• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.485-493
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• 2011

The proportional likelihood ratio order is an extension of the likelihood ratio order for the non-negative absolutely continuous random variables. In addition, the Lindley distribution has been over looked as a mixture of two exponential distributions due to the popularity of the exponential distribution. In this paper, we first recalled the above concepts and then obtained various properties of the Lindley distribution due to the proportional likelihood ratio order. These results are more general than the likelihood ratio ordering aspects related to this distribution. Finally, we discussed the proportional likelihood ratio ordering in view of the weighted version of the Lindley distribution.

• School Mathematics
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• v.19 no.2
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• pp.229-248
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• 2017

This study investigated the factors that should be considered when teaching proportional expression and proportional distribution through literature review. Based on these results, we analyzed and compared Korean and foreign mathematics textbooks on proportional expression and proportional distribution longitudinally and horizontally to search for desirable methods of organizing the unit of proportional expression and proportional distribution in mathematics textbooks. For longitudinal analysis, we took the mathematics textbooks according to the national curriculum since the 5th one. For horizontal analysis, we selected the mathematics textbooks of Japan, Singapore, and China. In each textbook, the contents and the order in relation to proportional expression and proportional distribution, the definitions of terminology, and the contexts and the visual representations for introducing related concepts are selected as the analysis framework. The results of analysis revealed many characteristics and the differences in ways of dealing contents about proportional expression and proportional distribution. Based on these results, we suggested some implications for writing the unit of proportional expression and proportional distribution in elementary mathematics textbooks.

• Journal of Environmental Science International
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• v.22 no.12
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• pp.1599-1610
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• 2013

In order to verify the healing effect in the variety of effects according to fountain type, anion which is the representatives factor of healing, as the center of case studies which in Gwanghwamun(Ground fountain), Cheonggyecheon(Waterfall) and Myeongdong(Formative fountain). According to fountain type, the anion distribution as follow, figures typically$ 15,721{\pm}419ea/cm^3$, Formative fountain $40,190{\pm}788ea/cm^3$, Waterfall $4.480{\pm}290ea/cm^3$ and ground fountain $2.492{\pm}180ea/cm^3$. It is usually exceed to the distribution in natural green, which is $1070{\sim}2100ea/cm^3$. The interrelation between air temperature, relative humidity, wind speed and relative humidity, and wind speed is that, the relative humidity is directly proportional to wind speed and inversely proportional to temperature. As the temperature goes up, the distribution of anion goes down. And as the wind speed and relative humidity goes up, the distribution of anion decrease sharply. The result of interrelation between fountain type and the anion distribution is that, the distance of water falling is directly proportional to the anion distribution in the formative fountain and inversely proportional in the ground fountain. And the distribution of anion is largest in formative fountain. The distribution of anion in ground fountain is lower than in formative fountain, but it is far more than in natural greenery. And as the distance from fountain increase, the distribution of anion goes down.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.57-79
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• 2022

Current mathematics It is necessary to ensure that ratio and proportion concept is not distorted or broken while being treated as if they were easy to teach and learn in school. Therefore, the purpose of this study is to analyze the activities presented in the textbook. Based on prior work, this study reinterpreted the proportional reasoning task from the proportional perspective of Beckmann and Izsak(2015) to the multiplicative structure of Vergnaud(1996) in four ways. This compared how they interpreted the multiplicative structure and relationships between two measurement spaces of ratio and rate units and proportional expression and proportional distribution units presented in the revised textbooks of 2007, 2009, and 2015 curriculum. First, the study found that the proportional reasoning task presented in the ratio and rate section varied by increasing both the ratio structure type and the proportional reasoning activity during the 2009 curriculum, but simplified the content by decreasing both the percentage structure type and the proportional reasoning activity. In addition, during the 2015 curriculum, the content was simplified by decreasing both the type of multiplicative structure of ratio and rate and the type of proportional reasoning, but both the type of multiplicative structure of percentage and the content varied. Second, the study found that, the proportional reasoning task presented in the proportional expression and proportional distribute sections was similar to the previous one, as both the type of multiplicative structure and the type of proportional reasoning strategy increased during the 2009 curriculum. In addition, during the 2015 curriculum, both the type of multiplicative structure and the activity of proportional reasoning increased, but the proportional distribution were similar to the previous one as there was no significant change in the type of multiplicative structure and proportional reasoning. Therefore, teachers need to make efforts to analyze the multiplicative structure and proportional reasoning strategies of the activities presented in the textbook and reconstruct them according to the concepts to teach them so that students can experience proportional reasoning in various situations.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.527-540
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• 2010

Rule-based classification analysis is widely used for massive datamining because it is easy to understand and its algorithm is uncomplicated. In this classification analysis, majority vote of rules or weighted combination of rules using their supports are frequently used in order to combine rules. We propose a method to combine rules by using the multinomial distribution in this paper. Iterative proportional fitting algorithm is used to estimate the multinomial distribution which maximizes entropy constrained on rules' support. Simulation experiments show that this method can compete with other well known classification models in the case of two similar populations.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.27 no.2
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• pp.102-113
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• 2004

