• Title/Summary/Keyword: i.i.d. random variables

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A Note on the Optimum Character of One-Sided Sequential Probability Ratio Tests

  • Abel, Volker
    • Journal of the Korean Operations Research and Management Science Society
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    • v.9 no.2
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    • pp.23-27
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    • 1984
  • We Observe a sequence of i. i. d random variables with density f or g. Only if g is true we should stop the process. Hence. the testing problem is completely described by a stopping time. Among all stopping times with error probability of first kind not exceeding a given bound, the one-sided sequential probability ratio test has smallest expected sample size if g is true. Moreover, the generalized one-sided SPRT has smallest expected sample size for g in the class of stopping times with expected sample size under f not falling below a given bound.

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Feasibility Study on Sampling Ocean Meteorological Data using Stratified Method (층화추출법에 의한 해양기상환경의 표본추출 타당성 연구)

  • Han, Song-I;Cho, Yong-Jin
    • Journal of Ocean Engineering and Technology
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    • v.28 no.3
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    • pp.254-259
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    • 2014
  • The infrared signature of a ship is largely influenced by the ocean environment of the operating area, which has been known to cause large changes in the signature. As a result, the weather condition has to be clearly set for an analysis of the infrared signatures. It is necessary to analyze meteorological data for all the oceans where the ship is supposed to be operated. This is impossibly costly and time consuming because of the huge size of the data. Therefore, the creation of a standard environmental variable for an infrared signature research is necessary. In this study, we compared and analyzed sampling methods to represent ocean data close to the Korean peninsula. In order to perform this research, we collected ocean meteorological records from KMA (Korea Meteorological Administration), and sampled these in numerous ways considering five variables that are known to affect the infrared signature. Specifically, a simple random sampling method for all the data and 1-D, 2-D, and 3-D stratified sampling methods were compared and analyzed by considering the mean square errors for each method.

CHARACTERIZATIONS BASED ON THE INDEPENDENCE OF THE EXPONENTIAL AND PARETO DISTRIBUTIONS BY RECORD VALUES

  • LEE MIN-YOUNG;CHANG SE-KYUNG
    • Journal of applied mathematics & informatics
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    • v.18 no.1_2
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    • pp.497-503
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    • 2005
  • This paper presents characterizations on the independence of the exponential and Pareto distributions by record values. Let ${X_{n},\;n {\ge1}$ be a sequence of independent and identically distributed(i.i.d) random variables with a continuous cumulative distribution function(cdf) F(x) and probability density function(pdf) f(x). $Let{\;}Y_{n} = max{X_1, X_2, \ldots, X_n}$ for n \ge 1. We say $X_{j}$ is an upper record value of ${X_{n},{\;}n\ge 1}, if Y_{j} > Y_{j-1}, j > 1$. The indices at which the upper record values occur are given by the record times {u(n)}, n \ge 1, where u(n) = $min{j|j > u(n-1), X_{j} > X_{u(n-1)}, n \ge 2}$ and u(l) = 1. Then F(x) = $1 - e^{-\frac{x}{a}}$, x > 0, ${\sigma} > 0$ if and only if $\frac {X_u(_n)}{X_u(_{n+1})} and X_u(_{n+1}), n \ge 1$, are independent. Also F(x) = $1 - x^{-\theta}, x > 1, {\theta} > 0$ if and only if $\frac {X_u(_{n+1})}{X_u(_n)}{\;}and{\;} X_{u(n)},{\;} n {\ge} 1$, are independent.

The Optimization Of SS-Type Deflection Yoke By Using Genetic Algorithm (유전 알고리즘을 이용한 SS형 편향코일의 형상 최적화)

  • Joo, K.J.;Yoon, I.G.;Kang, B.H.;Joe, M.C.;Hahn, S.Y.;Lee, H.B.
    • Proceedings of the KIEE Conference
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    • 1993.07b
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    • pp.971-973
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    • 1993
  • Deflection Yoke(the following, DY) is the important electric device of CRT which deflects R, G, B beans influencing magnetic field produced by yoke coils. Recently, DY is designed to the saddle/saddle type of coils, being proposed for high-definite and high-efficient CRT. This paper presents the optimization of pin-sectioned saddle coil's shape for minimizing gap between desired and practical deflections of electron beams by using Genetic Algorithm. Evolution Startegy is utilized in this paper, since evolution strategy is a kind of genetic algorithms finding the optimized values by choicing the better generation with comparing the parents and their children. Here, the children are generated by only mutations from the normal random variables. Evolution strategy has shown better powerful converge rate than the other genetic algorithms becuase of using only the mutation-operator.

