• Title/Summary/Keyword: normal distribution

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Polynomially Adjusted Normal Approximation to the Null Distribution of Ansari-Bradley Statistic

  • Ha, Hyung-Tae;Yang, Wan-Youn
    • The Korean Journal of Applied Statistics
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    • v.24 no.6
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    • pp.1161-1168
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    • 2011
  • The approximation for the distribution functions of nonparametric test statistics is a significant step in statistical inference. A rank sum test for dispersions proposed by Ansari and Bradley (1960), which is widely used to distinguish the variation between two populations, has been considered as one of the most popular nonparametric statistics. In this paper, the statistical tables for the distribution of the nonparametric Ansari-Bradley statistic is produced by use of polynomially adjusted normal approximation as a semi parametric density approximation technique. Polynomial adjustment can significantly improve approximation precision from normal approximation. The normal-polynomial density approximation for Ansari-Bradley statistic under finite sample sizes is utilized to provide the statistical table for various combination of its sample sizes. In order to find the optimal degree of polynomial adjustment of the proposed technique, the sum of squared probability mass function(PMF) difference between the exact distribution and its approximant is measured. It was observed that the approximation utilizing only two more moments of Ansari-Bradley statistic (in addition to the first two moments for normal approximation provide) more accurate approximations for various combinations of parameters. For instance, four degree polynomially adjusted normal approximant is about 117 times more accurate than normal approximation with respect to the sum of the squared PMF difference.

Novel approach to predicting the release probability when applying the MARSSIM statistical test to a survey unit with a specific residual radioactivity distribution based on Monte Carlo simulation

  • Chun, Ga Hyun;Cheong, Jae Hak
    • Nuclear Engineering and Technology
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    • v.54 no.5
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    • pp.1606-1615
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    • 2022
  • For investigating whether the MARSSIM nonparametric test has sufficient statistical power when a site has a specific contamination distribution before conducting a final status survey (FSS), a novel approach was proposed to predict the release probability of the site. Five distributions were assumed: lognormal distribution, normal distribution, maximum extreme value distribution, minimum extreme value distribution, and uniform distribution. Hypothetical radioactivity populations were generated for each distribution, and Sign tests were performed to predict the release probabilities after extracting samples using Monte Carlo simulations. The designed Type I error (0.01, 0.05, and 0.1) was always satisfied for all distributions, while the designed Type II error (0.01, 0.05, and 0.1) was not always met for the uniform, maximum extreme value, and lognormal distributions. Through detailed analyses for lognormal and normal distributions which are often found for contaminants in actual environmental or soil samples, it was found that a greater statistical power was obtained from survey units with normal distribution than with lognormal distribution. This study is expected to contribute to achieving the designed decision error when the contamination distribution of a survey unit is identified, by predicting whether the survey unit passes the statistical test before undertaking the FSS according to MARSSIM.

A Study on Taguchi's Feed-back Control System (다구찌의 피드백 제어 시스템에 관한 연구)

  • 김지훈;정해성;김재주
    • Journal of Korean Society for Quality Management
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    • v.26 no.3
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    • pp.60-70
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    • 1998
  • When driving the expected loss generated by the quality deviation, Taguchi(1991b) assumed that an objective characteristic has the uniform distribution in its control limit. But it is reasonable to assume that an objective characteristic has the normal distribution than the uniform distribution. Since the triangular distribution is similar to the normal distribution and easy to handle as well, in this article, we first find the optimum measurement interval and the optimum control limit under the triangular distribution. Under the normal assumption, the modified method is compared to Taguchi's. Secondly we find the numerical value solution of the optimum measurement interval and the optimum control limit under the normal distribution.

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Effects of Calibration Rounds on the Statistical Distribution of Muzzle Velocity in Acceptance Test of Propelling Charge (추진장약 수락시험시 포구속도 확률분포에 기준탄이 미치는 영향)

  • Park, Sung-Ho;Kim, Jae-Hoon
    • Journal of the Korea Institute of Military Science and Technology
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    • v.17 no.2
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    • pp.204-212
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    • 2014
  • The purpose of this paper is to investigate the effects of calibration rounds on the statistical distribution of the muzzle velocity in acceptance test of propelling charge. It is shown that the normal distribution fits best among statistical distributions from goodness-of fit test. The 3p-Weibull distribution is also acceptable because the shape of the probability density function curve is similar to that of normal distribution and it also has near zero skewness value. Muzzle velocities of test rounds uncompensated by calibration rounds showed high variation and had comparatively higher skewness. Because the skewness of normal distribution is defined to be zero, calibration rounds make the normality of data higher.

Discrimination of Arcing Faults from Normal Distribution Disturbances by Wave form Distortion Analysis

  • Kim, C. J.
    • Journal of Electrical Engineering and information Science
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    • v.1 no.2
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    • pp.52-57
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    • 1996
  • Detection of arcing high impedance faults has been a perplexing in the power distribution protection. Transient analysis of distribution disturbances for fault discrimination from other normal events is important for a secure protection of the power system. A simple parameter of wave form distortion quantification is used to analyze the behaviors of arcing faults and normal distribution disturbances. Theoretical perspectives of the transients were studied and actual disturbances were examined. From this investigation, a discrimination guideline based on the revised crest factor is developed. The discrimination method has a high potential to enhance the reliability and security for the distribution system protection.

