• Journal of Applied Reliability
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• v.18 no.3
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• pp.220-228
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• 2018

Purpose: The purpose of this study is to investigate the tail behavior of the life distribution which exhibits an increasing failure rate or other positive aging effects after a certain time point. Methods: We characterize the tail behavior of the life distribution with regard to certain reliability measures such as failure rate, mean residual life and reliability function and derive several stochastic properties regarding such life distributions. Also, utilizing an L-statistic and its asymptotic normality, we propose new nonparametric testing procedures which verify if the life distribution has an increasing tail failure rate. Results: We propose the IFR-Tail (Increasing Failure Rate in Tail), DMRL-Tail (Decreasing Mean Residual Life in Tail) and NBU-Tail (New Better than Used in Tail) classes, all of which represent the tail behavior of the life distribution. And we discuss some stochastic properties of these proposed classes. Also, we develop a new nonparametric test procedure for detecting the IFR-Tail class and discuss its relative efficiency to explore the power of the test. Conclusion: The results of our research could be utilized in the study of wide range of applications including the maintenance and warranty policy of the second-hand system.

• Journal of the Korean Data and Information Science Society
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• v.12 no.2
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• pp.65-69
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• 2001

MLE and UMVUE of the right-tail probability in a Levy distribution will be considered, and hence the UMVUE is more efficient in a sense of simulated MSE than the MLE of the right-tail probability.

• 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 $K\;\longrightarrow\;\infty$.

• Journal of Distribution Science
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• v.20 no.12
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• pp.81-87
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• 2022

Purpose: This study aims to explore the relationship between stock liquidity and skewness risk-tail risk (stock price crash risk) in an emerging market, in which problems on liquidity are more severe than in developed markets. Research design, data, and methodology: Based on the Thai market stock exchange over the period of 2000 to 2019, our sample include 13,462 firm-period observations. We employ a panel regression models regarding to five liquidity measures. These five liquidity measures cover three dimensions of liquidity namely the volume-based, price-based, and transaction cost-based measures for the liquidity-tail risk relationship. Results: We find a positively significant relationship between stock liquidity and tail risk in all cases. The finding here shows that the higher the stock liquidity, the larger the tail risk is. Conclusion: As the prior studies show inconclusive effect of stock liquidity on stock price crash risk, we demonstrate that mixed results found in prior studies are probably driven from the type of liquidity measure. The stock liquidity-tail risk association is present in the Stock Exchange of Thailand. The results remain the same regardless of the definition of tail risk and liquidity factors. An endogeneity issue is addressed by employing the two-stage least squares regression.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.507-513
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• 2006

We shall consider an inference of the reliability and an estimation of the right-tail probability in an exponentiated uniform distribution. And we shall compare numerically efficiencies for proposed estimators of the scale parameter and right-tail probability in the small sample sizes.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.343-350
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• 2015

We consider an M^X/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the M^X/G/1 retrial queue.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1171-1177
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• 2007

We consider estimation of the right-tail probability in a log-Laplace random variable, As we derive the density of ratio of two independent log-Laplace random variables, the k-th moment of the ratio is represented by a special mathematical function. and hence variance of the ratio can be represented by a psi-function.

• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.411-421
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• 2007

The recent work by the authors (see, Withers, 1999; Withers and McGavin, 2006; Withers and Nadarajah, 2006) provided new expressions for repeated upper tail integrals of the univariate normal density and so also for the general Hermite function. Here we derive new expressions for repeated lower tail integrals of the same. The calculations involve the use of Moran's L-function and the Airy function. In particular, the Hermite functions are expressed in terms of Moran's L-function and vice versa.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.239-259
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• 2019

The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401-407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847-1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.

• 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.