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Yang Yang - One of the best experts on this subject based on the ideXlab platform.
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Tail Probability of randomly weighted sums of subexponential random variables under a dependence structure
Statistics & Probability Letters, 2012Co-Authors: Yang Yang, Remigijus Leipus, Jonas SiaulysAbstract:Abstract This paper deals with the asymptotic behavior for the Tail Probability of randomly weighted sums of subexponential random variables under a dependence structure, where the random weights and the corresponding summands are dependent.
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estimates for the Tail Probability of the supremum of a random walk with independent increments
Chinese Annals of Mathematics Series B, 2011Co-Authors: Yang Yang, Kaiyong WangAbstract:The authors investigate the Tail Probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distributed random variables with O-subexponential integrated distributions. A uniform upper bound is derived for the distribution of the supremum of a random walk with independent but non-identically distributed increments, whose Tail distributions are dominated by a common Tail distribution with an O-subexponential integrated distribution.
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asymptotics for Tail Probability of total claim amount with negatively dependent claim sizes and its applications
Lithuanian Mathematical Journal, 2009Co-Authors: Yang Yang, Remigijus Leipus, Yuebao Wang, Jonas SiaulysAbstract:In this paper, we obtain the asymptotics for the Tail Probability of the total claim amount with negatively dependent claim sizes in two cases: in the first case, the distribution Tail of the claim number is dominatedly varying; in the second case, the distribution of the claim number is in the maximum domain of attraction of the Gumbel distribution, and the claim sizes are light-Tailed. In both cases, we assume that the claim sizes are nondegenerate negatively dependent and identically distributed random variables and that the claim number is not necessarily independent of the claim sizes. As applications, we derive asymptotics for the finite-time ruin probabilities in some dependent compound renewal risk models with constant interest rate.
Jonas Siaulys - One of the best experts on this subject based on the ideXlab platform.
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exponential bounds for the Tail Probability of the supremum of an inhomogeneous random walk
arXiv: Probability, 2018Co-Authors: Dominyka Kievinaitė, Jonas SiaulysAbstract:Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent but not necessarily identically distributed random variables. In this paper, the sufficient conditions are found under which the Tail Probability $\mathbb{P}(\sup_{n\geqslant0}\sum_{i=1}^n\xi_i>x)$ can be bounded above by $\varrho_1\exp\{-\varrho_2x\}$ with some positive constants $\varrho_1$ and $\varrho_2$. A way to calculate these two constants is presented. The application of the derived bound is discussed and a Lundberg-type inequality is obtained for the ultimate ruin Probability in the inhomogeneous renewal risk model satisfying the net profit condition on average.
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Tail Probability of randomly weighted sums of subexponential random variables under a dependence structure
Statistics & Probability Letters, 2012Co-Authors: Yang Yang, Remigijus Leipus, Jonas SiaulysAbstract:Abstract This paper deals with the asymptotic behavior for the Tail Probability of randomly weighted sums of subexponential random variables under a dependence structure, where the random weights and the corresponding summands are dependent.
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asymptotics for Tail Probability of total claim amount with negatively dependent claim sizes and its applications
Lithuanian Mathematical Journal, 2009Co-Authors: Yang Yang, Remigijus Leipus, Yuebao Wang, Jonas SiaulysAbstract:In this paper, we obtain the asymptotics for the Tail Probability of the total claim amount with negatively dependent claim sizes in two cases: in the first case, the distribution Tail of the claim number is dominatedly varying; in the second case, the distribution of the claim number is in the maximum domain of attraction of the Gumbel distribution, and the claim sizes are light-Tailed. In both cases, we assume that the claim sizes are nondegenerate negatively dependent and identically distributed random variables and that the claim number is not necessarily independent of the claim sizes. As applications, we derive asymptotics for the finite-time ruin probabilities in some dependent compound renewal risk models with constant interest rate.
Boris Pervan - One of the best experts on this subject based on the ideXlab platform.
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Bounding the integer bootstrapped GNSS baseline’s Tail Probability in the presence of stochastic uncertainty
Journal of Geodesy, 2016Co-Authors: Steven E. Langel, Samer M. Khanafseh, Boris PervanAbstract:Differential carrier phase applications that utilize cycle resolution need the Probability density function of the baseline estimate to quantify its region of concentration. For the integer bootstrap estimator, the density function has an analytical definition that enables Probability calculations given perfect statistical knowledge of measurement and process noise. This paper derives a method to upper bound the Tail Probability of the integer bootstrapped GNSS baseline when the measurement and process noise correlation functions are unknown, but can be upper and lower bounded. The Tail Probability is shown to be a non-convex function of a vector of conditional variances, whose feasible region is a convex polytope. We show how to solve the non-convex optimization problem globally by discretizing the polytope into small hyper-rectangular elements, and demonstrate the method for a static baseline estimation problem.
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bounding the integer bootstrapped gnss baseline s Tail Probability in the presence of stochastic uncertainty
Journal of Geodesy, 2016Co-Authors: Steven E. Langel, Samer M. Khanafseh, Boris PervanAbstract:Differential carrier phase applications that utilize cycle resolution need the Probability density function of the baseline estimate to quantify its region of concentration. For the integer bootstrap estimator, the density function has an analytical definition that enables Probability calculations given perfect statistical knowledge of measurement and process noise. This paper derives a method to upper bound the Tail Probability of the integer bootstrapped GNSS baseline when the measurement and process noise correlation functions are unknown, but can be upper and lower bounded. The Tail Probability is shown to be a non-convex function of a vector of conditional variances, whose feasible region is a convex polytope. We show how to solve the non-convex optimization problem globally by discretizing the polytope into small hyper-rectangular elements, and demonstrate the method for a static baseline estimation problem.
Yunan Liu - One of the best experts on this subject based on the ideXlab platform.
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staffing to stabilize the Tail Probability of delay in service systems with time varying demand
Operations Research, 2018Co-Authors: Yunan LiuAbstract:Analytic formulas are developed to set the time-dependent number of servers to stabilize the Tail Probability of customer waiting times for the Gt/GI/st + GI queueing model, which has a nonstationary non-Poisson arrival process (the Gt), nonexponential service times (the first GI), and allows customer abandonment according to a nonexponential patience distribution (the +GI). Specifically, for any delay target w > 0 and Probability target α ∈ (0, 1), we determine appropriate staffing levels (the st) so that the time-varying Probability that the waiting time exceeds a maximum acceptable value w is stabilized at α at all times. In addition, effective approximating formulas are provided for other important performance functions such as the probabilities of delay and abandonment, and the means of delay and queue length. Many-server heavy-traffic limit theorems in the efficiency-driven regime are developed to show that (i) the proposed staffing function achieves the goal asymptotically as the scale increases, a...
Dongwon Seo - One of the best experts on this subject based on the ideXlab platform.
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Tail Probability of transient and stationary waiting times in max linear systems
IEEE Transactions on Automatic Control, 2002Co-Authors: Hayriye Ayhan, Dongwon SeoAbstract:(Max,+) linear systems can be used to represent a class of queueing networks, such as acyclic or cyclic fork-and-join queueing networks, finite- or infinite-capacity tandem queueing networks with various types of blocking, synchronized queueing networks, and so on. In this paper, we derive explicit expressions for the Tail Probability of transient and stationary waiting times in Poisson-driven (max,+) linear systems. As an application of our results, we consider the problem of maximizing the long-run average throughput subject to a probabilistic constraint on stationary waiting times in (max,+) linear systems with deterministic service times.