• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.87-99
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• 2007

In this paper, we consider the Sparre Andersen risk model modified by the inclusion of interest on the surplus. By using the techniques of Cai and Dickson [Ins.: Math. Econ. 32(2003)], we give the functional and also the exponential type upper bounds for the tail probability of the deficit at ruin. Some special cases are also discussed.

• 대한수학회지
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• 제48권3호
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• pp.655-667
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• 2011

A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in $\mathbb{R}^{n-1}$ and $\mathbb{R}^n$ respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.

• 대한수학회지
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• 제60권3호
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• pp.537-564
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• 2023

In this paper, we are mainly concerned with two-sided estimates for transition probabilities of symmetric Markov chains on ℤ^d, whose one-step transition probability is comparable to |x - y|^-dϕ_j (|x - y|)^-1 with ϕ_j being a positive regularly varying function on [1, ∞) with index α ∈ [2, ∞). For upper bounds, we directly apply the comparison idea and the Davies method, which considerably improves the existing arguments in the literature; while for lower bounds the relation with the corresponding continuous time symmetric Markov chains are fully used. In particular, our results answer one open question mentioned in the paper by Murugan and Saloff-Coste (2015).

• 한국경영과학회지
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• 제29권4호
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• pp.1-10
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• 2004

In this paper we study bounds for characteristics of stationary waiting times in (max, +)-linear systems with a Poisson arrival process. which are prevalent in manufacturing systems, kanban systems, cyclic and acyclic fork-and-join type systems, finite or infinite capacity tandem queues with various kinds of blocking, transportation systems, and telecommunication networks, and so on. Recently, some results on series expansion for characteristics, such as higher moments, Laplace transform, and tail probability, of transient and stationary waiting times in a class of (max, +)-linear systems via Taylor series expansions have been studied. In order to overcome the computational complexity in those results, we consider bounds for characteristics of stationary waiting times using valuable stochastic ordering results. Some numerical examples are also provided.

• 대한수학회논문집
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• 제14권4호
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• pp.789-795
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• 1999

Let $A_1$,A$_2$…, A\ulcorner and B$_1$,B$_2$…, B\ulcorner be two sequences of events on the same probability space. Let X= X\ulcorner(A) and Y-Y\ulcorner)(B), repectively, by the number of those A\ulcorner and B\ulcorner which oc-cur. We establish bivariate lower bounds on the distribution P(X$\geq$1, Y, $\geq$1)and P(X$\geq$i , $Y\geq$j)by linear combinations of the bino-mial moments S\ulcorner, \ulcorner, 1$\leq$i$\leq$j

• Journal of the Korean Statistical Society
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• 제19권1호
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• pp.24-44
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• 1990

The purpose of this paper is to extend the idea of Tamhane and Bechhofer (1977, 1979) concerning the normal means problem to some general class of distributions. The key idea in Tamhane and Bechhofer is the derivation of the computable lower bounds on the probability of a correct selection. To derive such lower bounds, they used the specific covariance structure of a multivariate normal distribution. It is shown that such lower bounds can be obtained for a class of stochastically increasing distributions under certain conditions, which is sufficiently general so as to include the normal means problem as a special application. As an application of the general theory to the scale parameters problem, a two-stage elimination type procedure for selecting the population associated with the smallest variance from among several normal populations is proposed. The design constants are tabulated and the relative efficiencies are computed.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.725-742
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• 2021

The aim of this article is to estimate the coefficient bounds of certain subclasses of analytic functions. We claim that this is a novel and unique effort in combining the coefficient functional along with the new domains and the probability distributions which have not been found or are available in the literature of coefficients bounds. Here the authors analyze these bounds in the special domains associated with exponential function and sine function. Further we obtain Fekete-Szegö inequalities for the defined subclasses of analytic functions defined through Poisson distribution series and Pascal distribution series.

• 정보보호학회논문지
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• 제29권6호
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• pp.1259-1270
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• 2019

블록 암호를 설계할 때, 설계자는 주로 차분 특성 확률의 상한을 이용하여 라운드 수를 결정한다. 라운드 수는 블록 암호의 성능에 영향을 미치므로, 더 적은 라운드를 갖기 위해 차분 특성 확률의 상한을 정밀하게 계산하는 것이 중요하다. 이전까지의 활성 S-box의 최소 개수를 탐색하는 방법들은 비선형 연산과 선형 연산을 각각 제약식으로 구성하여 차분 특성 확률의 상한을 계산하였다. 하지만 선형 연산이 비선형 연산에 의존적으로 선택되는 BOGI 설계전략(Bad-Output Good-Input Design Strategy)의 경우 이전 탐색방법으로 구한 상한은 정밀하지 않을 수 있다. 본 논문에서는 BOGI 전략의 성질을 이용하여 기존의 방법보다 더 정밀한 차분 특성 확률의 상한을 구하는 새로운 방법을 제안한다. 그리고 이 방법을 이용하여 구한 상한의 타당성을 수학적으로 증명한다. 제안한 방법을 BOGI가 사용된 GIFT-64와 GIFT-128에 각각 적용하여 9라운드까지 차분 특성 확률의 상한을 탐색하였다. GIFT-64의 7라운드와 GIFT-128의 9라운드에 대해 기존의 방법을 적용하면 차분 특성 확률의 상한이 각각 2^-18.395와 2^-26.885이었으나, 제안한 방법을 적용하면 각각 2^-19.81과 2^-28.3으로 더 정밀하게 계산된다.

• 한국통신학회논문지
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• 제24권7A호
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• pp.1080-1089
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• 1999

병렬 연쇄 컨볼루션 부호 및 직렬 연쇄 컨볼루션 부호의 ML 연판정 복호에 대한 비트오율확률의 상한치는 가중치 열거함수(Weight Enumerating Function; WEF)를 통해서 구할 수 있으며, 이 상한치는 반복 택 알고리듬과 양방향 탐색 알고리듬을 혼합한 새로운 오류사건 탐색 알고복호를 통해 얻을 수 있는 비트오류확률의 하한치가 된다. 본 논문에서는 스리듬을 제안하고, 얻어진 오류사건을 이용하여 WEF를 계산하는 알고리듬을 제안한다. 컴퓨터 시뮬레이션을 통해, 반복복호를 통해 얻을 수 있는 비트오류확률의 하한치가 됨을 확인하였다.

• 대한수학회지
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• 제36권3호
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• pp.509-525
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• 1999

In this paper we obtain sharp upper and lower bounds of samll ball and large deviation probabilities for the increments of Gaussian processes with stationary increments, whose results are essential to establish Chung type laws of iteratted logarithm.