有限T-IPH/Geo/1/N排队平稳指标的数值计算

讨论了T-IPH/Geo/1/N有限排队,其中T-IPH表示可数状态吸收生灭链吸收时间的分布.对该排队模型,用有限位相拟生灭(QBD)过程进行建模.首先得到了计算该QBD过程率阵非零元素的迭代公式;其次在所得结果的基础上,进一步给出了T-IPH/Geo/1/N排队平稳队长以及等待时间分布的公式.     

一类休假排队平稳队长分布的无限位相表示

讨论休假时间服从T-SPH分布的M/M/1单重休假模型,其中T-SPH表示可数状态吸收生灭过程吸收时间的分布.该排队模型可以用可数位相拟生灭过程(QBD过程)和算子几何解的方法进行建模分析.首先得到了QBD过程算子几何解的具体形式;其次在所得结果的基础上,进一步给出了排队模型平稳队长的随机分解结果,并说明附加队长服从离散时间无限位相分布.     

对一类离散时间休假排队平稳指标的数值计算与渐近分析

本文研究休假时间服从T-IPH分布的Geo/Geo/1休假排队,其中T-IPH分布是由可数状态吸收生灭链定义的离散时间无限位相分布.对多重休假和单重休假两种情形,基于系统平稳方程和复分析方法,首先得到了排队系统平稳队长和平稳逗留时间的概率母函数(PGF);其次,通过对PGF分析,进一步得到了平稳附加队长和附加逗留时间分...     

T-SPH排队队长平稳分布的尾部分析

在复杂随机模型的研究中,经常会出现水平和位相都是无限的拟生灭过程,对这类过程,平稳分布的计算仍然是一个未很好解决的难题.然而对一类比较特殊三对角无限位相拟生灭过程,简记为T-QBD过程,文献[1]指出,在一定条件下可以估计其平稳分布的尾部特征.本文对文献[1]1中提出的方法在某一环节上作了改进,使之更适合于实际计算,并用此方法分析了两个具有实际应用背景的排队模型,即T-SPH/M/1排队和M/T-SPH/1排队,分析结果表明,在一定条件下,这两类排队系统的队长分布的尾部都具有几何衰减的特性.     

对Geo/Geo/1抢占优先权排队平稳队长的分析

讨论了Geo/Geo/1抢占优先权排队模型,该模型可以用一个具有可数位相的拟生灭(QBD)过程来描述.对该过程,首先给出率算子以及联合平稳分布的结果.在此基础上,进一步得到了平稳状态时低优先权顾客数分布的概率母函数,并证明低优先权顾客数可以分解为两个相互独立的随机变量之和.     

对一类等待空间有限的抢占优先权排队的分析

讨论M/M/1抢占优先权排队模型, 且假设低优先权顾客的等待空间有限. 该模型可以用有限位相拟生灭过程来描述. 由矩阵解析方法, 对该拟生灭过程进行了分析, 并得到排队模型平稳队长的计算公式, 最后还用数值 结果说明了方法的有效性.     

分析M/M/c排队忙期分布的一种新方法

用一种新方法讨论了经典M/M/c排队的忙期分布.通过构造吸收Markov过程,并应用无限位相分布方法,给出了计算该排队模型忙期分布Laplace-Stieltjes变换(LST)的迭代公式.特别,对c=1,2,3等特殊情形,得到了忙期分布LST的具体表达式,并讨论了c=1,2时数字特征的计算问题.     

具有相继两类休假的M/M/1休假排队模型

讨论一个具有相继的两种类型休假策略的M/M/1休假排队模型.模型可以用QBD过程及矩阵解析方法分析.首先,得到了该QBD过程的联合平稳分布,在此基础上,进一步给出了所讨论排队模型平稳队长和平稳逗留时间的随机分解结果.     

生灭型半马氏骨架过程

本文首先引进了生灭型半马氏骨架过程的定义,求出了两骨架时跳跃点τn-1(ω)与τn(ω)之间的嵌入过程X(n)(t,ω)的初始分布及寿命分布.得到了生灭型半马氏骨架过程的一维分布.其次引进了生灭型半马氏骨架过程的数字特征并讨论了它们的概率意义及相互关系.讨论了生灭型半马氏骨架过程的向上和向下的积分型随机泛函.最后讨论了它的遍历性及平稳分布,求出了平均首达时间及平均返回时间.得到了常返和正常返的充分必要条件,求出了在正常返的条件下的平稳分布.     

不动点与Markov过程的稳定性

运用不动点方法与耦合技巧得到一般状态空间上Markov过程平稳分布存在唯一性和KRW概率距离下的稳定性判据.作为应用,讨论了扩散过程的稳定性.     

