristics. we propose a dynamic coding scheme by using selectively among multiple codewords to encode the combined syntax element according to given image sequences. Simulation results show that our proposed scheme outperforms the existing (7) method in compression efficiency without loss of quality.

• Wind and Structures
• /
• v.4 no.5
• /
• pp.413-440
• /
• 2001

This paper presents an extensive analysis of unsteady wind loading data on a 18 m long and 2 m high wall in a rural environment, with the wind at a range of angles to the wall normal. The data is firstly analyzed using standard statistical techniques (moments of probability distributions, auto- and cross-correlations, auto- and cross-spectra etc.). The analysis is taken further using a variety of less conventional methods - conditional sampling, proper orthogonal decomposition and wavelet analysis. It is shown that, even though the geometry is simple, the nature of the unsteady flow is surprisingly complex. The fluctuating pressures on the front face of the wall are to a great extent caused by the turbulent fluctuations in the upstream flow, and reflect the oncoming flow structures. The results further suggest that there are distinct structures in the oncoming flow with a variety of scales, and that the second order quasi-steady approach can predict the pressure fluctuations quite well. The fluctuating pressures on the rear face are also influenced by the fluctuations in the oncoming turbulence, but also by unsteady fluctuations due to wake unsteadiness. These fluctuations have a greater temporal and spatial coherence than on the front face and the quasi-steady method over-predicts the extent of these fluctuations. Finally the results are used to check some assumptions made in the current UK wind loading code of practice.