• 제목/요약/키워드: mean and variance

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선형 캘리브레이션에서 베이지안 실험계획과 기존의 최적실험계획과의 효과비교 (Performance of a Bayesian Design Compared to Some Optimal Designs for Linear Calibration)

  • 김성철
    • 응용통계연구
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    • 제10권1호
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    • pp.69-84
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    • 1997
  • 선형 캘리브레이션 실험계획 문제에 대하여, 베이지안 의사결정론을 이용하여 평균제곱오차손실을 최소화한 Kim(1988, 1993)의 실험계획과 관련 문헌의 결과인 몇 가지 최적계획을 비교한다. 비교대상 실험계획으로서 고전적 추정량의 점근분산을 최소화하는 Buonaccorsi(1986)의 최적계획, 회귀분석 모형에서 $ M(x) = \sum x_i x_i '$의 함수를 최대화 또는 최소화하는 D-optimal 또는 A-optimal 계획, Hunter and Lamboy(1981)가 베이지안 추정량의 특성을 설명하기 위하여 그 논문에서 예로 들었던 실험계획을 고려한다. 서로 다른 기준에 의한 최적계획을 비교하기 위해서 우선 기대사후분산을 계산하여 비교하고 몇가지 사전분포에 대하여 몬테칼로 시뮬레이션을 통한 평균분산과 HPD 구간의 크기를 비교한다.

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다결정 대안을 갖는 생산공정에서 최적공정평균 및 스크리닝 한계선의 결정 (Determination of Optimum Process Mean and Screening Limits for Production Processes with Multi - Decision Alternatives)

  • 홍성훈;권혁무;김상부;이민구
    • 대한산업공학회지
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    • 제25권3호
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    • pp.336-341
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    • 1999
  • The problem of jointly determining the optimum process mean and screening limits for each market is considered in situations where there are several markets with different price/cost structures. The quality characteristic is assumed to be a normal distribution with unknown mean and known variance. A quadratic loss function is utilized for developing the economic model. Methods of finding the optimum process mean and screening limits are presented and a numerical example is given.

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Estimators Shrinking towards Projection Vector for Multivariate Normal Mean Vector under the Norm with a Known Interval

  • Baek, Hoh Yoo
    • 통합자연과학논문집
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    • 제11권3호
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    • pp.154-160
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    • 2018
  • Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-r{\geq}3)$, r = rank(K) with a projection matrix K under the quadratic loss, based on a sample $Y_1$, $Y_2$, ${\cdots}$, $Y_n$. In this paper a James-Stein type estimator with shrinkage form is given when it's variance distribution is specified and when the norm ${\parallel}{\theta}-K{\theta}{\parallel}$ is constrain, where K is an idempotent and symmetric matrix and rank(K) = r. It is characterized a minimal complete class of James-Stein type estimators in this case. And the subclass of James-Stein type estimators that dominate the sample mean is derived.

Lindley Type Estimators When the Norm is Restricted to an Interval

  • Baek, Hoh-Yoo;Lee, Jeong-Mi
    • Journal of the Korean Data and Information Science Society
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    • 제16권4호
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    • pp.1027-1039
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    • 2005
  • Consider the problem of estimating a $p{\times}1$ mean vector $\theta(p\geq4)$ under the quadratic loss, based on a sample $X_1$, $X_2$, $\cdots$, $X_n$. We find a Lindley type decision rule which shrinks the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $\parallel\;{\theta}-\bar{{\theta}}1\;{\parallel}$ is restricted to a known interval, where $bar{{\theta}}=\frac{1}{p}\;\sum\limits_{i=1}^{p}{\theta}_i$ and 1 is the column vector of ones. In this case, we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.

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Biochemical Indices of Vitamin E, Ascorbic Acid and Iron Status : Relation to Diet, Supplement Use and Other Lifestyle Variables in Urban and Rural (Amish) Populations

  • Ro, Hee-Kyung;Jean T. Snook;Elizabeth Prater
    • Preventive Nutrition and Food Science
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    • 제5권4호
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    • pp.205-212
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    • 2000
  • The relation of food and supplemental intake of iron, vitamin E and ascorbic acid and other lifestyle variables to packed cell volume (PCV) and serum vitamin levels was studied in urban and rural (71% Amish) communities. Subjects were interviewed (24-h dietary recalls) on three occasions over 18-months, and blood samples were taken (maximum observations = 442). Mean PCV was lower in rural males (43.3) than in urban males (45.4) despite higher man food iron intake (18.7 and 14.4 mg/day, respectively). Mean meal iron availability was higher at lunch and lower at breakfast and dinner for rural than for urban subjects. Smoking was the number one variable in males and females explaining variance in PCV. Supplemental vitamin E and ascorbate intakes explained the most variance in serum vitamin E and ascorbate levels, respectively. Serum vitamin E was also associated with supplemental ascorbate intake (r=0.29). Serum ascorbate was also associated with food ascorbate intake (r=0.28) and body weight (r=-0.24).