Discrete-time analysis of the GI/G/1 system with Bernoulli retrials: An algorithmic approach

In this paper, we show that the discrete GI/G/1 system with Bernoulli retrials can be analyzed as a level-dependent QBD process with infinite blocks; these blocks are finite when both the inter-arrival and service times have finite supports. The resulting QBD has a special structure which makes it convenient to analyze by the Matrix-analytic method (MAM). By representing both the inter-arrival and service times using a Markov chain based approach we are able to use the tools for phase type distributions in our model. Secondly, the resulting phase type distributions have additional structures which we exploit in the development of the algorithmic approach. The final working model approximates the level-dependent Markov chain with a level independent Markov chain that has a large set of boundaries. This allows us to use the modified matrix-geometric method to analyze the problem. A key task is selecting the level at which this level independence should begin. A procedure for this selection process is presented and then the distribution of the number of jobs in the orbit is obtained. Numerical examples are presented to demonstrate how this method works.     

Near-exact distributions for the independence and sphericity likelihood ratio test statistics

In this paper we show how, based on a decomposition of the likelihood ratio test for sphericity into two independent tests and a suitably developed decomposition of the characteristic function of the logarithm of the likelihood ratio test statistic to test independence in a set of variates, we may obtain extremely well-fitting near-exact distributions for both test statistics. Since both test statistics have the distribution of the product of independent Beta random variables, it is possible to obtain near-exact distributions for both statistics in the form of Generalized Near-Integer Gamma distributions or mixtures of these distributions. For the independence test statistic, numerical studies and comparisons with asymptotic distributions proposed by other authors show the extremely high accuracy of the near-exact distributions developed as approximations to the exact distribution. Concerning the sphericity test statistic, comparisons with formerly developed near-exact distributions show the advantages of these new near-exact distributions.     

一种四次有理插值样条及其逼近性质

1引言有理样条函数是多项式样条函数的一种自然推广,但由于有理样条空间的复杂性,所以有关它的研究成果不象多项式样条那样完美,许多问题还值得进一步的研究．近几十年来,有理插值样条,特别是有理三次有理插值样条,由于它们在曲线曲面设计中的应用,已有许多学者进行了深入研究,取得了一系列的成果(见[1]-[7])．但四次有理插值样条由于其构造所花费的计算量太大以及在使用上很不方便而让人们忽视了其重要的应用价值,因此很少有人研究他们．实际上,在某些情况下四次有理插值样条有其独特的应用效果,如文[8]建立的一种具有局部插值性质的分母为二次的四次有理样条,即一个剖分     

Dependence between two multivariate extremes

We extend the characterizations given by Takahashi (1988) for the independence and the total dependence of the univariate marginals of a multivariate extreme value distribution to its multivariate marginals. We also deal with the problem of how to measure the strength of the dependence among multivariate extremes. By presenting new definitions for the extremal coefficient, we propose measures that summarize the dependence between two multivariate extreme value distributions and preserve the main properties of the known bivariate coefficient for two univariate extreme value distributions. Finally, we illustrate these contributions to model the dependence among multivariate marginals with examples.     

The Matsumoto-Yor property and the structure of the Wishart distribution

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart.     

Second order tail asymptotics for the sum of dependent, tail-independent regularly varying risks

In this paper we consider dependent random variables with common regularly varying marginal distribution. Under the assumption that these random variables are tail-independent, it is well known that the tail of the sum behaves like in the independence case. Under some conditions on the marginal distributions and the dependence structure (including Gaussian copula’s and certain Archimedean copulas) we provide the second-order asymptotic behavior of the tail of the sum.     

Spectral analysis of large block random matrices with rectangular blocks

In this paper, we study the spectral properties of the large block random matrices when the blocks are general rectangular matrices. Under some moment assumptions of the underlying distributions, we prove the existence of the limiting spectral distribution (LSD) of the block random matrices. Further, we determine the Stieltjes transform of the LSD under the same moment conditions by demonstrating that it is the same as in the case where the underlying distributions are Gaussian.     

On sum of 0–1 random variables I. Univariate case

Summary Distribution of sum of 0–1 random variables is considered. No assumption is made on the independence of the 0–1 variables. Using the notion of “central binomial moments” we derive distributional properties and the conditions of convergence to standard distributions in a clear and unified manner.     

Application of the phase‐type mortality law to life contingencies and risk management

The class of phase‐type distributions has recently gained much popularity in insurance applications due to its mathematical tractability and denseness in the class of distributions defined on positive real line. In this paper, we show how to use the phase‐type mortality law as an efficient risk management tool for various life insurance applications. In particular, pure premiums, benefit reserves, and risk‐loaded premiums using CTE for standard life insurance products are shown to be available in analytic forms, leading to efficient computation and straightforward implementation. A way to explicitly determine provisions for adverse deviation for interest rate and mortality is also proposed. Furthermore, we show how the interest rate risk embedded in life insurance portfolios can be analyzed via interest rate sensitivity index and diversification index which are constructed based on the decomposition of portfolio variance. We also consider the applicability of phase‐type mortality law under a few non‐flat term structures of interest rate. Lastly, we explore how other properties of phase‐type distributions may be applied to joint‐life products as well as subgroup risk ordering and pricing within a given pool of insureds. Copyright © 2017 John Wiley & Sons, Ltd.