• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.359-368
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• 2006

In this paper we derived the asymptotic relative efficiency, ARE(ms, rs), of our new score function with respect to the McKean and Sievers scores for the asymmetric error distributions which often occur in practice. We thoroughly explored the asymptotic relative efficiency, ARE(ms, rs), of our score function that provides much improvement over the McKean and Sievers scores for all values of r and s under asymmetric distributions.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.455-463
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• 2004

In this paper, we derive sharp upper and lower expectation bounds on the extreme order statistics from possibly dependent random variables whose marginal distributions are only known. The marginal distributions of the considered random variables may not be the same and the expectation bounds are completely determined by the marginal distributions only.

• 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.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.85-95
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• 2012

In this paper we define extended negative quadrant dependence which is weaker negative quadrant dependence and show conditions for having extended negative quadrant dependence property. We also derive generalized Farlie-Gumbel-Morgenstern uniform distributions that possess the extended quadrant dependence property.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.875-883
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• 2001

We derive the asymptotic relative efficiencies in two special cases of Chaudhuri's estimators for the multivariate one sample problem. And we compare those two when observations are independent and identically distributed from a family of spherically symmetric distributions including normal distributions.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.91-103
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• 2006

Yun (2005) introduced an estimator of the second order parameter characterizing the tail behavior of probability distributions and proved its consistency. In this paper we prove its asymptotic normality under a third order condition.

• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.265-274
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• 2004

The paper extends earlier work on the skew-normal distribution, a family of distributions including normal, but with extra parameter to regulate skewness. The present work introduces a singly truncated parametric family that strictly includes a truncated normal distribution, and studies its properties, with special emphasis on the relation with bivariate normal distribution.

• Journal of the Korean Statistical Society
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• v.34 no.4
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• pp.273-280
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• 2005

In this paper we introduce an estimator of the second order parameter characterizing the tail behavior of probability distributions and prove its consistency.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.411-424
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• 2021

Inference following two-stage adaptive designs (also known as two-stage randomization designs) with survival endpoints usually focuses on estimating and comparing survival distributions for the different treatment strategies. The aim is to identify the treatment strategy(ies) that leads to better survival of the patients. The objectives of this study were to assess the performance three commonly cited methods for estimating survival distributions in two-stage randomization designs. We review three non-parametric methods for estimating survival distributions in two-stage adaptive designs and compare their performance using simulation studies. The simulation studies show that the method based on the marginal mean model is badly affected by high censoring rates and response rate. The other two methods which are natural extensions of the Nelson-Aalen estimator and the Kaplan-Meier estimator have similar performance. These two methods yield survival estimates which have less bias and more precise than the marginal mean model even in cases of small sample sizes. The weighted versions of the Nelson-Aalen and the Kaplan-Meier estimators are less affected by high censoring rates and low response rates. The bias of the method based on the marginal mean model increases rapidly with increase in censoring rate compared to the other two methods. We apply the three methods to a leukemia clinical trial dataset and also compare the results.

• 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.