• Journal of Korea Water Resources Association
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• v.49 no.6
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• pp.481-493
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• 2016

The statistical analysis to the torrential rainfall data that is defined as a rainfall amount more than 80 mm/day is performed with Daegu and Busan rainfall data which is collected during 384 months. The number of occurrence of the torrential rainfall events can be simulated usually using Poisson distribution. However, the Poisson distribution can be frequently failed to simulate the statistical characteristics of the observed value when the observed data is zero-inflated. Therefore, in this study, Generalized Poisson distribution (GPD), Zero-Inflated Poisson distribution (ZIP), Zero-Inflated Generalized Poisson distribution (ZIGP), and Bayesian ZIGP model were used to resolve the zero-inflated problem in the torrential rainfall data. Especially, in Bayesian ZIGP model, a informative prior distribution was used to increase the accuracy of that model. Finally, it was suggested that POI and GPD model should be discouraged to fit the frequency of the torrential rainfall data. Also, Bayesian ZIGP model using informative prior provided the most accurate results. Additionally, it was recommended that ZIP model could be alternative choice on the practical aspect since the Bayesian approach of this study was considerably complex.

• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.585-594
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• 2010

This study, investigates the effects of dispersion parameters between two response variables in zero-truncated bivariate generalized Poisson distributions. A Monte Carlo study shows that the zero-truncated bivariate Poisson and negative binomial models fit poorly wherein the zero-truncated bivariate count data has heterogeneous dispersion parameters on dependent variables. In addition, we derive the score test for testing the equality of the dispersion parameters and compare its efficiency with the likelihood ratio test.

• 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.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.311-325
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• 2022

For count responses, the situation of excess zeros often occurs in various research fields. Zero-inflated model is a common choice for modeling such count data. Bayesian inference for the zero-inflated model has long been recognized as a hard problem because the form of conditional posterior distribution is not in closed form. Recently, however, Pillow and Scott (2012) and Polson et al. (2013) proposed a Pólya-Gamma data-augmentation strategy for logistic and negative binomial models, facilitating Bayesian inference for the zero-inflated model. We apply Bayesian zero-inflated negative binomial regression model to longitudinal pharmaceutical data which have been previously analyzed by Min and Agresti (2005). To facilitate posterior sampling for longitudinal zero-inflated model, we use the Pólya-Gamma data-augmentation strategy.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.455-466
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• 2007

The zero-distribution of the Fourier integral $${\int}^{\infty}_{-{\infty}}\;Q(u)e^{p(u)+^{izu}du$$, where P is a polynomial with leading term $-u^{2m}(m\;{\geq}\;1)$ and Q an arbitrary polynomial, is described. To this end, an asymptotic formula for the integral is established by applying the saddle point method.

• The Korean Journal of Applied Statistics
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• v.22 no.4
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• pp.819-827
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• 2009

Kim et al. (2006) analyzed the donation data surveyed by Voluneteer 21 in year 2002 at South Korea using a Poisson regression based on the mixture of two Poissons and detected significant variables for affecting the number of donations. However, noting the large deviation between the predicted and the actual frequencies of zero, we developed in this note a Poisson regression model based on a distribution in which zero inflated Poisson was added to the mixture of two Poissons. Thus the population distribution is now a mixture of three Poissons in which one component is concentrated on zero mass. We used the EM algorithm for estimating the regression parameters and detected the same variables with Kim et al's for significantly affecting the response. However, we could estimate the proportion of the fixed zero group to be 0.201, which was the characteristic of this model. We also noted that among two significant variables, the income and the volunteer experience(yes, no), the second variable could be utilized as a strategric variable for promoting the donation.

• Journal of Korean Society on Water Environment
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• v.30 no.5
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• pp.524-531
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• 2014

Korea has been trying to manage water quality of rivers and lakes in many ways. Ministry of Environment is making continuous efforts of operation control improvement such as strengthening effluent standards in sewage treatment plants and expanding Tele-Monitoring System (TMS). However, evaluation method for operations of sewage treatment plants and establishment system of effluent standards are inadequate. The objective of this study is to evaluate for operations of sewage treatment plants using statistics technique such as frequency analysis, percentile, normal distribution analysis. We used the effluent data (BOD, COD, SS) collected at 299 plants in 2012. The values were very low by comparison with standards. The Data followed a normal distribution. We think that distribution characteristics are closely related with effluent standards, especially T-P and BOD. Statistics technique attempted in this study can be used to evaluate for operations of sewage treatment plants and assess the appropriateness of effluent standards based on TBEL(Technology-based effluent limitation). And, this technique can be used to figure out the overall level of plants, the status of each plant and the favorable treatment process for each item (BOD, COD etc.). Data acquired through this method can be used to improve facilities and operation techniques and decide on a sewerage policy.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.1
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• pp.19-25
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• 2010

Most faults are single-phase-to-ground fault in ungrounded system. The fault currents of single-phase-to-ground are much smaller than detection thresholds of measurement devices, so detecting single-phase-to-ground faults is difficult and important in ungrounded system. The protection coordination method using SGR(Selective Ground Relay) and OVGR(Overvoltage Ground Relay) is generally used in ungrounded system. But this method only detects fault line and it has the possibility of malfunction. This paper proposed to advanced protection coordination method in ungrounded system. The method just using zero-sequence current can detect fault line, fault phase, fault section at terminal device. The general protection method is used to back up protection. In the case study, the proposed method has been testified in demo system by Matlab/Simulink simulations.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.7
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• pp.1141-1149
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• 2008

Most faults are single-phase-to-ground fault in ungrounded system. The fault currents of single-phase-to-ground are much smaller than detection thresholds of measurement devices, so detecting single-phase-to-ground faults is difficult and important in ungrounded system. This paper proposed to a FI(Fault Indicator) generation algorithm in ungrounded system. The algorithm just using line-to-line voltage and zero-sequence current detects fault line, fault phase, fault section and FI(Fault Indicator) at terminal device, This paper also proposed to application plan for this algorithm. In the case study, the proposed algorithm has been testified in demo system by Matlab/Simulink simulations.

• Journal of Applied Reliability
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• v.14 no.1
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• pp.53-57
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• 2014

In the fields of reliability application, the most commonly used test methods for reliability demonstration are zero-failure acceptance tests since they require fewer test samples and less test time compared to other test methods that guarantee the same reliability with a given confidence level. For products with lognormal lifetime distribution, the value of scale parameter is usually assumed to be known in designing reliability demonstration tests. It is important to select correct values of scale parameters to guarantee the specified reliability with given confidence level exactly. The effect of using wrong values of scale parameters in designing reliability demonstration test for products with lognormal lifetime distribution is examined and selecting proper values of scale parameters for conservative reliability demonstration is discussed.