This paper addresses the transportation planning that is based on genetic algorithm for determining transportation time and transportation amount of minimizing cost of distribution system. The vehicle routing of minimizing the transportation distance of vehicle is determined. A distribution system is consisted of a distribution center and many retailers. The model is assumed that the time horizon is discrete and finite, and the demand of retailers is dynamic and deterministic. Products are transported from distribution center to retailers according to transportation planning. Cost factors are the transportation cost and the inventory cost, which transportation cost is proportional to transportation distance of vehicle when products are transported from distribution center to retailers, and inventory cost is proportional to inventory amounts of retailers. Transportation time to retailers is represented as a genetic string. The encoding of the solutions into binary strings is presented, as well as the genetic operators used by the algorithm. A mathematical model is developed. Genetic algorithm procedure is suggested, and a illustrative example is shown to explain the procedure.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.27 no.4
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• pp.23-32
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• 2004

This paper addresses a model for the transportation planning that determines the transportation cycle time and the vehicle size to minimize the cost in a distribution system. The vehicle routing to minimize the transportation distance of the vehicles is also determined. A distribution system is consisted of a distribution center and many retailers. Products are transported from distribution center to retailers according to transportation planning. A model is assumed that the time horizon is continuous and infinite, and the demand of retailers is constant and deterministic. Cost factors are the transportation cost and the inventory cost, which the transportation cost is proportional to the transportation distance of vehicle when products are transported from distribution center to retailers, and the inventory cost is proportional to inventory amounts of retailers. A transportation cycle time and a vehicle size are selected among respective finite alternatives. The problem is analyzed, and a illustrative example is shown.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.509-518
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• 2002

This paper is concerned with semiparametric Bayesian analysis of the proportional intensity regression model of the Poisson process for multiple event time data. A nonparametric prior distribution is put on the baseline cumulative intensity function and a usual parametric prior distribution is given to the regression parameter. Also we allow heterogeneity among the intensity processes in different subjects by using unobserved random frailty components. Gibbs sampling approach with the Metropolis-Hastings algorithm is used to explore the posterior distributions. Finally, the results are applied to a real data set.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.793-800
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• 2023

In this paper, we propose a generalization of Lindley distribution (GLD) via a special structure that is concern with progressively Type-II right censoring and time failure data. We study the modern properties that we have built by such combination, for example, survival function, hazard function, moments, and estimation by non-Bayesian methods. Application on some selected data related to Lindley distribution (LD) and (ED) have been employed to find out the best distribution that can fit data comparing with the GLD.

• Journal of Environmental Health Sciences
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• v.47 no.4
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• pp.303-309
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• 2021

Background: Humidifier disinfectant is a biocidal product used in the water tanks of humidifiers to prevent the growth of microorganisms. Although there are a huge number of cases of reported humidifier disinfectant-related health effects across the entire Korean population, their numbers are distributed differently depending on the region. Objectives: This study aimed to investigate the regional distribution of enrollment cases who reported humidifier disinfectant-related health effects. Methods: This study used data on 6,240 subjects who experienced humidifier disinfectant-related health effects and who enrolled their cases which is conducted by the Korea Ministry of Environment. We examined the regional distribution of the enrolled cases based on sixteen administrative divisions and assessed the: 1) crude number; 2) proportional rate; and 3) age-standardized proportional rate of enrollment by region. Results: When we examined the crude number of enrollments by region, the highest number were in Gyeonggi-do Province (n=1,896), followed in order by Seoul (n=1,405), Incheon (n=436) Busan, Daegu, Gyeongsangnam-do Province, Daejeon, Chungcheongnam-do Province, Gyeongsangbuk-do Province, Jeollabuk-do Province, Gwangju, Chungcheongbuk-do Province, Gangwon-do Province, Jeollanam-do Province, Ulsan, and Jeju-do. When we examined proportional rate of the regional enrollment (cases per 100,000 population), Daejeon (n=16.2) was the region with the highest rate, followed in order by Gyeonggi-do Province (n=16.1), Incheon-do Province (n=15.9), Seoul, Daegu, Gwangju, Jeollabuk-do Province, Chungcheongnam-do Province, Busan, Chungcheongbuk-do Province, Gangwon-do Province, Gyeongsanbuk-do Province, Gyeongsangnam-do Province, Ulsan, Jeju-do, and Jeollanam-do Province, which is inconsistent with the order in terms of crude numbers. However, when we examined the age-standardized proportional rate of regional enrollment (cases per 100,000 population), their ranked distribution is consistent with the crude rate. Conclusions: This study observed that the regional distribution of the enrolled cases who reported humidifier disinfectant-related health effects is inconsistent with the regional distribution of the proportional rate of enrollment cases, which may be caused in part by the volume of the inherent population of each region.