• Communications for Statistical Applications and Methods
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• 제26권2호
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• pp.91-102
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• 2019

In this paper, we propose a new estimation method based on a weighted linear regression framework to obtain some estimators for unknown parameters in a two-parameter Rayleigh distribution under a progressive Type-II censoring scheme. We also provide unbiased estimators of the location parameter and scale parameter which have a nuisance parameter, and an estimator based on a pivotal quantity which does not depend on the other parameter. The proposed weighted least square estimator (WLSE) of the location parameter is not dependent on the scale parameter. In addition, the WLSE of the scale parameter is not dependent on the location parameter. The results are compared with the maximum likelihood method and pivot-based estimation method. The assessments and comparisons are done using Monte Carlo simulations and real data analysis. The simulation results show that the estimators ${\hat{\mu}}_u({\hat{\theta}}_p)$ and ${\hat{\theta}}_p({\hat{\mu}}_u)$ are superior to the other estimators in terms of the mean squared error (MSE) and bias.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.105-121
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• 2019

One of the main objective of manufacturing industries is to assess the capability performance of different processes. In this paper, we use the lifetime performance index $C_L$ as a criterion to measure larger-the-better type quality characteristic for evaluating the product performance. The lifetimes of products are assumed to follow a general class of inverted exponentiated distributions. We use maximum likelihood estimator to estimate the lifetime performance index under the assumption that data are progressive type I interval censored. We also obtain asymptotic distribution of this estimator. Based on this estimator, a new hypothesis testing procedure is developed with respect to a given lower specification limit. Finally, two numerical examples are discussed in support of the proposed testing procedure.

• 한국안전학회지
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• 제36권2호
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• pp.32-38
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• 2021

This paper suggests an approach to evaluate the reliability of an intelligent power module with information deficiency of prior distribution and the characteristics of censored data through Bayesian statistics. This approach used a prior distribution of Bayesian statistics using the lifetime information provided by the manufacturer and compared and evaluated diffuse prior (vague prior) distributions. To overcome the computational complexity of Bayesian posterior distribution, it was computed with Gibbs sampling in the Monte Carlo simulation method. As a result, the standard deviation of the prior distribution developed using simple information was smaller than that of the posterior distribution calculated with the diffuse prior. In addition, it showed excellent error characteristics on RMSE compared with the Kaplan-Meier method.

• Communications for Statistical Applications and Methods
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• 제29권6호
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• pp.665-677
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• 2022

This paper proposes a new estimation method based on the maximum product of spacings for estimating unknown parameters of the three-parameter Weibull distribution under a generalized Type-II progressive hybrid censoring scheme which guarantees a constant number of observations and an appropriate experiment duration. The proposed approach is appropriate for a situation where the maximum likelihood estimation is invalid, especially, when the shape parameter is less than unity. Furthermore, it presents the enhanced performance in terms of the bias through the Monte Carlo simulation. In particular, the superiority of this approach is revealed even under the condition where the maximum likelihood estimation satisfies the classical asymptotic properties. Finally, to illustrate the practical application of the proposed approach, the real data analysis is conducted, and the superiority of the proposed method is demonstrated through a simple goodness-of-fit test.

• 유통과학연구
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• 제15권10호
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• pp.41-50
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• 2017

Purpose - Online product review has become a crucial part of the online retailer's market performance for a wide range of products. This research aims to investigate how an individual reviewer's review frequency and timing affect her/his average attitude toward products. Research design, data, and methodology - To conduct reviewer-level analysis, this study uses 42,172 posted online review messages generated by 6,941 identified reviewers for 59 movies released in the South Korea from July 2015 to December 2015. This study adopts Tobit model specification to take into account the censored nature and the selection bias arising from the nature of J-shaped distribution of movie rating. Results - Our estimation results support that the negative impact of review frequency and timing on valence. Furthermore, review timing has an inverted-U relationship with the user's average valence and enhance the negative effect of review frequency. Conclusions - This study contributes to the growing literature on the understanding how eWOM is generated at the individual consumer level. On the basis of the main empirical findings, this study provides insights into building a recommendation system in online retail store based on the consumer's review history data - frequency, timing, and valence.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• 응용통계연구
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• 제8권2호
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• pp.109-119
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• 1995

두 모집단에서 임의로 관측중단도니 두 표본을 얻었을 때, 두 모집단의 분포가 같다는 가설을 검정하기 위한 카이제곱 검정방법이 제안되었다. 여기서 제안된 통계량은 대립가설이 두 모집단의 분포가 같지 않다는 양측가설일 때 쓰일 수 있다. 귀무가설이 사실일 때 제안된 통계량의 극한분포는 카이제곱 분포가 된다. 두 가지 형태의 카이제곱 검정통계량이 제안되었는데, 하나는 product-limit 추정치로부터 얻은 관측된 칸(cell) 확률의 차이들의 벡터의 이차형식으로 표현된 것이고, 다른 하나는 간단한 합의 모양으로 표현된 것이다. 두 형태의 검정통계량을 사용하여 암치료를 위한 화학요법 실험으로부터 얻은 자료를 분석하여 보았다.

• 응용통계연구
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• 제23권4호
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• pp.705-713
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• 2010

마이크로어레이 실험 결과로부터 생존예측지표를 개발하는 일은 관찰 유전자수가 환자의 수보다 훨씬 많고 또 반응변수가 중도절단이 포함된 생존시간이기 때문에 어려운 작업이다. 또한 개별유전자 분석의 문제점이 대두되면서 동일한 대사기능을 수행하는 유전자들의 집합을 대상으로 분석하는 방법이 대두되고 있다. DLBCL 환자들의 마이크로어레이 유전자 발현 자료와 생존시간, 유전자들의 대사경로 정보를 바탕으로 생물학적 해석이 쉬운 생존예측지표를 찾고 그 정확성을 검정하는 pilot study를 실시하였다. 또한 유전자 걸러내기가 지표의 효율성에 미치는 영향력도 비교하여 보았다.

• 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.

• Toxicological Research
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• 제19권4호
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• pp.297-301
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• 2003

To investigate biomarker-based exposure to phthalates and related factors with demographics, 100 subjects who had participated in comprehensive health check-up were selected. We collected demographics through questionnaires and analyzed urine samples for 5 phthalates. Statistical likelihoods and regression methods were applied for data analysis using censored data. The highest levels of urine phthalates were 216$\mu\textrm{g}$/ml in di-isodecyl phthalate, 29.0$\mu\textrm{g}$/ml in di-butyl phthalate, 5.78$\mu\textrm{g}$/ml in di-(2-ethylhexyl) phthalate. The median values of di-(2-ethylhexyl) phthalate were 0.2340 $\mu\textrm{g}$/ml for male smokers, 0.0399 $\mu\textrm{g}$/ml for male non-smokers and 0.0085 $\mu\textrm{g}$/ml for female non-smokers, respectively. Di-(2-ethylhexyl) phthalate, benzyl butyl phthalate and di-isodecyl phthalate were higher in males than in females. In addition, mono-2-ethylhexyl phthalate was decreased with age. Our findings suggest that there might be significant demographic variations in exposure and/or metabolism of phthalates, and that health-risk assessment for phthalate exposure in humans should consider different potential risk groups.