• Title/Summary/Keyword: chi-square distribution

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Detection of Random Effects in a Random Effects Model of a One-way Layout Contingency Table

  • Kim, Byung-Soo
    • Journal of the Korean Statistical Society
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    • v.13 no.1
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    • pp.1-19
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    • 1984
  • A random effects model of a one-way layout contingency table is developed using a Dirichlet-multinomial distribution. A test statistic, say $T_k$, is suggested for detecting Dirichlet-multinomial departure from a multinomial distribution. It is shown that the $T_k$ test is asymptotically superior to the classical chi-square test based on the asymptotic relative efficiency. This superiority is further evidenced by a Monte Carlo simulation.

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Tests For and Against a Positive Dependence Restriction in Two-Way Ordered Contingency Tables

  • Oh, Myongsik
    • Journal of the Korean Statistical Society
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    • v.27 no.2
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    • pp.205-220
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    • 1998
  • Dependence concepts for ordered two-way contingency tables have been of considerable interest. We consider a dependence concept which is less restrictive than likelihood ratio dependence and more restrictive than regression dependence. Maximum likelihood estimation of cell probability under this dependence restriction is studied. The likelihood ratio statistics for and against this dependence are proposed and their large sample distributions are derived. A real data is analyzed to illustrate the estimation and testing procedures.

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The Selection of Optimal Probability Distribution and Estimation for Design Hourly Factor in National Highway Roads (일반국도 설계시간계수의 적정 확률분포 선정 및 추정)

  • Jo, Jun-Han;Han, Jong-Hyeon;Kim, Seong-Ho;Lee, Byeong-Saeng
    • Journal of Korean Society of Transportation
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    • v.24 no.6 s.92
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    • pp.33-43
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    • 2006
  • This research is to the selection of optimal probability distribution as well as the estimation for design hourly factor in consideration of traffic characteristic, such as road function, lane number and AADT. To accomplish the objectives, we are applied to various probability distribution using traffic data that observed at permanent traffic count points in 2005. The parameters or the selected 14 probability distribution were estimated based on the method of maximum likelihood and the validity condition of the estimated parameter The goodness-of-fit test, such as chi-square test. was performed as well as the estimation of design hourly factor. As a result, An appropriate distributions of each case were selected : Pearson V for two lane of rural roads, LogLogistic for the four lane of rural roads, LogLogistic for the urban roads, Extreme value for recreation roads. And optimal K factor are as following : $0.1{\sim}0.2 $ for two lane of rural roads, $0.09{\sim}0.14$ for the four lane of rural roads. $0.07{\sim}0.13$ for the urban roads, $0.1{\sim}0.2$ for recreation roads.

Enhancing the Customer's Information-sharing Intention Through Omnichannel Strategies

  • Nguyen Thi Tuyet, NHUNG;Van Thanh-Truong, NGUYEN;Nguyen Tuong An, HUYNH;Bui Thanh, KHOA
    • Journal of Distribution Science
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    • v.21 no.3
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    • pp.83-92
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    • 2023
  • Purpose: An omnichannel strategy creates a consistent brand image and customer experience across all channels, making it easier for customers to interact with a business and share information. This research aimed to investigated the relationship between consumers' information-sharing intention and their omnichannel experiences. Research design, data, and methodology: Through an online survey conducted in Vietnam, the study obtained 915 responses. The study used Partial Least Square Structural Equation Modeling (PLS-SEM) to analyze research data and confirm proposed research hypotheses. Results: Research results indicated that information-sharing intention is affected by both online and offline customer experience, and at the same time, the study also confirmed that omnichannel's three characteristics (integration, individualization, interaction) positively impact on customer experience. Conclusions: From the research result, businesses may boost consumer trust and loyalty with the help of an omnichannel approach, which in turn increases customers' propensity to provide personally identifying information to the firm. One way to do this is to facilitate information exchange by delivering customized and relevant offers. Furthermore, companies show consumers the benefit of providing their data by utilizing it to enhance the customer experience.

Estimating Paddy Rice Evapotranspiration of 10-Year Return Period Drought Using Frequency Analysis (빈도 분석법을 이용한 논벼의 한발 기준 10년 빈도 작물 증발산량 산정)

  • Yoo, Seung-Hwan;Choi, Jin-Yong;Jang, Min-Won
    • Journal of The Korean Society of Agricultural Engineers
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    • v.49 no.3
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    • pp.11-20
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    • 2007
  • Estimation of crop consumptive use is a key term of agricultural water resource systems design and operation. The 10-year return period drought has special aspects as a reference period in design process of irrigation systems in terms of agricultural water demand analysis so that crop evapotranspiration (ETc) about the return period also has to be analyzed to assist understanding of crop water requirement of paddy rice. In this study, The ETc of 10-year return period drought was computed using frequency analysis by 54 meteorological stations. To find an optimal probability distribution, 8 types of probability distribution function were tested by three the goodness of fit tests including ${\chi}^2$(Chi-Square), K-S (Kolmogorov-Smirnov) and PPCC (Probability Plot Correlation Coefficient). Optimal probability distribution function was selected the 2-parameter Log-Normal (LN2) distribution function among 8 distribution functions. Using the two selected distribution functions, the ETc of 10-year return period drought was estimated for 54 meteorological stations and compared with prior study results suggested by other researchers.