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Development of NASTRAN-based Optimization Framework for Vibration Optimum Design of Ship Structure. (선박 구조물의 진동 최적설계를 위한 NASTRAN 기반 최적화 프레임웍의 제안)

  • Kong, Y.M.;Choi, S.H.;Chae, S.I.;Song, J.D.;Kim, Y.H.;Yang, B.S.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.11 s.104
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    • pp.1223-1231
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    • 2005
  • Recently, the issue of ship nitration due to the large scale, high speed and lightweight of ship is emerging. For pleasantness in the cabin, shipbuilders are asked for strict vibration criteria and the degree of nitration level at a deckhouse became an important condition for taking order from customers. This study proposes a new optimization framework that is NASTRAN external call type optimization method (OptShip) and applies to an optimum design to decrease the nitration level of a deckhouse. The merits of this method are capable of using of global searching method and selecting of various objective function and design variables. The global optimization algorithms used here are random tabu search method which has fast converging speed and searches various size domains and genetic algorithm which searches multi-point solutions and has a good search capability in a complex space. By adapting OptShip to full-scale model, the validity of the suggested method was investigated.

Production responses of Holstein dairy cows when fed supplemental fat containing saturated free fatty acids: a meta-analysis

  • Hu, Wenping;Boerman, Jacquelyn P.;Aldrich, James M.
    • Asian-Australasian Journal of Animal Sciences
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    • v.30 no.8
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    • pp.1105-1116
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    • 2017
  • Objective: A meta-analysis was conducted to evaluate the effects of supplemental fat containing saturated free fatty acids (FA) on milk performance of Holstein dairy cows. Methods: A database was developed from 21 studies published between 1991 and 2016 that included 502 dairy cows and a total of 29 to 30 comparisons between dietary treatment and control without fat supplementation. Only saturated free FA (>80% of total FA) was considered as the supplemental fat. Concentration of the supplemental fat was not higher than 3.5% of diet dry matter (DM). Dairy cows were offered total mixed ration, and fed individually. Statistical analysis was conducted using random- or mixed-effects models with Metafor package in R. Results: Sub-group analysis showed that there were no differences in studies between randomized block design and Latin square/crossover design for dry matter intake (DMI) and milk production responses to the supplemental fat (all response variables, $p{\geq}0.344$). The supplemental fat across all studies improved milk yield, milk fat concentration and yield, and milk protein yield by 1.684 kg/d (p<0.001), 0.095 percent unit (p = 0.003), 0.072 kg/d (p<0.001), and 0.036 kg/d (p<0.001), respectively, but tended to decrease milk protein concentration (mean difference = -0.022 percent unit; p = 0.063) while DMI (mean difference = 0.061 kg/d; p = 0.768) remained unchanged. The assessment of heterogeneity suggested that no substantial heterogeneity occurred among all studies for DMI and milk production responses to the supplemental fat (all response variables, $I^2{\leq}24.1%$; $p{\geq}0.166$). Conclusion: The effects of saturated free FA were quantitatively evaluated. Higher milk production and yields of milk fat and protein, with DMI remaining unchanged, indicated that saturated free FA, supplemented at ${\leq}3.5%$ dietary DM from commercially available fat sources, likely improved the efficiency of milk production. Nevertheless, more studies are needed to assess the variation of production responses to different saturated free FA, either C16:0 or C18:0 alone, or in combination with potentially optimal ratio, when supplemented in dairy cow diets.

