• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1397-1403
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• 2006

This paper considers the testing problem for scale changes in autoregressive processes with heavy-tailed innovations. For a test, we propose the CUSUM test statistic based on the trimmed residuals. We perform a simulation study for the mixture normal and Cauchy innovations.

• Proceedings of the KIEE Conference
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• 2006.04a
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• pp.18-20
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• 2006

The statistics for the neighbor differences between the particular pixels and their neighbors are introduced. They are incorporated into the filter to remove additive Gaussian noise contaminating images. The derived denoising method corresponds to the maximum likelihood estimator for the heavy-tailed Gaussian distribution. The error norm corresponding to our estimator from the robust statistics is equivalent to Huber's minimax norm. Our estimator is also optimal in the respect of maximizing the efficacy under the above noise environment.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.717-732
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• 2011

We consider bootstrap confidence intervals for high quantiles of heavy-tailed distribution. A semi-parametric method is compared with the non-parametric and the parametric method through simulation study.

• Proceedings of the Safety Management and Science Conference
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• 2010.11a
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• pp.35-39
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• 2010

The research classifies three types of asymptotic tail distributions such as long(heavy, thick) tailed distribution, medium tailed distribution and short(light, thin) tailed distribution. The extreme value distributions(EVD) classified in this paper can be used in SPC(Statistical Process Control) control chart and reliability engineering.

• Journal of the Korean Mathematical Society
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• v.61 no.5
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• pp.853-874
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• 2024

Let {X, X_n; n ≥ 1} be a 𝛽-mixing sequence of identical nonnegative random variables with super-heavy tailed distributions and S_n = X₁ + X₂ + · · · + X_n. For 𝜀 > 0, b > 1 and appropriate values of x, we obtain the logarithmic asymptotics behaviors for the tail probabilities ℙ(S_n > e^𝜀nx) and P(S_n > e^𝜀bn). Moreover, our results are applied to the log-Pareto distribution and the distribution for the super-Petersburg game.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.225-233
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• 1996

In this paper, we propose Bayes estimators of the finite population mean based on heavy-tailed prior distributions using scale mixtures of normals. Also, the asymptotic optimality property of the proposed Bayes estimators is proved. A numerical example is provided to illustrate the results.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.733-739
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• 2011

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.313-318
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• 2000

This article addresses aspects of combining information, with special attention to meta-analysis. In specific, we consider hierarchical Bayesian models for meta-analysis under priors which are scale mixtures of normal, and thus have tail heavier than that of the normal. Numerical methods of finding Bayes estimators under these heavy tailed prior are given, and are illustrated with an actual example.

• The KIPS Transactions:PartA
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• v.10A no.3
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• pp.189-198
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• 2003

In this paper, we propose a method of analysis to show the heavy-tailed statistical distribution of file sizes in web servers, using TTT plot technique. TTT plot technique, a well-known method in the area of reliability engineering, determines that a distribution of samples fellows a heavy tailed one when their TTT statistical plots are lied on a straight line. We performed an intensive simulation using data gathered from real web servers. The simulation indicates that the proposed method is superior to Hill estimation technique or LLCD plot method in efficiency of data analysis. Moreover, the proposed method eliminates the possible decision error, which Pareto distribution or traditional method might cause.