• Title/Summary/Keyword: Standard normal Distribution

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Effective Depth of Field Implementation Based on Standard Normal Distribution and Multiple Layers (표준 정규 분포 및 다층 레이어 기반의 효과적인 피사계 심도 구현)

  • Choi, Mookang;Kim, Yeri;Kim, Minji;Oh, Kyoungsu
    • Journal of Korea Game Society
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    • v.20 no.6
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    • pp.53-62
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    • 2020
  • This paper proposes on the implementation method of depth of field effect based on backward mapping method available in real-time rendering enviroment using calculation of sampling range based on standard normal distribution and alpha blending of color of layers. To implement the effect, this paper describe how to calculate radius of circle of confusion, establish sampling radius using circle of confusion, and determine color through alpha blending of the multiple layer and denoising.

Small sample likelihood based inference for the normal variance ratio

  • Lee, Woo Dong
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.4
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    • pp.911-918
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    • 2013
  • This study deals with the small sample likelihood based inference for the ratio of two normal variances. The small sample likelihood inference is an approximation method. The signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic, which converge to standard normal distribution, are proposed for the normal variance ratio. Through the simulation study, the coverage probabilities of confidence interval and power of the exact, the signed log-likelihood and the modified signed log-likelihood ratio statistic will be compared. A real data example will be provided.

Direct approximations for t percentage points (t 분포 퍼센트점의 직접근사공식)

  • 김현철;송규문;허문렬
    • The Korean Journal of Applied Statistics
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    • v.2 no.1
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    • pp.48-53
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    • 1989
  • In contrast to the customary approximations based on standard normal percentage points, direct approximations involve simple functions of parameters (such as degrees of freedom and tail area of the t distributions). This article used techniques of exploratory data analysis following Hoaglin to develop direct approximations for percentage points in the commonly used portions of upper tail of the t distribution with small to moderate numbers of degrees of freedom. These approximations are convenient to use and they compare favorably in accuracy with the popular approximations based on standard normal percentage points such as Peiser's. They can be used as an initial value generator in algorithms for getting more accurate percentage points.

A comparative study of the Gini coefficient estimators based on the regression approach

  • Mirzaei, Shahryar;Borzadaran, Gholam Reza Mohtashami;Amini, Mohammad;Jabbari, Hadi
    • Communications for Statistical Applications and Methods
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    • v.24 no.4
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    • pp.339-351
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    • 2017
  • Resampling approaches were the first techniques employed to compute a variance for the Gini coefficient; however, many authors have shown that an analysis of the Gini coefficient and its corresponding variance can be obtained from a regression model. Despite the simplicity of the regression approach method to compute a standard error for the Gini coefficient, the use of the proposed regression model has been challenging in economics. Therefore in this paper, we focus on a comparative study among the regression approach and resampling techniques. The regression method is shown to overestimate the standard error of the Gini index. The simulations show that the Gini estimator based on the modified regression model is also consistent and asymptotically normal with less divergence from normal distribution than other resampling techniques.

A Study on the Anthropometry and Healh-Related Lifestyle Habits of Women College Students in Kunsan (군산시 일부 여대생의 신체적 특성과 식생활 관련습관에 관한 연구)

  • 장혜순;김미라
    • Korean Journal of Community Nutrition
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    • v.8 no.4
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    • pp.526-537
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    • 2003
  • The purpose of this study was to compare the anthropometry and nutrition knowledge, food behaviour and lifestyle of women college students with different obesity indexes. The subjects were 251 women college students who were randomly selected from Kunsan National University. The height, body weight, soft/lean mass, fat mass, percentage of body fat, and fat distribution were measured, and health-related lifestyle habits were evaluated based on questionnaires. The subjects were assigned to one of the following groups based on their Body Mass Index (BMI) : underweight, normal weight and overweight. The results were as follows. Their body weight, soft/lean mass, fat mass, percentage of body fat, and fat distribution were significantly higher in the overweight subjects when compared to the underweight or normal weight subjects. Standard of living, self-recognition of health status and duration of exercise were significantly correlated with their BMIs. Self-satisfaction with body weight decreased as the BMI increased. Most subjects had poor habits such as skipping meals and lack of exercises. The overweight and the underweight groups skipped meals more frequently than the normal weight group. There were no significant differences in the scores on the nutritional knowledge and the dietary behaviour of the subjects with different BMIs. Therefore, proper nutritional education on regular meals and intervention are required if women college students are to have normal weights and healthy lifestyles. (Korean J Community Nutrition 8(4) L: 526∼537, 2003)

Estimation on Altitudinal Spectrum of Suitability for Four Species of the Mayfly Genus Ephemera (Ephemeroptera: Ephemeridae) Using Probability Distribution Models (확률분포모형을 이용한 하루살이속(Ephemera) 4종의 고도구배에 따른 서식처적합도 평가)