The Study of Correlation between Parent-Child Relationship, Birth Order, and Creavity (부모(父母)-자녀관계(子女關係) 및 출생순위(出生順位)와 창의성간(創意性間)의 상관관계(相關關係) 연구(硏究))

  • Kim, Young-Nam
    • Korean Journal of Child Studies
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    • v.1
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    • pp.28-39
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    • 1980
  • I. OBJECTIVES The aim of this study lies in examining following items: 1. Difference in creativity between boys and girls 2. Inter correlation of the sub-variables of creativity 3. Correlation between parent-child relationship and creativity 4. The relationship between creativity and number of siblings 5. Creativity and birth-order II. METHODS & PROCED URES 1. Instruments: Standardized Creativity Test and Parent-Child Relationship Test for children 2. Objects: 118 boys and 97 girls enrolled in primary schools in Seoul who were selected by random sampling 3. Procedure: (1) The data of the boy group and the girl group were analized by means of M,t, SD. (2)The relationships between creativity and the number of siblings as well as the relationship between creativity and birth order were analyzed by M. (3) Inter-correlations among the sub-factors of creativity were obtained in boys and girls. (4) Complex-correlations between creativity and parent child relationship were produced. III. RESULTS 1. There were no significant differences between boy and girl in creativity. 2. Inter correlation among the sub-factors of creativity Boy: The highest scores were obtained in fluidity, and adaptability, the lowest in originality and openness. Girl: The highest score were obtained in world scribbling and fluidity, the comparatively low were in originality and a match-problem. 3. Inter-correlation between creativity and parent-child relationship a. Father-son: The positive refusal type has the most significant relation and conflict type, discrepancy type, negative type in turn have significant inter-coorelations. b. Mother-son: Discrepancy type, conflict type, positive refusal type have high correlations, while negative refusal type, anticipation type, and anxiety show significance in 5% level. c. Father-daughter: Positive refusal type shows correlation of 5% level significance, while indulgence type shows negative correlation in 1% level significance. d. Mother-daughter: Discrepancy type shows 5% level significance, while indulgence type shows negative correlation in 1% level. 4. Concerning the number of siblings, it was found that, boys and girls alike, those grown among 3 or 5 showed most creativity. 5. Concerning the birth order, it was found that, boys and girls alike, the first child showed the most creativity, and the youngest showed the next to the most, while the middle showed the least creativity.

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Methods for Genetic Parameter Estimations of Carcass Weight, Longissimus Muscle Area and Marbling Score in Korean Cattle (한우의 도체중, 배장근단면적 및 근내지방도의 유전모수 추정방법)

  • Lee, D.H.
    • Journal of Animal Science and Technology
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    • v.46 no.4
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    • pp.509-516
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    • 2004
  • This study is to investigate the amount of biased estimates for heritability and genetic correlation according to data structure on marbling scores in Korean cattle. Breeding population with 5 generations were simulated by way of selection for carcass weight, Longissimus muscle area and latent values of marbling scores and random mating. Latent variables of marbling scores were categorized into five by the thresholds of 0, I, 2, and 3 SD(DSI) or seven by the thresholds of -2, -1, 0,1I, 2, and 3 SD(DS2). Variance components and genetic pararneters(Heritabilities and Genetic correlations) were estimated by restricted maximum likelihood on multivariate linear mixed animal models and by Gibbs sampling algorithms on multivariate threshold mixed animal models in DS1 and DS2. Simulation was performed for 10 replicates and averages and empirical standard deviation were calculated. Using REML, heritabilitis of marbling score were under-estimated as 0.315 and 0.462 on DS1 and DS2, respectively, with comparison of the pararneter(0.500). Otherwise, using Gibbs sampling in the multivariate threshold animal models, these estimates did not significantly differ to the parameter. Residual correlations of marbling score to other traits were reduced with comparing the parameters when using REML algorithm with assuming linear and normal distribution. This would be due to loss of information and therefore, reduced variation on marbling score. As concluding, genetic variation of marbling would be well defined if liability concepts were adopted on marbling score and implemented threshold mixed model on genetic parameter estimation in Korean cattle.

The Variation of Nutural Population of Pinus densiflora S. et Z. in Korea -Change of variance due to number of family as sample size to affirm the population and family variations- (소나무 천연집단(天然集團)의 변이(變異)에 관(關)한 연구(硏究)(IV) -집단간(集團間) 및 가계간분산(家系間分散) 추정(推定)에 영향하는 가계수(家系數)에 대하여-)