Probability Models of W-CDMA Signals in Realistic Wideband Multipath Channels (광대역 다중경로 실측채널에서 W-CDMA 수신 신호의 화률 모델)

  • 오동진;이주석;이귀상;김철성
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.27 no.4B
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    • pp.308-315
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    • 2002
  • This paper proposes new probability models for wideband code division multiple access (W-CDMA) signals. The performance of a W-CDMA system is evaluated by calculating the average bit error rate(BER) which is derived from the probability distribution of the W-CDMA receiver output. If a probability model of the receiver output is available, the performance evaluation becomes much simpler and it enables diverse analyses of the system for channel coding and other purposes. In this paper, probability distributions of W-CDMA signals, more specifically those of the receiver output, are represented as Rayleigh and noncentral chi distribution, considering various bandwidths and channel environments. The adequacy of a probability model is verified by chi-square test of 1% significance level. The BER of the system obtained from the simulation results is compared to that obtained from the probability model to demonstrate the usefulness of the proposed models.

우리나라 주요지점에 있어서의 강우해석에 관한 수문통계학적 연구

  • 이원환
    • Water for future
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    • v.5 no.2
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    • pp.30-43
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    • 1972
  • The paper describes on the hydrologic analysis of point rainfall data of the three major areas, such as in Seoul, Pusan and Taegu. Scheme of the paper is analyzed five research cases. Contents of the analysis are carried out five kinds of transformed variables for determination of rainfall distribution types and two kinds of reliability tests on unusual(extraordinary) values each rainfall durations:short durations, long durations, long durations, monthly and yearly. Rainfall depth probability had been computed methods of hydrologic amounts analysis namely logarithmic transformations or Gumbel-Chow method and so on, but in this paper it is calculated log xi, n-square root transformations by using normal distribution function and normalization of rainfall distributions is examined graphical tests and $X^2-test$(chi-square test). Furthermore, rainfall depth probability is calculated taking into account the safty factors of project life of hydraulic structures. We think it is advanced contents that considering priceless experiences, the life of structures, conditions and more problems of planning engineers and designers, proposed rainfall amounts(proposed values) are presented charts or figures.

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Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data

  • Sharma, Vikas Kumar;Singh, Sanjay Kumar;Singh, Umesh
    • Communications for Statistical Applications and Methods
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    • v.24 no.3
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    • pp.193-209
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    • 2017
  • The power Lindley distribution with some of its properties is considered in this article. Maximum likelihood, least squares, maximum product spacings, and Bayes estimators are proposed to estimate all the unknown parameters of the power Lindley distribution. Lindley's approximation and Markov chain Monte Carlo techniques are utilized for Bayesian calculations since posterior distribution cannot be reduced to standard distribution. The performances of the proposed estimators are compared based on simulated samples. The waiting times of research articles to be accepted in statistical journals are fitted to the power Lindley distribution with other competing distributions. Chi-square statistic, Kolmogorov-Smirnov statistic, Akaike information criterion and Bayesian information criterion are used to access goodness-of-fit. It was found that the power Lindley distribution gives a better fit for the data than other distributions.

ON ESTIMATION OF NEGATIVE POLYA-EGGENBERGER DISTRIBUTION AND ITS APPLICATIONS

  • Hassan, Anwar;Bilal, Sheikh
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.2
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    • pp.81-95
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    • 2008
  • In this paper, the negative Polya-Eggenberger distribution has been introduced by compounding negative binomial distribution with beta distribution of I-kind which generates a number of univariate contagious or compound (or mixture of) distributions as its particular cases. The distribution is unimode, over dispersed and all of its positive and negative integer moments exist. The difference equation of the proposed model shows that it is a member of the Ord's family of distribution. Some of its interesting properties have been explored besides different methods of estimation been discussed. Finally, the parameters of the proposed model have been estimated by using a computer programme in R-software. Application of the proposed model to some data, available in the literature, has been given and its goodness of fit demonstrated.

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Derivation and utilization of probability distribution of credit card usage behavior (신용카드 이용행태의 확률분포 도출과 활용)

  • Lee, Chan-Kyung;Roh, Hyung-Bong
    • Journal of Korean Society for Quality Management
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    • v.46 no.1
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    • pp.95-112
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    • 2018
  • Purpose: To find out the appropriate probability distribution of credit card usage behavior by considering the relationship among income, expenditure and credit card usage amount. Such relationship is enabled by Korea's especially high penetration of credit card. Method: Goodness-of-fit test and effect size statistic W were used to identify the distribution of income and credit card usage amount. A simulation model is introduced to generate the credit card transactions on individual user level. Result: The three data sets for testing had either passed the chi-square test or showed low W values, meaning they follow the exponential distribution. And the exponential distribution turned out to fit the data sets well. The r values were very high. Conclusion: The credit card usage behavior, denoted as the counts of users by usage amount band, follows the exponential distribution. This distribution is easy to manipulate, has a variety of applications and generates important business implications.