• Journal of Korea Water Resources Association
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• v.35 no.1
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• pp.109-124
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• 2002

This study is an effort to develop a stochastic model of precipitation series that preserves the pattern of occurrence of precipitation events throughout the year as well as several characteristics of the duration, amount, and intensity of precipitation events. In this study an event cluster model is used to describe the occurrence of precipitation events. A logarithmic negative mixture distribution is used to describe event duration and separation. The number of events within each cluster is also described by the Poisson cluster process. The duration of each event within a cluster and the separation of events within a single cluster are described by a logarithmic negative mixture distribution. The stochastic model for hourly precipitation occurrence process is fitted to historical precipitation data by estimating the model parameters. To allow for seasonal variations in the precipitation process, the model parameters are estimated separately for each month. an analysis of thirty-four years of historical and simulated hourly precipitation data for Seoul indicates that the stochastic model preserves many features of historical precipitation. The seasonal variations in number of precipitation events in each month for the historical and simulated data are also approximately identical. The marginal distributions for event characteristics for the historical and simulated data were similar. The conditional distributions for event characteristics for the historical and simulated data showed in general good agreement with each other.

• Proceedings of the Safety Management and Science Conference
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• 2010.11a
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• pp.551-557
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• 2010

The research proposes the hypergeometric, binomial and Poisson yield models for defective and defect. The paper also presents the hypothesis test, confidence interval and control charts for DPU(Defect Per Unit) and DPO(Defect Per Opportunity). Especially the study considers the analysis of compound Poisson yield models using various DOU density distributions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.153-160
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• 2008

A size-biased Poisson distribution is defined. Its characterization by using a recurrence relation for first order negative moment of the distribution is obtained. Different estimation methods for the parameter of the model are also discussed. R-Software has been used for making a comparison among the three different estimation methods.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.105-110
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• 1997

The distribution of staff in a hierachial organization has been studied in a variety of forms and models. Results here show that the promotion process follows a binomial distribution with parameters n and $\alpha=e^{-pt}$ and the recruitment process follows a poisson distribution with parameter $\lambda$. Futhermore, the mean time to promotion in the grade was estimated.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.729-744
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• 2021

In this paper we prove global existence and uniqueness of axisymmetric strong solutions for the three dimensional electro-hydrodynamic model based on the coupled Navier-Stokes-Poisson-Nernst-Planck system in the exterior of a cylinder. The key ingredient is that we use the axisymmetry of functions to derive the L^p interpolation inequalities, which allows us to establish all kinds of a priori estimates for the velocity field and charged particles via several cancellation laws.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.433-443
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• 2011

We consider a compound Poisson risk model in which the premiums may depend on the state of the surplus process. By using the overflow probability of the workload process in the corresponding M/G/1 queueing model, we obtain the probability that the ruin occurs before the surplus reaches a given large value in the risk model. We also examplify the ruin probability in case of exponential claims.

• Smart Media Journal
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• v.8 no.1
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• pp.82-91
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• 2019

This study provides the analysis and prediction of fruits diseases related to weather conditions (temperature, wind speed, solar power, rainfall and humidity) using Linear Model and Poisson Regression. The main goal of the research is to control the method of fruits diseases and also to prevent diseases using less agricultural pesticides. So, it is needed to predict the fruits diseases with weather data. Initially, fruit data is used to detect the fruit diseases. If diseases are found, we move to the next process and verify the condition of the fruits including their size. We identify the growth of fruit and evidence of diseases with Linear Model. Then, Poisson Regression used in this study to fit the model of fruits diseases with weather conditions as an input provides the predicted diseases as an output. Finally, the residuals plot, Q-Q plot and other plots help to validate the fitness of Linear Model and provide correlation between the actual and the predicted diseases as a result of the conducted experiment in this study.

• Communications for Statistical Applications and Methods
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• v.30 no.3
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• pp.291-309
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• 2023

Longitudinal count data has been widely collected in biomedical research, public health, and clinical trials. These repeated measurements over time on the same subjects need to account for an appropriate dependency. The Poisson regression model is the first choice to model the expected count of interest, however, this may not be an appropriate when data exhibit over-dispersion or under-dispersion. Recently, Conway-Maxwell-Poisson (CMP) distribution is popularly used as the distribution offers a flexibility to capture a wide range of dispersion in the data. In this article, we propose a Bayesian CMP regression model to accommodate over and under-dispersion in modeling longitudinal count data. Specifically, we develop a regression model with random intercept and slope to capture subject heterogeneity and estimate covariate effects to be different across subjects. We implement a Bayesian computation via Hamiltonian MCMC (HMCMC) algorithm for posterior sampling. We then compute Bayesian model assessment measures for model comparison. Simulation studies are conducted to assess the accuracy and effectiveness of our methodology. The usefulness of the proposed methodology is demonstrated by a well-known example of epilepsy data.

• Communications for Statistical Applications and Methods
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• v.25 no.2
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• pp.173-184
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• 2018

In medical or public health research, it is common to encounter clustered or longitudinal count data that exhibit excess zeros. For example, health care utilization data often have a multi-modal distribution with excess zeroes as well as a multilevel structure where patients are nested within physicians and hospitals. To analyze this type of data, zero-inflated count models with mixed effects have been developed where a count response variable is assumed to be distributed as a mixture of a Poisson or negative binomial and a distribution with a point mass of zeros that include random effects. However, no study has considered a situation where data are also censored due to the finite nature of the observation period or follow-up. In this paper, we present a weighted version of zero-inflated Poisson model with random effects accounting for variable individual follow-up times. We suggested two different types of weight function. The performance of the proposed model is evaluated and compared to a standard zero-inflated mixed model through simulation studies. This approach is then applied to Medicaid data analysis.

• Communications for Statistical Applications and Methods
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• v.30 no.3
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• pp.273-289
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• 2023

In this paper, we develop a new time series model for predicting IPO (initial public offering) data with non-negative integer value. The proposed model is based on integer-valued autoregressive (INAR) model with a Poisson thinning operator. Just as the heterogeneous autoregressive (HAR) model with daily, weekly and monthly averages in a form of cascade, the integer-valued heterogeneous autoregressive (INHAR) model is considered to reflect efficiently the long memory. The parameters of the INHAR model are estimated using the conditional least squares estimate and Yule-Walker estimate. Through simulations, bias and standard error are calculated to compare the performance of the estimates. Effects of model fitting to the Korea's IPO are evaluated using performance measures such as mean square error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) etc. The results show that INHAR model provides better performance than traditional INAR model. The empirical analysis of the Korea's IPO indicates that our proposed model is efficient in forecasting monthly IPO volumes.