• Journal of Korean Society for Quality Management
• /
• v.45 no.2
• /
• pp.209-225
• /
• 2017

Purpose: Since traditional p chart is unable to deal with the variation of attribute data, this paper proposes a new attribute control chart for nonconforming proportions incorporating overdispersion with a beta-binomial model. Methods: Statistical theories for control chart developed under the beta-binomial model and a new approach using this control chart are presented Results: False alarm probabilities of p chart with the beta-binomial model are evaluated and demerits of p chart under overdispersion are discussed from three examples. Hence a concrete procedure for the proposed control chart is provided and illustrated with examples Conclusion: The proposed chart is more useful than traditional p chart, individual chart to treat observed proportions nonconforming as variable data and Laney p' chart.

• Journal of the Korean Statistical Society
• /
• v.21 no.2
• /
• pp.187-200
• /
• 1992

Samples are often found to be too heterogeneous to be explained by a one-parameter family of models in the sense that the implicit mean-variance relationship in such a family is violated by the data. This phenomenon is often called over-dispersion. The most frequently used method in dealing with over-dispersion is to mix a one-parameter family creating a two parameter marginal mixture family for the data. In this paper, we investigate performance of estimators such as maximum likelihood estimator, method of moment estimator, and maximum quasi-likelihood estimator in negative binomial and beta-binomial distribution. Simulations are done for various mean parameter and dispersion parameter in both distributions, and we conclude that the moment estimators are very superior in the sense of bias and asymptotic relative efficiency.

• Communications for Statistical Applications and Methods
• /
• v.31 no.3
• /
• pp.263-277
• /
• 2024

This paper proposes new parameterizations of the tilted beta binomial distribution, obtained from the combination of the binomial distribution and the tilted beta distribution, where the beta component of the mixture is parameterized as a function of their mean and variance. These new parameterized distributions include as particular cases the beta rectangular binomial and the beta binomial distributions. After that, we propose new linear regression models to deal with overdispersed binomial datasets. These new models are defined from the proposed new parameterization of the tilted beta binomial distribution, and assume regression structures for the mean and variance parameters. These new linear regression models are fitted by applying Bayesian methods and using the OpenBUGS software. The proposed regression models are fitted to a school absenteeism dataset and to the seeds germination rate according to the type seed and root.

• Journal of Korean Society of Transportation
• /
• v.17 no.5
• /
• pp.123-135
• /
• 1999

The rapid increase of Passenger cars which is caused by the discomfort of Public transit and the Preference of automobiles is the major factor of increasing traffic congestions in Seoul With the point that leading the automobilists to the Public transit can be the most important Policy to ease these traffic congestions, this study focuses on the behavioral aspects of company employees and university students and investigates factors influencing bus ridership. To be brief, by estimating bus ridership through count models, this study investigates factors which influence bus ridership and elicits Political suggestions which lead automobilists to Public transit. The Purpose in this study is the application of appropriate count data model. The count data models have been widely applied to the economic area from the middle of the 1980s and to transportation aspect mainly in the foreign countries from the latter half of the 1980s. Even though a few studies in this country employed count data model to count data. all of them were Poisson regression models without suitable tests for the importance of the model specification. In the end, as the result of statistical test, negative binomial regression model which is suitable for overdispersed data was found to be appropriate for the data of weekly bus ridership. To emphasize the importance of model specification, both of poisson regression model and negative binomial regression model were estimated and the results were compared.