• Title/Summary/Keyword: Standard normal Distribution

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Likelihood based inference for the shape parameter of Pareto Distribution

  • Lee, Jae-Un;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.19 no.4
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    • pp.1173-1181
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    • 2008
  • In this paper, when the parameter of interest is the shape parameter in Pareto distribution, we develop likelihood based inference for this parameter. Specially, we develop signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic for the shape parameter. It is well-known that as sample size grows, the modified signed log-likelihood ratio statistic converges to standard normal distribution faster than the signed log-likelihood ratio statistic. But the computation of the modified signed log-likelihood statistic is hard or even impossible when the sufficient statistics and the ancillary statistics are not clear. In this case, one can consider an approximation to the modified signed log-likelihood statistic. Specially, when the parameter of interest is informationally orthogonal to the nuisance parameters, we propose the approximate modified signed log-likelihood statistic. Through simulation, we investigate the performances of the proposed statistics with the signed log-likelihood statistic.

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An Economic Optimization of the Target Value (경제성을 고려한 공정 목표값 최적화)

  • 윤철환;유정현;윤덕균
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.21 no.45
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    • pp.201-213
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    • 1998
  • We address the problem of choosing the most economic mean value for an automatic filling operation on a production line through the sampling inspection. If quality characteristic of a unit is less than inspection specification then the goods is not accepted. Otherwise, it is accepted. The lots that the numbers of non-conforming units in a sample are larger than the allowable number of non-conforming units are rejected. The non-conforming units in the rejected lots are separated by the screening inspection. The non-conforming units separated are sold in discount price. We assume that quality characteristic is larger-the-better characteristic, the distribution of quality characteristic is normal distribution, and the standard deviation of the distribution is known. This paper presents total expected profit function model considering sales revenue, inspection costs, and material costs. The manufacturing process mean value maximizing total expected profit is determined, and the results of the process target value and total expected profit is analyzed as coefficients change.

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On Estimation and Distribution of Game Satisfaction (게임만족도 추정 및 분포에 관한 연구)

  • Ham, Hyung-Bum
    • Journal of Korea Multimedia Society
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    • v.10 no.5
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    • pp.679-686
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    • 2007
  • Every year, although the number of game enterprises increases, every game which is developed and distributed by these enterprises do not have competitiveness. One game even increasing competitiveness and added value of game industry, we have to develop games which are satisfied with users, and for it, we need scientific research which evaluates about satisfaction. In this paper, We quantatively estimate game satisfaction by using AHP and statistical method. Also we discuss the method which derive distribution of game satisfaction. We can acquire expected effect which predicts satisfaction level and standard about games by using these methods.

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Estimating Infection Distribution and Prevalence of Malaria in South Korea Using a Back-calculation Formula (후향연산식을 활용한 국내 삼일열 말라리아의 감염분포와 유병자수 추정)

  • Jang, Hyun-Gap;Park, Jeong-Soo;Jun, Mi-Jeong;Rhee, Jeong-Ae;Kim, Han-Me-Ury
    • The Korean Journal of Applied Statistics
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    • v.21 no.6
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    • pp.901-910
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    • 2008
  • Incidence of Plasmodium vivax malaria in South Korea have been reemerged from mid-1990 and infected around 1600 patients annually recent years. The authors calculated the distribution of malaria infection and prevalence in South Korea using incidence (2001-2006) and incubation period distributions by a back-calculation formula and the least squares estimation method. The estimated infection has a normal distribution with a mean 207 and a standard deviation 30.7 days. In addition, the authors found the estimated daily average prevalence is 628.8 patients.

