• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.519-527
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• 2004

Relationship between the partial likelihood ratio statistics for logisitic models and the partial goodness-of-fit statistics for corresponding log-linear models is discussed. This paper shows how definitions of suppression in logistic model can be adapted for log-linear model and how they are related to confounding in terms of collapsibility for categorical data. Several $2{times}2{times}2$ contingency tables are illustrated.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.425-445
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• 2021

A generalization of the log-logistic (LL) distribution called exponentiated log-logistic (ELL) distribution on lines of exponentiated Weibull distribution is considered. In this paper, based on progressive type-II censored samples, we have derived the maximum likelihood estimators and Bayes estimators for three parameters, the survival function and hazard function of the ELL distribution. Then, under the balanced squared error loss (BSEL) and the balanced linex loss (BLEL) functions, their corresponding Bayes estimators are obtained using Lindley's approximation (see Jung and Chung, 2018; Lindley, 1980), Tierney-Kadane approximation (see Tierney and Kadane, 1986) and Markov Chain Monte Carlo methods (see Hastings, 1970; Gelfand and Smith, 1990). Here, to check the convergence of MCMC chains, the Gelman and Rubin diagnostic (see Gelman and Rubin, 1992; Brooks and Gelman, 1997) was used. On the basis of their risks, the performances of their Bayes estimators are compared with maximum likelihood estimators in the simulation studies. In this paper, research supports the conclusion that ELL distribution is an efficient distribution to modeling data in the analysis of survival data. On top of that, Bayes estimators under various loss functions are useful for many estimation problems.

• Journal of Digital Convergence
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• v.12 no.3
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• pp.219-226
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• 2014

In this study, reliability software cost model considering shape parameter based on life distribution from the process of software product testing was studied. The shape parameter using the Erlang and Log-logistic model that is widely used in the field of reliability problems presented. The software failure model was used finite failure non-homogeneous Poisson process model, the parameters estimation using maximum likelihood estimation was conducted. In comparison result of software cost model based on the Erlang distribution and the log-logistic distribution software cost model, because Erlang model is to predict the optimal release time can be software, but the log-logistic model to predict to optimal release time can not be, Erlang distribution than the log-logistic distribution appears to be effective. In this research, software developers to identify software development cost some extent be able to help is considered.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.227-235
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• 2014

In this paper, we develop the noninformative priors for the scale parameter and the shape parameter in the log-logistic distribution. We developed the first and second order matching priors. It turns out that the second order matching prior matches the alternative coverage probabilities, and is a highest posterior density matching prior. Also we revealed that the derived reference prior is the second order matching prior for both parameters, but Jerffrey's prior is not a second order matching prior. We showed that the proposed reference prior matches the target coverage probabilities in a frequentist sense through simulation study, and an example based on real data is given.

• International Journal of Reliability and Applications
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• v.17 no.1
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• pp.85-105
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• 2016

In this paper accelerated life testing is incorporated in quality control technique of acceptance sampling plan to induce early failures in high reliability products.Stress under accelerated condition can be applied in constant-stress, step-stress and progressive-stress or combination of such loadings. A ramp-stress results when stress is increased linearly (from zero) with time. In this paper optimum failure-censored ramp-stress accelerated life test sampling plan for log-logistic distribution has been formulated with cost considerations. The log-logistic distribution has been found appropriate for insulating materials. The optimal plans consist in finding optimum sample size, sample proportion allocated to each stress, and stress rate factor such that producer's and consumer's interests are safeguarded. Variance optimality criterion is used when expected cost per lot is not taken into consideration, and bilevel programming approach is used in cost optimization problems. The methods developed have been illustrated using some numerical examples, and sensitivity analyses carried out in the context of ramp-stress ALTSP based on variable SSP for proportion nonconforming.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1583-1592
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• 2015

This paper deals with the problem of testing on the shape parameter in the log-logistic distribution. We propose default Bayesian testing procedures for the shape parameter under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. We can solve the this problem by the intrinsic Bayes factor and the fractional Bayes factor. Therefore we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1501-1511
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• 2015

This paper deals with the problem of testing on the equality of the scale parameters in the log-logistic distributions. We propose default Bayesian testing procedures for the scale parameters under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Therefore, we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factor under the reference priors. To justify proposed procedures, a simulation study is provided and also, an example is given.

• Design Convergence Study
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• v.16 no.3
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• pp.17-37
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• 2017

The purpose of this study is to evaluate the value of the center of age-friendly goods to confirm the public value of the center. 152 elderly participants, either who have utilized the center themselves or who have experienced the center indirectly through the image have participated in the study. The experience of age-friendly product center was evaluated by the contingent valuation method, which is widely used in the public services. A double-bounded dichotomous choice (DB-DC) log-logistic model and a log-normal model were conducted. As the result of the estimation, the truncated mean of the log-logistic model was 3,401 Korean won, with the mean of 4,937 won. In addition, the truncated mean of the log-normal model was 3,433 won, with the mean of 4,144 won. Elderly who have not experienced the center placed a higher value on the center, compared to the experienced elderly. The results imply the necessity to enlarge the opportunity for future suppliers to experience the center for age-friendly products, in order to improve their objective understandings. In addition, the necessity of expanding exhibition products and applying age-friendly designs is proposed, to offer various attractive experiences to elderly.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.14
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• pp.5883-5888
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• 2014

Background: Breast cancer is the most common cancers in female populations. The exact cause is not known, but is most likely to be a combination of genetic and environmental factors. Log-logistic model (LLM) is applied as a statistical method for predicting survival and it influencing factors. In recent decades, artificial neural network (ANN) models have been increasingly applied to predict survival data. The present research was conducted to compare log-logistic regression and artificial neural network models in prediction of breast cancer (BC) survival. Materials and Methods: A historical cohort study was established with 104 patients suffering from BC from 1997 to 2005. To compare the ANN and LLM in our setting, we used the estimated areas under the receiver-operating characteristic (ROC) curve (AUC) and integrated AUC (iAUC). The data were analyzed using R statistical software. Results: The AUC for the first, second and third years after diagnosis are 0.918, 0.780 and 0.800 in ANN, and 0.834, 0.733 and 0.616 in LLM, respectively. The mean AUC for ANN was statistically higher than that of the LLM (0.845 vs. 0.744). Hence, this study showed a significant difference between the performance in terms of prediction by ANN and LLM. Conclusions: This study demonstrated that the ability of prediction with ANN was higher than with the LLM model. Thus, the use of ANN method for prediction of survival in field of breast cancer is suggested.

• The Korean Journal of Applied Statistics
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• v.33 no.1
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• pp.107-114
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• 2020

Extreme value distributions have often been used for the analysis (e.g., prediction of return level) of data which are observed from natural disaster. By the extreme value theory, the block maxima asymptotically follow the generalized extreme value distribution as sample size increases; however, this may not hold in a small sample case. For solving this problem, this paper proposes the use of a log-logistic (LLG) distribution whose validity is evaluated through goodness-of-fit test and model selection. The proposed method is illustrated with data from annual maximum earthquake magnitudes of China. Here, we present the predicted return level and confidence interval according to each return period using LLG distribution.