  • Dongsoo Kong;Bomi Kang
    • Journal of Korean Society on Water Environment
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    • v.39 no.4
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    • pp.302-315
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    • 2023
  • Distribution characteristics and altitudinal gradient of four species (E. strigata, E. separigata, E. orientalis-sachalinensis group) of the mayfly genus Ephemera (Order Ephemeroptera) were analyzed with probability distribution models (exponential, normal, lognormal, logistic, Weibull, gamma, beta, Gumbel). Data was collected from 23,846 sampling units of 6,787 sites in Korea from 2010 to 2021. The beta distribution model showed the best fit for positively skewed E. orientalis-sachalinensis and little-skewed E. strigata along with altitudinal gradient. The reversed lognormal distribution model showed the best-fit for negatively skewed E. separigata. E. orientalis-sachalinensis distributed at the range of altitude 1~700 m (mean 251 m, median 226 m, mode 124 m, and standard deviation 161 m), E. strigata distributed at the range of altitude 5~871 m (mean 474 m, median 478 m, mode 492 m, and standard deviation 200 m), E. separigata distributed at the range of altitude 7~846 m (mean 620 m, median 659 m, mode 760 m, and standard deviation 181 m). Altitudinal habitat suitability ranges were estimated to be 42~257 m for E. orientalis-sachalinensis, 335~644 m for E. strigata, and 641~824 m for E. separigata. Based on the altitudinal spectrum of suitability and altitude-related temperature analysis results, E. orientalis-sachalinensis was estimated to be thermophilic, E. strigata to be mesophilic, and E. separigata to be thermophobic. This is the first national-scale evaluation of the altitudinal distribution of Ephemera in Korea. These results will be used in a further research study on altitudinal shift of the species of Ephemera under climate change.

Probabilistic Load Analysis for Tailplane Considering Uncertainties in Design Variables (설계변수의 불확실성을 고려한 미익 하중의 확률론적 해석)

  • Choi, Yong-Joon;Kim, In-Gul;Lee, Seok-Je
    • Journal of the Korea Institute of Military Science and Technology
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    • v.13 no.6
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    • pp.1043-1050
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    • 2010
  • This paper examined the probabilistic load analysis for the tailplane during pitching maneuvering in the conceptual aircraft design phase. The flight load analysis based on the probabilistic distribution of design variables are compared with the results of the deterministic analysis. Two forms of variable distribution are used in this paper. One is standard normal distribution, the other distribution is calculated from the results of short-period longitudinal equation of aircraft motion. The influence of the distribution parameter on the probabilistic load analysis was investigated and the significant design variables that have an impact on the mean and variance of probabilistic load were identified. The comparison indicates that probabilistic load analysis provides more reliable probabilistic load distribution for the structural design than the traditional deterministic analysis.

Particle Detachment in Granular Media Filtration (입상여과에서 입자물질의 탈리)

  • Kim, Jinkeun
    • Journal of Korean Society of Water and Wastewater
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    • v.18 no.5
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    • pp.673-679
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    • 2004
  • Particle breakthrough can occur by either the breakoff of previously captured particles (or flocs) or the direct passage of some influent particles through the filter. Filtration experiments were performed in a laboratory-scale filter using spherical glass beads with a diameter of 0.55 mm as collectors. A single type of particle suspension (Min-U-Sil 5, nearly pure $SiO_2$) and three different destabilization methods (pH control, alum and polymer destabilization) were utilized. The operating conditions were similar to those of standard media filtration practice: a filtration velocity of 5 m/h. To assess the possibility of particle detachment during the normal filtration, a hydraulic shock load (20% increase of flow rate) was applied after 4 hours of normal filtration. The magnitude of particle detachment was proportional to the particle size for non-Brownian particles. At the same time, less favorable particles, i.e., particles with larger surface charge, were easily detached during the hydraulic shock load. Therefore, proper particle destabilization before filtration is crucial for maximum particle removal as well as minimum particle breakthrough.

Comparison of ISO-GUM and Monte Carlo Method for Evaluation of Measurement Uncertainty (몬테카를로 방법과 ISO-GUM 방법의 불확도 평가 결과 비교)

  • Ha, Young-Cheol;Her, Jae-Young;Lee, Seung-Jun;Lee, Kang-Jin
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.38 no.7
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    • pp.647-656
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    • 2014
  • To supplement the ISO-GUM method for the evaluation of measurement uncertainty, a simulation program using the Monte Carlo method (MCM) was developed, and the MCM and GUM methods were compared. The results are as follows: (1) Even under a non-normal probability distribution of the measurand, MCM provides an accurate coverage interval; (2) Even if a probability distribution that emerged from combining a few non-normal distributions looks as normal, there are cases in which the actual distribution is not normal and the non-normality can be determined by the probability distribution of the combined variance; and (3) If type-A standard uncertainties are involved in the evaluation of measurement uncertainty, GUM generally offers an under-valued coverage interval. However, this problem can be solved by the Bayesian evaluation of type-A standard uncertainty. In this case, the effective degree of freedom for the combined variance is not required in the evaluation of expanded uncertainty, and the appropriate coverage factor for 95% level of confidence was determined to be 1.96.

Statistical Parameter Estimation to Calculate Collision Probability Between Mokpo Harbor Bridge and Passing Vessels (목포 대교와 통항 선박 사이의 충돌 확률 계산을 위한 통계 변수 추정)

  • Yim, Jeong-Bin;Kim, Dae-Hee
    • Journal of Navigation and Port Research
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    • v.34 no.8
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    • pp.609-614
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    • 2010
  • This paper describes statistical parameter estimation to calculate collision probabilities between Mokpo Harbor Bridge and passing vessels. At first, we obtained AIS (Automatic Identification System) information from passing vessels, then after, analyzed the lateral distributions of vessel tracks and estimated the mean and the standard deviation for the distance away from bridge center, the passing course and the passing speed. The analysis results of track distribution for the distance away and the passing course are shown as normal type, otherwise the speed distribution shown as two kinds of different normal type. In addition, we testified that the usefulness of estimated parameter values through the relative comparison between the track distributions and it's normal probability distributions.