  • Yim, Kyong Bin;Kwon, Ki Won;Lee, Kyong Jae
    • Journal of Korean Society of Forest Science
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    • v.35 no.1
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    • pp.39-46
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    • 1977
  • In the analysis of variance between population and between individual trees (families), the fluctuation of values of variances due to sample size, (number of family) was analysed by two different designs, i.e. 2-level nested design with equal sample size and randomized complete block design. The variables were seedling heights and root calipers of 1-0 and 1-1 seedlings of Pinus densiflora S. et Z. The details of three natural stands and their progeny characters were presented in previous reports. 1. In nested design analysis. increase of sample size resulted the decrease of F-values among families in general, however, the F-values among populations showen the increasing tendency. The smaller the sample size, the larger the F-values fluctuation was resulted in general. At the point of beyond sample size 10, however, the fluctuation become to be stabilized. The F-value fluctuation seemed to be more in the case of analysis with random sampling method than with sequentially accumulated sampling method. And also such a tendency was more obvious in smaller sample size than in large one. 2. In R.C.B.D. analysis, the sample size to affirm the family variation was smaller than that for population variations.

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A Time Series Graph based Convolutional Neural Network Model for Effective Input Variable Pattern Learning : Application to the Prediction of Stock Market (효과적인 입력변수 패턴 학습을 위한 시계열 그래프 기반 합성곱 신경망 모형: 주식시장 예측에의 응용)

  • Lee, Mo-Se;Ahn, Hyunchul
    • Journal of Intelligence and Information Systems
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    • v.24 no.1
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    • pp.167-181
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    • 2018
  • Over the past decade, deep learning has been in spotlight among various machine learning algorithms. In particular, CNN(Convolutional Neural Network), which is known as the effective solution for recognizing and classifying images or voices, has been popularly applied to classification and prediction problems. In this study, we investigate the way to apply CNN in business problem solving. Specifically, this study propose to apply CNN to stock market prediction, one of the most challenging tasks in the machine learning research. As mentioned, CNN has strength in interpreting images. Thus, the model proposed in this study adopts CNN as the binary classifier that predicts stock market direction (upward or downward) by using time series graphs as its inputs. That is, our proposal is to build a machine learning algorithm that mimics an experts called 'technical analysts' who examine the graph of past price movement, and predict future financial price movements. Our proposed model named 'CNN-FG(Convolutional Neural Network using Fluctuation Graph)' consists of five steps. In the first step, it divides the dataset into the intervals of 5 days. And then, it creates time series graphs for the divided dataset in step 2. The size of the image in which the graph is drawn is $40(pixels){\times}40(pixels)$, and the graph of each independent variable was drawn using different colors. In step 3, the model converts the images into the matrices. Each image is converted into the combination of three matrices in order to express the value of the color using R(red), G(green), and B(blue) scale. In the next step, it splits the dataset of the graph images into training and validation datasets. We used 80% of the total dataset as the training dataset, and the remaining 20% as the validation dataset. And then, CNN classifiers are trained using the images of training dataset in the final step. Regarding the parameters of CNN-FG, we adopted two convolution filters ($5{\times}5{\times}6$ and $5{\times}5{\times}9$) in the convolution layer. In the pooling layer, $2{\times}2$ max pooling filter was used. The numbers of the nodes in two hidden layers were set to, respectively, 900 and 32, and the number of the nodes in the output layer was set to 2(one is for the prediction of upward trend, and the other one is for downward trend). Activation functions for the convolution layer and the hidden layer were set to ReLU(Rectified Linear Unit), and one for the output layer set to Softmax function. To validate our model - CNN-FG, we applied it to the prediction of KOSPI200 for 2,026 days in eight years (from 2009 to 2016). To match the proportions of the two groups in the independent variable (i.e. tomorrow's stock market movement), we selected 1,950 samples by applying random sampling. Finally, we built the training dataset using 80% of the total dataset (1,560 samples), and the validation dataset using 20% (390 samples). The dependent variables of the experimental dataset included twelve technical indicators popularly been used in the previous studies. They include Stochastic %K, Stochastic %D, Momentum, ROC(rate of change), LW %R(Larry William's %R), A/D oscillator(accumulation/distribution oscillator), OSCP(price oscillator), CCI(commodity channel index), and so on. To confirm the superiority of CNN-FG, we compared its prediction accuracy with the ones of other classification models. Experimental results showed that CNN-FG outperforms LOGIT(logistic regression), ANN(artificial neural network), and SVM(support vector machine) with the statistical significance. These empirical results imply that converting time series business data into graphs and building CNN-based classification models using these graphs can be effective from the perspective of prediction accuracy. Thus, this paper sheds a light on how to apply deep learning techniques to the domain of business problem solving.