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本文研究了索赔服从Phase-type分布的风险模型在第n次索赔时破产的概率问题.利用Phasetype分布的性质及索赔时刻的盈余与净收入之间的关系,得到盈余密度函数的Laplace变换递推关系,进而得出风险过程在第n次索赔时的破产概率,最后举例说明之. 相似文献
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在解决某些涉及自然数n的概率问题时,如果能从问题的背景中探究出概率问题的递推关系,往往可以起到事半功倍的效果.下面通过几个例子加以说明. 相似文献
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利用某些概率问题可以发现等价的递推公式.以下先从概率模型入手,得到等价的递推公式,再将其进行推广,并在推导Fibonac ci数列通项公式中加以应用.1.由概率模型导出的两个等价递推式设有甲、乙、丙、丁四个人进行传球练习, 相似文献
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概率问题是高中数学新增的重要问题,具有实践性和操作性强的特点,它融许多分支于一体,形成了一个新的“交汇点”.下面列举概率计算中的两类数列递推关系的几个例子. 相似文献
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本文研究引入利率的完全离散经典风险模型,得到一个有限时间内的破产概率的递推公式,最后给出了一个数值算例. 相似文献
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在随机利率服从有限齐次Markov链下,建立相关险种离散风险模型,采用递推方法得到了有限时间破产概率的递推等式和最终破产概率的积分等式;给出了有限时间破产概率和最终破产概率的上界,导出了破产时刻余额分布的计算等式. 相似文献
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带息双二项风险模型的破产问题 总被引:1,自引:0,他引:1
本文研究了带随机利率的双二项风险模型的破产问题,得到了描述破产严重程度的破产前盈余分布,破产持续时间分布的递推公式,有限时间破产概率的递推公式及终极破产概率满足的积分方程. 相似文献
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Constantinos Goutis George Casella 《Annals of the Institute of Statistical Mathematics》1997,49(4):711-726
In the usual frequentist formulation of testing and interval estimation there is a strong relationship between -level tests and 1 - confidence intervals. Such strong relationships do not always persist for post-data, or Bayesian, measures of accuracy of these procedures. We explore the relationship between post-data measures of accuracy of both tests and interval estimates, measures that are derived under a decision-theoretic structure. We find that, in general, there are strong post-data relationships in the one-sided case, and some relationships in the two-sided case. 相似文献
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Nenad Radakovic Douglas McDougall 《International Journal of Mathematical Education in Science & Technology》2013,44(7):949-953
This classroom note illustrates how dynamic visualization can be used to teach conditional probability and Bayes’ theorem. There are two features of the visualization that make it an ideal pedagogical tool in probability instruction. The first feature is the use of area-proportional Venn diagrams that, along with showing qualitative relationships, describe the quantitative relationship between two sets. The second feature is the slider and animation component of dynamic geometry software enabling students to observe how the change in the base rate of an event influences conditional probability. A hypothetical instructional sequence using a well-known breast cancer example is described. 相似文献
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Convergence of a transition probability tensor of a higher‐order Markov chain to the stationary probability vector
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In this paper, first we introduce a new tensor product for a transition probability tensor originating from a higher‐order Markov chain. Subsequently, some properties of the new tensor product are explained, and its relationship with the stationary probability vector is studied. Also, similarity between results obtained by this new product and the first‐order case is shown. Furthermore, we prove the convergence of a transition probability tensor to the stationary probability vector. Finally, we show how to achieve a stationary probability vector with some numerical examples and make some comparison between the proposed method and another existing method for obtaining stationary probability vectors. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Chun Su Tao Jiang Qi-he TangDepartment of Statistics Finance University of Science Technology of China Hefei 《应用数学学报(英文版)》2002,18(4):675-680
Embrechts and Veraverbeke investigated the renewal risk model and gave a tail equivalence relationship of the ruin probabilities (?)(x) under the assumption that the claim size is heavy-tailed, which is regarded as a classical result in the context of extremal value theory. In this note we extend this result to the delayed renewal risk model. 相似文献
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JIN Yang & AN Hongzhi School of Statistics Renmin University of China Beijing China Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2005,48(3):333-340
In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability. 相似文献
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Mrinal Kanti Roychowdhury 《Journal of Mathematical Analysis and Applications》2011,383(2):499-505
The quantization dimension function for a probability measure induced by a set of infinite contractive similarity mappings and a given probability vector is determined. A relationship between the quantization dimension function and the temperature function of the thermodynamic formalism arising in multifractal analysis is established. The result in this paper is an infinite extension of Graf and Luschgy [S. Graf, H. Luschgy, The quantization dimension of self-similar probabilities, Math. Nachr. 241 (2002) 103-109]. 相似文献
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研究了既没有平稳增量性,也没有scaling性质的N指标d维广义布朗单的容度问题.证明了广义布朗单“好象”一个局部平稳增量过程,应用Cairoli极大不等式和多参数鞅的方法得到了广义布朗单的碰撞概率与容度之间的关系,给出了其碰撞概率的确切容度估计.所得结果包含了布朗单和可加布朗运动的相应结果. 相似文献
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We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are
assumed to occur only when the Markov chain is in a particular state. This assumption implies that off-periods in the arrival
process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length
distributions in a finite-buffer queue and the corresponding infinite-buffer queue. With the result, the exact loss probability
is obtained in terms of the queue length distribution in the corresponding infinite-buffer queue. Note that this result enables
us to compute the loss probability very efficiently, since the queue length distribution in the infinite-buffer queue can
be efficiently computed when off-periods are geometrically distributed.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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基于时变Copula模型,获得预测方差,确定单个基金收益率序列的边缘分布.利用常见的静态Copula和时变Copula模型对基金收益率序列间两两相依关系进行建模并进行对比分析.应用研究表明,基于MCMC方法的时变Copula模型能更有效地度量基金收益率序列的风险. 相似文献
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一类指数和函数的性质及其应用 总被引:1,自引:0,他引:1
丁勇 《数学的实践与认识》2005,35(11):194-198
对一类指数和函数的递推关系、积分公式、曲线的单峰形态等性质进行了讨论,证明了该函数为概率密度函数,并给出了该函数在等式证明、物质转化反应的微分方程模型等方面的应用. 相似文献