• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.55-66
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• 2018

By making use of the Riemann-Liouville fractional integrals, we establish further results on Chebyshev inequality. Other Steffensen integral results of the weighted Chebyshev functional are also proved. Some classical results of the paper:[ Steffensen's generalization of Chebyshev inequality. J. Math. Inequal., 9(1), (2015).] can be deduced as some special cases.

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.261-266
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• 1999

We present a geometric interpretation of Chebyshev type inequalities. This uses a simple diagram which illustrates the functional bound for the indicator function of the event whose probability we want to assess. We also give a geometric interpretation of the inequalities in terms of volume in a Euclidean space of appropriate dimension. Markov's inequality and Chebyshev's inequality are treated in more detail.

• 호남수학학술지
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• 제43권3호
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• pp.503-511
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• 2021

In this present work, we obtain certain coefficients of the subclass 𝓗_λ,𝛄(s, b, n) of non-Bazilević functions and estimate the relevant connection to the famous classical Fekete-Szegö inequality of functions belonging to this class.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.47-54
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• 2000

This article is concerned with the algorithm for the Chebyshev estimation with/without linear equality and/or inequality constraints. The algorithm employs a linear scaling transformation scheme to reduce the computational burden which is induced when the data set is quite large. The convergence of the proposed algorithm is proved. And the updating and orthogonal decomposition techniques are considered to improve the computational efficiency and numerical stability.

• 한국항공우주학회지
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• 제33권2호
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• pp.32-38
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• 2005

본 연구에서는 근사모델을 이용하여 설계공간의 타당성을 높일 수 있는 방법을 제시하였다. 이때 설계공간을 이동시키기 위한 기준으로 Chebyshev Inequality를 사용하였다. 이를 공탄성을 고려한 항공기 익형 설계문제에 적용함으로써 타당성이 크게 향상됨을 확인하였으며 이렇게 구한 설계공간 내에서 최적화를 수행함으로써 보다 우수한 최적값도 얻을 수 있었다. 즉 설계공간 내에서 주어진 제약조건을 만족할 확률이 증가하였으며, 설계공간을 이동시킴으로써 보다 우수한 최적점이 설계공간 내에 포함되었다고 할 수 있다. 또한 이 과정에서 반응면 모델과 크리깅 모델, 두 가지 근사모델을 사용하여 정확성과 효율성, 실험점에 대한 강건성 등을 비교하였으며, 본 연구에서 설계한 문제의 경우 비교적 선형적인 특징으로 인해 반응면이 보다 우수한 결과를 보여줌을 확인하였다.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.647-657
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• 2023

The aim of this paper is to study certain subclass ${\tilde{S^q_{\Sigma}}}({\lambda},\,{\alpha},\,t,\,s,\,p,\,b)$ of analytic and bi-univalent functions which are defined by using symmetric q-derivative operator. We estimate the second and third coefficients of the Taylor-Maclaurin series expansions belonging to the subclass and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

• ETRI Journal
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• 제30권5호
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• pp.653-662
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• 2008

Arbitration of tag collision is a significant issue for fast tag identification in RFID systems. A good tag anti-collision algorithm can reduce collisions and increase the efficiency of tag identification. EPCglobal Generation-2 (Gen2) for passive RFID systems uses probabilistic slotted ALOHA with a Q algorithm, which is a kind of dynamic framed slotted ALOHA (DFSA), as the tag anti-collision algorithm. In this paper, we analyze the performance of the Q algorithm used in Gen2, and analyze the methods for estimating the number of slots and tags for DFSA. To increase the efficiency of tag identification, we propose new tag anti-collision algorithms, namely, Chebyshev's inequality, fixed adjustable framed Q, adaptive adjustable framed Q, and hybrid Q. The simulation results show that all the proposed algorithms outperform the conventional Q algorithm used in Gen2. Of all the proposed algorithms, AAFQ provides the best performance in terms of identification time and collision ratio and maximizes throughput and system efficiency. However, there is a tradeoff of complexity and performance between the CHI and AAFQ algorithms.

• 한국통신학회논문지
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• 제33권8A호
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• pp.805-814
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• 2008

Both EPCglobal Generation-2 (Gen2) for passive RFID systems and Intelleflex for semi-passive RFID systems use probabilistic slotted ALOHA with Q algorithm, which is a kind of dynamic framed slotted ALOHA (DFSA), as the tag anti-collision algorithm. A better tag anti-collision algorithm can reduce collisions so as to increase the efficiency of tag identification. In this paper, we introduce and analyze the estimation methods of the number of slots and tags for DFSA. To increase the efficiency of tag identification, we propose two new tag anti-collision algorithms, which are Chebyshev's inequality (CHI) algorithm and hybrid Q algorithm, and compare them with the conventional Q algorithm and adaptive adjustable framed Q (AAFQ) algorithm, which is mentioned in Part I. The simulation results show that AAFQ performs the best in Gen2 scenario. However, in Intelleflex scenario the proposed hybrid Q algorithm is the best. That is, hybrid Q provides the minimum identification time, shows the more consistent collision ratio, and maximizes throughput and system efficiency in Intelleflex scenario.

• International Journal of Reliability and Applications
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• 제3권1호
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• pp.37-50
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• 2002

Simultaneous estimation of accuracy and probability corresponding to a prediction interval is considered in this study. Traditional application of confidence interval forecasting consists in evaluation of interval limits for a given significance level. The wider is this interval, the higher is probability and the lower is the forecast precision. In this paper a measure of stochastic forecast accuracy is introduced, and a procedure for balanced estimation of both the predicting accuracy and confidence probability is elaborated. Solution can be obtained in an optimizing approach. Suggested method is applied to constructing confidence intervals for parameters estimated by normal and t distributions

• 방사성폐기물학회지
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• 제8권2호
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• pp.123-133
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• 2010

방사성핵종의 분포유형에 관한 정보에 기초하여 극저준위폐기물의 자체처분 적합성을 통계학적으로 해석할 수 있는 방법론을 개발하였다. 방사성핵종의 분포에 관한 정보를 알 수 없는 경우에 대해서는 널리 알려진 마코프 부등식과 체비셰프 부등식을 적용하여 방사능농도의 산술평균과 허용되는 최대 표준편차의 상관관계식을 제시하였고, 방사성핵종의 농도가 정규분포 또는 로그정규분포를 갖는 경우에 대해서는 확률밀도함수, 누적확률밀도함수 등의 통계학적 관계식을 이용하여 방사능농도의 산술평균과 허용되는 최대 표준편차의 상관관계식을 새롭게 유도하였다. 또한, 자체처분기준 100 Bq/g 및 신뢰수준 95%인 조건에 대한 사례 적용연구를 통하여 방사능농도의 산술평균과 허용되는 표준편차의 범위를 방사성핵종의 분포유형에 따라 정량적으로 비교 제시하고, 자체처분 대상 폐기물의 방사성핵종 분포유형에 관한 정보가 확보될 경우 동일한 신뢰수준에서 자체처분이 허용될 수 있는 범위가 확장될 수 있음을 통계학적으로 입증하였다.