• Communications for Statistical Applications and Methods
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• 제24권4호
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• pp.325-337
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• 2017

In this paper, we proposed a new long-term lifetime distribution with four parameters inserted in a risk competitive scenario with decreasing, increasing and unimodal hazard rate functions, namely the Weibull-Poisson long-term distribution. This new distribution arises from a scenario of competitive latent risk, in which the lifetime associated to the particular risk is not observable, and where only the minimum lifetime value among all risks is noticed in a long-term context. However, it can also be used in any other situation as long as it fits the data well. The Weibull-Poisson long-term distribution is presented as a particular case for the new exponential-Poisson long-term distribution and Weibull long-term distribution. The properties of the proposed distribution were discussed, including its probability density, survival and hazard functions and explicit algebraic formulas for its order statistics. Assuming censored data, we considered the maximum likelihood approach for parameter estimation. For different parameter settings, sample sizes, and censoring percentages various simulation studies were performed to study the mean square error of the maximum likelihood estimative, and compare the performance of the model proposed with the particular cases. The selection criteria Akaike information criterion, Bayesian information criterion, and likelihood ratio test were used for the model selection. The relevance of the approach was illustrated on two real datasets of where the new model was compared with its particular cases observing its potential and competitiveness.

• Communications for Statistical Applications and Methods
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• 제26권3호
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• pp.325-336
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• 2019

In this article we extend the discrete Weibull regression model in the presence of missing data. Discrete Weibull regression models can be adapted to various type of dispersion data however, it is not widely used. Recently Yoo (Journal of the Korean Data and Information Science Society, 30, 11-22, 2019) adapted the discrete Weibull regression model using single imputation. We extend their studies by using multiple imputation also with several various settings and compare the results. The purpose of this study is to address the merit of using multiple imputation in the presence of missing data in discrete count data. We analyzed the seventh Korean National Health and Nutrition Examination Survey (KNHANES VII), from 2016 to assess the factors influencing the variable, 1 month hospital stay, and we compared the results using discrete Weibull regression model with those of Poisson, negative Binomial and zero-inflated Poisson regression models, which are widely used in count data analyses. The results showed that the discrete Weibull regression model using multiple imputation provided the best fit. We also performed simulation studies to show the accuracy of the discrete Weibull regression using multiple imputation given both under- and over-dispersed distribution, as well as varying missing rates and sample size. Sensitivity analysis showed the influence of mis-specification and the robustness of the discrete Weibull model. Using imputation with discrete Weibull regression to analyze discrete data will increase explanatory power and is widely applicable to various types of dispersion data with a unified model.

• 한국산학기술학회논문지
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• 제10권8호
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• pp.1903-1910
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• 2009

본 연구에서는 소프트웨어 제품을 개발하여 테스팅을 거친 후 사용자에게 인도하는 시기를 결정하는 방출문제에 대하여 연구하였다. 인도시기에 관한 모형은 무한 고장수에 의존하는 비동질적인 포아송 과정을 적용하였다. 이러한 포아송 과정은 소프트웨어의 결함을 제거하거나 수정 작업 중에도 새로운 결함이 발생될 가능성을 반영하는 모형이다. 고장발생 수명분포는 여러 분포들을 적합시키는데 효율적인 특성을 가진 와이블분포를 이용하였다. 따라서 소프트웨어 요구 신뢰도를 만족시키고 소프트웨어 개발 및 유지 총비용을 최소화시키는 방출시간이 최적 소프트웨어 방출 정책이 된다. 본 논문의 수치적인 예에서는 고장 간격 시간 자료를 적용하고 모수추정 방법은 최우추정법과 추세분석을 통하여 자료의 효율성을 입증한 후 최적 방출시기를 추정하였다.

• 산업경영시스템학회지
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• 제11권17호
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• pp.67-80
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• 1988

This study is concerned with the comparison of two time homogeneous Poisson processes. Traditionally, the methods of testing equality of Poisson processes were based on the binomial distribution or its normal approximations. The sampling plans used in these methods are to observe the processes concurrently over a predetermined time interval, possibly different for each process. However, when the values of the intensities of the processes are small, inverse type sampling plans are more appropriate since there may be cases where only a few or even no events are observed in the predetermined time interval. This study considers 9 inverse type sampling plans for the comparison of two Poisson processes. For each sampling plans considered, critical regions and the design parameters of the sampling plan are determined to guarantee the significance level and the power at some values of the alternative hypothesis. The Problem of comparing of two Weibull processes are also considered.

