• The Korean Journal of Applied Statistics
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• v.26 no.5
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• pp.759-766
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• 2013

The paper examines several classes of probability distributions with heavy tails. An (asymptotic) expression for tail probability needs to be known to understand which class a given probability distribution belongs to. It is usually not easy to get expressions for tail probabilities since most absolutely continuous probability distributions are specified by probability density functions and not by distribution functions. The paper proposes a method to obtain asymptotic expressions for tail probabilities using only probability density functions. Some examples are given to illustrate the proposed method.

• 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.40 no.1
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• pp.87-107
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• 2003

In this paper, we consider a discrete time queueing system fed by a superposition of an ON and OFF source with heavy tail ON periods and geometric OFF periods and a D-BMAP (Discrete Batch Markovian Arrival Process). We study the tail behavior of the queue length distribution and both infinite and finite buffer systems are considered. In the infinite buffer case, we show that the asymptotic tail behavior of the queue length of the system is equivalent to that of the same queueing system with the D-BMAP being replaced by a batch renewal process. In the finite buffer case (of buffer size K), we derive upper and lower bounds of the asymptotic behavior of the loss probability as $K\;\longrightarrow\;\infty$.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.667-674
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• 2008

We develop new family of the t distributions for modeling semicircular data. It has convenient mathematical features. It is extended to the l-axial t distribution and a generalized semicircular t distribution.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1879-1903
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• 2017

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.

• Communications for Statistical Applications and Methods
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• v.23 no.4
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• pp.321-334
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• 2016

In this paper, we propose power t distribution based on t distribution. We also study the properties of and inferences for power t model in order to solve the problem of real data showing both skewness and heavy tails. The comparison of skew t and power t distributions is based on density plots, skewness and kurtosis. Note that, at the given degree of freedom, the kurtosis's range of the power t model surpasses that of the skew t model at all times. We draw inferences for two parameters of the power t distribution and four parameters of the location-scale extension of power t distribution via maximum likelihood. The Fisher information matrix derived is nonsingular on the whole parametric space; in addition we obtain the profile log-likelihood functions on two parameters. The response plots for different sample sizes provide strong evidence for the estimators' existence and unicity. An application of the power t distribution suggests that the model can be very useful for real data.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.775-781
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• 2008

It is developed that a family of the semicircular Laplace distributions for modeling semicircular data by simple projection method. Mathematically it is simple to simulate observations from a semicircular Laplace distribution. We extend it to the l-axial Laplace distribution by a simple transformation for modeling any arc of arbitrary length. Similarly we develop the l-axial log-Laplace distribution based on the log-Laplace distribution. A bivariate version of l-axial Laplace distribution is also developed.

• 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 Korea Spatial Information System Society
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• v.11 no.2
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• pp.13-18
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• 2009

This paper presents the implementation procedure of encoding and decoding algorithms for Tornado code that can provide fault tolerance for storage and transmission system. The degree distribution satisfying heavy tail distribution is produced. Based on this distribution, a good random irregular bipartite graph is attained after plenty of trails. Such graph construction is proved to be efficient, and the experiments also demonstrate that the implementation obtains good performance in terms of decoding overhead.

• Journal of Digital Convergence
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• v.11 no.9
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• pp.103-111
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• 2013

As the demand-oriented management has been getting important in Supply Chain Management (SCM), various forecasting methods have been suggested including regression analyses. However, dependency structures among variables have been captured by a correlation coefficient, only. It results in inaccurate demand predictions. This paper suggests a new and effective forecasting modeling framework using student's t-copula function. In order to show overall modeling procedures framework, heavy tail typed numerical data and its copula estimations are provided. The suggested methodology can contribute to decrease the bullwhip effect and to stabilize volatile environment in a supply chain network.