• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.33-55
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• 2007

The economic world is full of patterns, many of which exert a profound influence over society and business. One of the most contentious is the distribution of wealth. Way back in 1897, an Italian engineer-turned-economist named Vilfredo Pareto discovered a pattern in the distribution of wealth that appears to be every bit as universal as the laws of thermodynamics or chemistry. The present paper proposes some Bayes estimators of shape parameter of Pareto income distribution in censored sampling. Asymmetric LINEX loss function has been considered to study the effects of overestimation and underestimation. For the prior distribution of the parameter involved a number of priors including one and two-parameter exponential, truncated Erlang and doubly truncated gamma have been contemplated to express the belief of the experimenter s/he has regarding the parameter. The estimators thus obtained have been compared theoretically and empirically with the corresponding estimators under squared error loss function, some of which were reported by Bhattacharya et al. (1999).

• Journal of the Korean Data and Information Science Society
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• 제26권6호
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• pp.1573-1582
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• 2015

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.

• Journal of the Korean Data and Information Science Society
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• 제28권3호
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• pp.659-668
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• 2017

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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제18권3호
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• pp.670-684
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• 2024

3D Cross-Modal Retrieval (3DCMR) is a task that retrieves 3D objects regardless of modalities, such as images, meshes, and point clouds. One of the most prominent methods used for 3DCMR is the Cross-Modal Center Loss Function (CLF) which applies the conventional center loss strategy for 3D cross-modal search and retrieval. Since CLF is based on center loss, the center features in CLF are also susceptible to subtle changes in hyperparameters and external inferences. For instance, performance degradation is observed when the batch size is too small. Furthermore, the Mean Squared Error (MSE) used in CLF is unable to adapt to changes in batch size and is vulnerable to data variations that occur during actual inference due to the use of simple Euclidean distance between multi-modal features. To address the problems that arise from small batch training, we propose a Noisy Center Loss (NCL) method to estimate the optimal center features. In addition, we apply the simple Siamese representation learning method (SimSiam) during optimal center feature estimation to compare projected features, making the proposed method robust to changes in batch size and variations in data. As a result, the proposed approach demonstrates improved performance in ModelNet40 dataset compared to the conventional methods.