Approximate maximum product spacing estimation of Weibull distribution under progressive hybrid censoring

Kyeongjun Lee 한국데이터정보과학회 2022 한국데이터정보과학회지 Vol.33 No.1

Under classical estimation set up, the maximum product spacings estimation (MPSE) method is quite effective and several authors advocated the use of this method as an alternative to maximum likelihood estimation (MLE) method, and found that this estimation method provides better estimates than maximum likelihood estimates in various situations. In this paper, we propose the estimators of the parameters of the Weibull distribution (WeibD) under progressive hybrid censoring scheme. First, we derive the MPSEs for the parameters of WeibD. Also, we derive the approximate MPSEs for the parameters of WeibD using Talyor series expansion. And we compare the proposed estimators in the sense of mean squared error (MSE) and bias under progressive hybrid censoring scheme. Finally, the validity of the proposed methods are demonstrated by a real data.

Estimation of entropy of the inverse weibull distribution under generalized progressive hybrid censored data

Kyeongjun Lee 한국데이터정보과학회 2017 한국데이터정보과학회지 Vol.28 No.3

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estima tors cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

Estimation of the entropy with generalized type I hybrid censored Weibull data

Kyeongjun Lee 한국데이터정보과학회 2020 한국데이터정보과학회지 Vol.31 No.3

In this paper, the estimation of the entropy of a Weibull distribution based on the generalized type I hybrid censoring scheme (GeHyC) has been considered. The maximum likelihood estimator (MLE) and approximate MLE are provided. The Bayes estimators for the entropy of the Weibull distribution based on the symmetric and asymmetric loss functions, such as the squared error (SqEL) balanced SqEL (BSqEL), linex (LinL), balanced LinL (BLinL), general entropy loss (GeEL) and balanced GeEL (BGeEL) functions, are provided. The Bayes estimators cannot be obtained explicitly, and Lindley"s approximation (LinA) is used to obtain the Bayes estimators. Simulation results are performed to see the effectiveness of the different estimators. Also, a real data set has been analyzed for illustrative purposes.

Estimation of entropy of the inverse weibull distribution under generalized progressive hybrid censored data

Lee, Kyeongjun The Korean Data and Information Science Society 2017 한국데이터정보과학회지 Vol.28 No.3

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

Bayes estimation of entropy of exponential distribution based on multiply Type II censored competing risks data

Lee, Kyeongjun,Cho, Youngseuk The Korean Data and Information Science Society 2015 한국데이터정보과학회지 Vol.26 No.6

In lifetime data analysis, it is generally known that the lifetimes of test items may not be recorded exactly. There are also situations wherein the withdrawal of items prior to failure is prearranged in order to decrease the time or cost associated with experience. Moreover, it is generally known that more than one cause or risk factor may be present at the same time. Therefore, analysis of censored competing risks data are needed. In this article, we derive the Bayes estimators for the entropy function under the exponential distribution with an unknown scale parameter based on multiply Type II censored competing risks data. The Bayes estimators of entropy function for the exponential distribution with multiply Type II censored competing risks data under the squared error loss function (SELF), precautionary loss function (PLF) and DeGroot loss function (DLF) are provided. Lindley's approximate method is used to compute these estimators.We compare the proposed Bayes estimators in the sense of the mean squared error (MSE) for various multiply Type II censored competing risks data. Finally, a real data set has been analyzed for illustrative purposes.

Estimation of the exponentiated half-logistic distribution under generalized type I hybrid censored samples

Kyeongjun Lee 한국데이터정보과학회 2021 한국데이터정보과학회지 Vol.32 No.5

In this paper, we consider the shape parameter for the exponentiated half logistic distribution (ExHL) when samples are generalized type I hybrid censored samples. The shape parameter for the ExHL is estimated by the Bayesian method. We consider conjugate prior and corresponding posterior distribution is obtained. We also obtain the maximum likelihood estimator (MLE) of the shape parameter under the generalized type I hybrid censored samples (GenT1HCs). We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 1,000 times for the sample size n = 20, 30, 40 and various generalized type I hybrid censored samples. Finally, a real data set has been analysed for illustrative purpose.

Estimating the parameters of the Weibull distribution under generalized type II hybrid censoring

Kyeongjun Lee 한국데이터정보과학회 2021 한국데이터정보과학회지 Vol.32 No.4

In hybrid censoring both the time and the number of failures are considered for the life testing of the product. The combination of type I and type II censoring is called the hybrid censoring. Though the type II hybrid censored scheme guarantees a pre-fixed number of failures, it might take a long time to complete the test. In order to provide a guarantee in terms of the time to complete the test, generalized type II hybrid censoring scheme was introduced. In this paper, we consider the MLEs of the parameters and reliability when the data are generalized type II hybrid censored Weibull data. However, the MLEs cannot be obtained in a closed form. We use the approximate MLEs using Taylor series expansion. Also, we consider the Bayes estimation for the parameters and reliability when the data are generalized type II hybrid censored Weibull data. In Bayes estimation, Lindley"s approximation is used to obtain the Bayes estimators. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, a real data set has been analysed for illustrative purposes.

Approximate maximum product spacing estimation of half logistic distribution under progressive type II censored samples

Kyeongjun Lee 한국데이터정보과학회 2019 한국데이터정보과학회지 Vol.30 No.3

In most of the life testing and reliability experiments, the experimenter is often, unable to observe life time of all items put on test and the data avilable to the experimenter is censored data. Under classical estimation set up, the maximum product spacings method is quite effective and several authors advocated the use of this method as an alternative to MLE, and found that this estimation method provides better estimates than MLE in various situations. In this paper, we derive the MPSE for the parameter and reliability function of half-logistic (HL) distribution. And we derive the approximate MPSE for the parameter and reliability function of HL distribution using Talyor series expansion. We also compare the proposed estimators in the sense of the root mean squared error (RMSE) and bias for various progressive type II censored samples. In addition, real data example based on progressive type II censoring scheme have been also analysed for illustrative purposes.

Bayesian and maximum likelihood estimation of entropy of the inverse Weibull distribution under generalized type I progressive hybrid censoring

Lee, Kyeongjun The Korean Statistical Society 2020 Communications for statistical applications and me Vol.27 No.4

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

Predicting the customer of cafeteria using unstructured data

Kyeongjun Lee 한국자료분석학회 2023 한국자료분석학회 학술대회자료집 Vol.2023 No.1

This study aimed to predict the number of meals served in a group cafeteria using machine learning techꠓnology. Menu feature variables were created through the Word2Vec technique and clustering, and a stacking ensemble model was constructed using Random Forest, Gradient Boosting, and Cat Boost as sub-models. Reꠓsults showed that Cat Boost had the best performance, and the ensemble model showed an 8% improvement in performance. The study also found that the date factor had the greatest influence on the number of diners in a cafeteria, followed by menu characteristics and other factors. The implications of the study include the potenꠓtial for machine learning technology to improve predictive performance and reduce food waste, as well as the removal of subjective elements in menu classification. Limitations of the research include limited data cases and a weak model structure when new menus or foreign words are not included in the learning data. Future studies should aim to address these limitations.