A Graphical Method to Assess Goodness-of-Fit for Inverse Gaussian Distribution (역가우스분포에 대한 적합도 평가를 위한 그래프 방법)

  • Choi, Byungjin
    • The Korean Journal of Applied Statistics
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    • v.26 no.1
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    • pp.37-47
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    • 2013
  • A Q-Q plot is an effective and convenient graphical method to assess a distributional assumption of data. The primary step in the construction of a Q-Q plot is to obtain a closed-form expression to represent the relation between observed quantiles and theoretical quantiles to be plotted in order that the points fall near the line y = a + bx. In this paper, we introduce a Q-Q plot to assess goodness-of-fit for inverse Gaussian distribution. The procedure is based on the distributional result that a transformed random variable $Y={\mid}\sqrt{\lambda}(X-{\mu})/{\mu}\sqrt{X}{\mid}$ follows a half-normal distribution with mean 0 and variance 1 when a random variable X has an inverse Gaussian distribution with location parameter ${\mu}$ and scale parameter ${\lambda}$. Simulations are performed to provide a guideline to interpret the pattern of points on the proposed inverse Gaussian Q-Q plot. An illustrative example is provided to show the usefulness of the inverse Gaussian Q-Q plot.

Utilization of Skewness for Statistical Quality Control (통계적 품질관리를 위한 왜도의 활용)

  • Kim, Hoontae;Lim, Sunguk
    • Journal of Korean Society for Quality Management
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    • v.51 no.4
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    • pp.663-675
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    • 2023
  • Purpose: Skewness is an indicator used to measure the asymmetry of data distribution. In the past, product quality was judged only by mean and variance, but in modern management and manufacturing environments, various factors and volatility must be considered. Therefore, skewness helps accurately understand the shape of data distribution and identify outliers or problems, and skewness can be utilized from this new perspective. Therefore, we would like to propose a statistical quality control method using skewness. Methods: In order to generate data with the same mean and variance but different skewness, data was generated using normal distribution and gamma distribution. Using Minitab 18, we created 20 sets of 1,000 random data of normal distribution and gamma distribution. Using this data, it was proven that the process state can be sensitively identified by using skewness. Results: As a result of the analysis of this study, if the skewness is within ± 0.2, there is no difference in judgment from management based on the probability of errors that can be made in the management state as discussed in quality control. However, if the skewness exceeds ±0.2, the control chart considering only the standard deviation determines that it is in control, but it can be seen that the data is out of control. Conclusion: By using skewness in process management, the ability to evaluate data quality is improved and the ability to detect abnormal signals is excellent. By using this, process improvement and process non-sub-stitutability issues can be quickly identified and improved.

Analysis of the flow distribution and mixing characteristics in the reactor pressure vessel

  • Tong, L.L.;Hou, L.Q.;Cao, X.W.
    • Nuclear Engineering and Technology
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    • v.53 no.1
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    • pp.93-102
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    • 2021
  • The analysis of the fluid flow characteristics in reactor pressure vessel is an important part of the hydraulic design of nuclear power plant, which is related to the structure design of reactor internals, the flow distribution at core inlet and the safety of nuclear power plant. The flow distribution and mixing characteristics in the pressurized reactor vessel for the 1000MWe advanced pressurized water reactor is analyzed by using Computational Fluid Dynamics (CFD) method in this study. The geometry model of the full-scaled reactor vessel is built, which includes the cold and hot legs, downcomer, lower plenum, core, upper plenum, top plenum, and is verified with some parameters in DCD. Under normal condition, it is found that the flow skirt, core plate holes and outlet pipe cause pressure loss. The maximum and minimum flow coefficient is 1.028 and 0.961 respectively, and the standard deviation is 0.019. Compared with other reactor type, it shows relatively uniform of the flow distribution at the core inlet. The coolant mixing coefficient is investigated with adding additional variables, showing that mass transfer of coolant occurs near the interface. The coolant mainly distributes in the 90° area of the corresponding core inlet, and mixes at the interface with the coolant from the adjacent cold leg. 0.1% of corresponding coolant is still distributed at the inlet of the outer-ring components, indicating wide range of mixing coefficient distribution.