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Self-adaptive Online Sequential Learning Radial Basis Function Classifier Using Multi-variable Normal Distribution Function

  • Dong, Keming;Kim, Hyoung-Joong;Suresh, Sundaram
    • 한국정보통신설비학회:학술대회논문집
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    • 2009.08a
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    • pp.382-386
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    • 2009
  • Online or sequential learning is one of the most basic and powerful method to train neuron network, and it has been widely used in disease detection, weather prediction and other realistic classification problem. At present, there are many algorithms in this area, such as MRAN, GAP-RBFN, OS-ELM, SVM and SMC-RBF. Among them, SMC-RBF has the best performance; it has less number of hidden neurons, and best efficiency. However, all the existing algorithms use signal normal distribution as kernel function, which means the output of the kernel function is same at the different direction. In this paper, we use multi-variable normal distribution as kernel function, and derive EKF learning formulas for multi-variable normal distribution kernel function. From the result of the experience, we can deduct that the proposed method has better efficiency performance, and not sensitive to the data sequence.

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Development of Probability Computation Program for Standard Normal Distribution (표준정규분포의 확률계산 프로그램 개발)

  • 송서일
    • Journal of Korean Society for Quality Management
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    • v.25 no.1
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    • pp.182-192
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    • 1997
  • The well-known standard normal distribution has been used within the limit of standard variable value of u=3.59. However, the probability values above the limit are not given in the literature. In this study, a probability computation program for standard normal distribution to u=5.99 with the proportional normal distribution a, pp.oximation suggested by Abramowitz and Stegun, Hastings is developed. The new standard normal distribution table developed by the program is presented and will be of help to estimate of probability values for testing and estimation of process mean value, lot acceptable probability, defective percentage of PPM unit of an out-of specification limit, process capability, test power of control charts, probability and statistics.

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A Study of Technology Trends for Effective Process Control under Non-Normal Distribution (비정규분포하에서의 효과적 공정관리를 위한 기술체계동향 연구)

  • Kim, Jong-Gurl;Um, Sang-Joon;Kim, Young-Sub;Ko, Jae-Kyu
    • Proceedings of the Safety Management and Science Conference
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    • 2008.11a
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    • pp.599-610
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    • 2008
  • It is an important and urgent issue to improve process capability in quality control. Process capability refers to the uniformity of the process. The variability in the process is a measure of the uniformity of output. A simple, quantitative way to express process capability, the degree of variability from target in specification is defined by process capability index(PCI). Almost process capability indices are defined under normal distribution. However, these indices can not be applied to the process of non-normal distribution including reliability. We investigate current research on the process of non-normal distribution, and advanced method and technology for developing more reliable and efficient PCI. Finally we suggest the perspective for future study.

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Variable Sampling Inspection with Screening When Lot Quality Follows Mixed Normal Distribution

  • Suzuki, Yuichiro;Takemoto, Yasuhiko;Arizono, Ikuo
    • Industrial Engineering and Management Systems
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    • v.8 no.3
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    • pp.131-138
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    • 2009
  • The variable sampling inspection scheme with screening for the purpose of assuring the upper limit of maximum expected surplus loss after inspection has been proposed. In this inspection scheme, it has been assumed that a product lot consists of products manufactured through a single production line and lot quality characteristics follow a normal distribution. In the previous literature with respect to inspection schemes, it has been commonly assumed that lot quality characteristics obey a single normal distribution under the condition that all products are manufactured in the same condition. On the other hand, the production line is designed in order that the workload of respective processes becomes uniform from the viewpoint of line balancing. One of the solutions for the bottleneck process is to arrange the workshops in parallel. The lot quality characteristics from such a production line with the process consisting of some parallel workshops might not follow strictly the single normal distribution. Therefore, we expand an applicable scope of the above mentioned variable sampling inspection scheme with screening in this article. Concretely, we consider the variable sampling inspection with screening for the purpose of assuring the upper limit of average outgoing surplus quality loss in the production lots when the lot quality follows the mixed normal distribution.

A Study of Estimation Method for Auto-Regressive Model with Non-Normal Error and Its Prediction Accuracy (비정규 오차를 고려한 자기회귀모형의 추정법 및 예측성능에 관한 연구)

  • Lim, Bo Mi;Park, Cheong-Sool;Kim, Jun Seok;Kim, Sung-Shick;Baek, Jun-Geol
    • Journal of Korean Institute of Industrial Engineers
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    • v.39 no.2
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    • pp.109-118
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    • 2013
  • We propose a method for estimating coefficients of AR (autoregressive) model which named MLPAR (Maximum Likelihood of Pearson system for Auto-Regressive model). In the present method for estimating coefficients of AR model, there is an assumption that residual or error term of the model follows the normal distribution. In common cases, we can observe that the error of AR model does not follow the normal distribution. So the normal assumption will cause decreasing prediction accuracy of AR model. In the paper, we propose the MLPAR which does not assume the normal distribution of error term. The MLPAR estimates coefficients of auto-regressive model and distribution moments of residual by using pearson distribution system and maximum likelihood estimation. Comparing proposed method to auto-regressive model, results are shown to verify improved performance of the MLPAR in terms of prediction accuracy.