• Communications for Statistical Applications and Methods
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• 제31권1호
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• pp.55-64
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• 2024

In this study, we consider the sample size determination problem for clustered count data with many zeros. In general, zero-inflated Poisson and binomial models are commonly used for zero-inflated data; however, in real data the assumptions that should be satisfied when using each model might be violated. We calculate the required sample size based on a discrete Weibull regression model that can handle both underdispersed and overdispersed data types. We use the Monte Carlo simulation to compute the required sample size. With our proposed method, a unified model with a low failure risk can be used to cope with the dispersed data type and handle data with many zeros, which appear in groups or clusters sharing a common variation source. A simulation study shows that our proposed method provides accurate results, revealing that the sample size is affected by the distribution skewness, covariance structure of covariates, and amount of zeros. We apply our method to the pancreas disorder length of the stay data collected from Western Australia.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.1017-1026
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• 2005

We consider the problem of modeling count data where the observation period is determined by the survival time of the individual under study. We assume random effects or frailty model to allow for a possible association between the death times and the counts. We assume that, given a random effect, the death times follow a Weibull distribution with a rate that depends on some covariates. For the counts, given the random effect, a Poisson process is assumed with the intensity depending on time and the covariates. A gamma model is assumed for the random effect. Maximum likelihood estimators of the model parameters are obtained. The model is applied to data set of patients with breast cancer who received a bone marrow transplant. A model for the time to death and the number of supportive transfusions a patient received is constructed and consequences of the model are examined.

• 한국식품위생안전성학회지
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• 제19권1호
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• pp.19-24
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• 2004

미생물 위해성 평가의 용량-반응 모델은 생물학적 모델과 경험적 모델로 나눌 수 있다. 생물학적 모델은 미생물의 분포형태, 미생물에 대한 숙주의 감수성, 감염을 일으킬 수 있는 미생물 수에 대한 가정을 바탕으로 성립된 모델로서, 대표적으로 Exponential model과 $\beta$-Poisson model이 있다. 경험적 모델은 주로 화학물질의 독성을 나타내는데 이용되어 온 모델로, Weibull-Gamma model등이 있다. 여러 용량-반응 모델 중에서 실험 데이터에 적합한 모델을 걱정하는 데에는 deviance function(Y)을 이용하며, 현재 일부 식중독균에 대해서는 사람과 실험동물에서의 용량-반응 모델이 연구되어 있다.

• International Journal of Reliability and Applications
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• 제2권3호
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• pp.199-207
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• 2001

The failure rate functions between successive failures are of concatenated form. We allow the parameters of failure rate function change after a certain failure and its fixing. We confine out attention to a model wherein the interfailure times are described by its failure rate function. We suggest an adaptive failure rate function with a change-point under the assumption that interfailure times are record value statistics from a Weibull distribution. The proposed model will be applied through a practical example of software failure data.

• 디지털산업정보학회논문지
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• 제6권2호
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• pp.183-191
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• 2010

Decision problem called an optimal release policies, after testing a software system in development phase and transfer it to the user, is studied. The applied model of release time exploited infinite non-homogeneous Poisson process. This infinite non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The failure life-cycle distribution used mixture which has various intensity, if the system is complicated. Thus, software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time.

• Journal of Preventive Medicine and Public Health
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• 제35권1호
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• pp.65-71
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• 2002

Objective : To estimate the status of HIV infection and AIDS incidence using a back-calculation model in Korea. Methods : Back-calculation is a method for estimating the past infection rate using AIDS incidence data. The method has been useful for obtaining short-term projections of AIDS incidence and estimating previous HIV prevalence. If the density of the incubation periods is known, together with the AIDS incidence, we can estimate historical HIV infections and forecast AIDS incidence in any time period up to time t. In this paper, we estimated the number of HIV infections and AIDS incidence according to the distribution of various incubation periods Results : The cumulative numbers of HIV infection from 1991 to 1996 were $708{\sim}1,426$ in Weibull distribution and $918{\sim}1,980$ in Gamma distribution. The projected AIDS incidence in 1997 was $16{\sim}25$ in Weibull distribution and $13{\sim}26$ in Gamma distribution. Conclusions : The estimated cumulative HIV infections from 1991 to 1996 were $1.4{\sim}4.0$ times more than notified cumulative HIV infections. Additionally, the projected AIDS incidence in 1997 was less than the notified AIDS cases. The reason for this underestimation derives from the very low level of HIV prevalence in Korea, further research is required for the distribution of the incubation period of HIV infection in Korea, particularly for the effects of combination treatments.