The Study on the Somatotype and Spinal Deformity among Middle and High School Girls (중·고 여학생의 체형분류 및 척추변형에 관한 연구)

  • Lee, Hea-Ju;Ham, Ok-Song
    • Fashion & Textile Research Journal
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    • v.1 no.2
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    • pp.137-147
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    • 1999
  • The purpose of this study was to classify female students' somatotypes, to investigate the relationship between five somatotypes obtained from anthropometric measurements and to examine the relationship between the spinal deformity and somatotypes. The subjects for anthropometric measurements were 844 female middle and high school students. The data were analyzed by cluster analysis, correspondence analysis, Duncan test, and T-test. The results were as follows. Cluster analysis on the factors extracted from directly measured items classified subjects into five types (middle height and a little slim type (39.6%), low height and a little slim type (13.1%), middle height and a little fat type (18.0%), tall and very fat type (7.7%), and very tall and standard type (21.6%). In examining the relationship between the normal people and those of the spinal deformity, the normal showed higher mean value in almost all the items of the girth, the depth, and the length. High school students had more spinal deformity in number than middle school students. The degree of deformity was higher in the right spinal deformity than in the left spinal deformity as the age increased. In terms of the distribution of the spinal deformity classified by the somatotype, Type 1 (middle height and a little slim type) and Type 5 (very tall and standard type) appeared the highest.

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A study on the traceability and uncertainty of skin hydration measurement on the sole of the foot

  • Yang, Gi-Young;Choi, Ji-Won;Chae, Han;Lee, Byung-Ryul
    • The Journal of Korean Medicine
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    • v.38 no.4
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    • pp.55-61
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    • 2017
  • Objectives: In order to accurately measure skin moisture and accumulate normal skin moisture data, analyzing the uncertainty of the skin moisture measurement and establishing standard reference data is essential. It helps to evaluate the skin's condition and has great significance in diagnosis and treatment. In this study, the traceability of the equipment and the uncertainty of the results were analyzed for their potential use in the field of Korean medicine. The data was collected measuring skin moisture on the sole of the foot. Methods: One professional measured the moisture of the adult male's foot 10 times following a determined protocol. The standard uncertainty of repeated measurements was calculated from the mean value of 10 repeated measurements. Ten trainee participants also measured the adult male's foot following a determined protocol. The standard uncertainty by tester was calculated from the value of repeated measurements. Results: As a result of analyzing the difference between the mean and standard uncertainties in both the expert and trainees, it was confirmed that the variance in this study did not satisfy the normal distribution. In addition, the Mann-Whitney U-test was carried out, and it was found that there was no significant difference in the measured values of the two groups. The authorized uncertainty of measurements and traceability of all the equipment was not confirmed. Conclusions: This paper establishes the basis for later measurement-equipment research to provide the objective indicators to approach the dryness of plantar skin from dehydration, the Korean medicine perspective.

Analysis of hematological changes in normal and diarrhea calves

  • Song, Ru-hui;Kang, Jin-hee;Park, Kwang-man;Youm, Jung-ho;Park, Jin-ho
    • Korean Journal of Veterinary Service
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    • v.43 no.3
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    • pp.161-165
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    • 2020
  • In order to effective treats a sick calf, it is necessary to obtain accurate information about the patient's condition. However, the standard references for Korean cattle claves are not well known. Therefore, this study aims to present useful clinical values by analyzing normal blood and diarrhea blood of Hanwoo calf. Recently, with the advent of a portable blood analyzer, it is possible to immediately analyze the patient's condition and severity in the field, not in the laboratory, and to calculate a suitable dosage for supporting fluid therapy. Therefore, in this study, the distribution of red blood cells (RBC) and white blood cells (WBC) were analyzed in normal and diarrhea Hanwoo calves. As a result, Hematocrit (HCT) levels increase significantly between 1 and 20 days in diarrhea positive calves. Changes in leukocyte composition had similar growth patterns in normal and diarrhea calves. As it grew, the proportion of neutrophils decreased and lymphocytes increased. However, the number of WBCs increased from 1 to 10 and 21 to 30 days in diarrhea positive calves, which is closely related to the increase in neutrophils. Therefore, those data can be used for diagnosis and treatment of diarrhea calf.