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임상실습 전 간호대학생의 올바른 손씻기와 실천에 대한 지각된 통제행위와 자기효능감의 영향 (Influences of Perceived Behavior Control and Self-efficacy on Proper Hand Cleansing and Hand Washing Practices among Pre-practicum Nursing Students)

  • 박경연
    • 기본간호학회지
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    • 제19권3호
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    • pp.313-321
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    • 2012
  • Purpose: The purpose of the study was to investigate hand washing practice and proper hand cleansing among first and second year nursing students who are prone to be exposed to nosocomial infections, and to identify the influence of perceived behavior control and self-efficacy on hand washing practices and proper hand cleansing. Method: Data for 91 students were collected from a nursing college in a metropolitan city in Korea. Data were analyzed using descriptive, t-test, one way ANOVA, Pearson correlation coefficient, and multiple regression with SPSS/WIN 19.0. Result: The mean score for hand washing practice was 38.35 out of a possible score of 48, and the mean sore for proper hand cleansing was 18.63 out of a possible score of 28. The significant factors affecting student hand washing practice were 'residential type' (p=.016), 'perceived behavior control' (p=.021), and 'self-efficacy' (p=.033) which explained 19.9% of the variance. The significant factors affecting proper hand cleansing by the students were 'perceived behavior control' (p<.001) and 'regular exercise' (p=.026) which explained 29.8% of the variance. Conclusion: These results indicate a need for education programs on hand washing including strategies to improve perceived behavior control and self-efficacy to promote more effective hand washing practices.

Lindley Type Estimation with Constrains on the Norm

  • Baek, Hoh-Yoo;Han, Kyou-Hwan
    • 호남수학학술지
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    • 제25권1호
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    • pp.95-115
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    • 2003
  • Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p{\geq}4)$ under the quadratic loss, based on a sample $X_1,\;{\cdots}X_n$. We find an optimal decision rule within the class of Lindley type decision rules which shrink the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $||{\theta}-{\bar{\theta}}1||$ is known, where ${\bar{\theta}}=(1/p)\sum_{i=1}^p{\theta}_i$ and 1 is the column vector of ones. When the norm is restricted to a known interval, typically no optimal Lindley type rule exists but we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.

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Detection of the Normal Population with the Largest Absolute Value of Mean

  • Kim, Woo-Chul;Jeong, Gyu-Jin
    • Journal of the Korean Statistical Society
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    • 제22권1호
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    • pp.71-81
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    • 1993
  • Among k independent normal populations with unknown means and a common unknown variance, the problem of detecting the population with the largest absolute value of mean is considered. This problem is formulated in a manner close to the framework of testing hypotheses, and the maximum error probability and the minimum power are considered. The power charts necessary to determine the sample size are provided. The problem of detecting the population with the smallest absolute value of mean is also considered.

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인공신경망을 이용한 로버스트설계에 관한 연구 (Robust Parameter Design Based on Back Propagation Neural Network)

  • ;김영진
    • 경영과학
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    • 제29권3호
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    • pp.81-89
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    • 2012
  • Since introduced by Vining and Myers in 1990, the concept of dual response approach based on response surface methodology has widely been investigated and adopted for the purpose of robust design. Separately estimating mean and variance responses, dual response approach may take advantages of optimization modeling for finding optimum settings of input factors. Explicitly assuming functional relationship between responses and input factors, however, it may not work well enough especially when the behavior of responses are poorly represented. A sufficient number of experimentations are required to improve the precision of estimations. This study proposes an alternative to dual response approach in which additional experiments are not required. An artificial neural network has been applied to model relationships between responses and input factors. Mean and variance responses correspond to output nodes while input factors are used for input nodes. Training, validating, and testing a neural network with empirical process data, an artificial data based on the neural network may be generated and used to estimate response functions without performing real experimentations. A drug formulation example from pharmaceutical industry has been investigated to demonstrate the procedures and applicability of the proposed approach.

Characterization of the Spatial Variability of Paper Formation Using a Continuous Wavelet Transform

  • Keller, D.Steven;Luner, Philip;Pawlak, Joel J.
    • 펄프종이기술
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    • 제32권5호
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    • pp.14-25
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    • 2000
  • In this investigation, a wavelet transform analysis was used to decompose beta-radiographic formation images into spectral and spatial components. Conventional formation analysis may use spectral analysis, based on Fourier transformation or variance vs. zone size, to describe the grammage distribution of features such as flocs, streaks and mean fiber orientation. However, these methods have limited utility for the analysis of statistically stationary data sets where variance is not uniform with position, e.g. paper machine CD profiles (especially those that contain streaks). A continuous wavelet transform was used to analyze formation data arrays obtained from radiographic imaging of handsheets and cross machine paper samples. The response of the analytical method to grammage, floc size distribution, mean fiber orientation an sensitivity to feature localization were assessed. From wavelet analysis, the change in scale of grammage variation as a function of position was used to demonstrate regular and isolated differences in the formed structure.

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