过离散次数分布模型的尾部特征

在保险精算和生物统计等领域,离散型次数分布模型的应用十分广泛.当实际数据的尾部较长(即过离散),且零点的概率较大时,许多模型的拟合效果往往欠佳.本文通过计算概率之比的极限和偏度系数,对混合泊松分布和复合泊松分布的右尾特征和零点概率进行了比较,给出了它们的尾部排列顺序,以及尾部长短与零点概率的关系,从而为模型的构造或选择提供了一种指导.本文最后应用一组实际数据说明了在构造或选择次数分布模型时如何考虑尾部特征,从而改善对实际数据的拟合效果.     

The Exact and Limiting Distributions for the Number of Successes in Success Runs Within a Sequence of Markov-Dependent Two-State Trials

The total number of successes in success runs of length greater than or equal to k in a sequence of n two-state trials is a statistic that has been broadly used in statistics and probability. For Bernoulli trials with k equal to one, this statistic has been shown to have binomial and normal distributions as exact and limiting distributions, respectively. For the case of Markov-dependent two-state trials with k greater than one, its exact and limiting distributions have never been considered in the literature. In this article, the finite Markov chain imbedding technique and the invariance principle are used to obtain, in general, the exact and limiting distributions of this statistic under Markov dependence, respectively. Numerical examples are given to illustrate the theoretical results.     

Generalized binomial and negative binomial distributions of order<Emphasis Type="Italic">k</Emphasis> by the<Emphasis Type="Italic">l</Emphasis>-overlapping enumeration scheme

In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number of trials and derive the probability generating functions. The present work extends several properties of distributions of orderk and leads us a new type of geneses of the discrete distributions.     

The Total Embedding Distributions of Cacti and Necklaces

Total embedding distributions have been known for only a few classes of graphs. In this paper the total embedding distributions of the cacti and the necklaces are obtained. Furthermore we obtain the total embedding distributions of all graphs with maximum genus 1 by using the method of this paper.     

Joint Distributions of the Numbers of Visits for Finite-State Markov Chains

For a discrete-time Markov chain with finite state space {1, …, r} we consider the joint distribution of the numbers of visits in states 1, …, r−1 during the firstNsteps or before theNth visit tor. From the explicit expressions for the corresponding generating functions we obtain the limiting multivariate distributions asN→∞ when staterbecomes asymptotically absorbing and forj=1, …, r−1 the probability of a transition fromrtojis of order 1/N.     

Exact and limiting distributions of the number of successions in a random permutation

Traditionally the distributions of the number of patterns and successions in a random permutation ofn integers 1,2, ..., andn were studied by combinatorial analysis. In this short article, a simple way based on finite Markov chain imbedding technique is used to obtain the exact distribution of successions on a permutation. This approach also gives a direct proof that the limiting distribution of successions is a Poisson distribution with parameter =1. Furthermore, a direct application of the main result, it also yields the waiting time distribution of a succession.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant NSERC A-9216, and National Science Council of Republic of China under Grant 85-2121-M-259-003.     

On the Law of The Iterated Logarithm for Rapidly Increasing Subsequences

The usual law of the iterated logarithm states that the partial sums S_n of independent and identically distributed random variables can be normalized by the sequence a_n = √nlog log n, such that limsup_n→∞ S_n/a_n = √2 a.s. As has been pointed out by Gut (1986) the law fails if one considers the limsup along subsequences which increase faster than exponentially. In particular, for very rapidly increasing subsequences {n_k≥1} one has limsup_k→∞ S_nk/a_nk = 0 a.s. In these cases the normalizing constants a_nk have to be replaced by √nk log k to obtain a non-trivial limiting behaviour: limsup_k→∞ S_nk/ √nk log k = √2 a.s. We will present an intelligible argument for this structural change and apply it to related results.     

Theorems of Large Deviations in the Approximation by the Compound Poisson Distribution

The paper is devoted to the research of large deviation probabilities in the approximation by compound Poisson law.     

线形(n,f,k)系统和系统的可靠度计算新方法

本文应用两端同时进行的有限马尔可夫链嵌入法给出了具有复合失效准则的(n,f,k)系统和系统可靠度计算公式及公式中连接矩阵的结构特点。数值计算结果表明,随着构成系统的单元个数的增加,应用两端同时进行的有限马尔可夫链嵌入法比应用传统的有限马尔可夫链嵌入法计算可靠度能节省大量运算时间,特别是对于具有对称结构的(n,f,k)和系统效果更加明显。     

利用皮尔逊分布族计算非正态分布工序能力指数

本文利用皮尔逊分布族设计了一种计算非正态分布工序能力的方法。它可用于工序分布形式完全未知的情况。     

双复合泊松风险模型下的投资问题

在经典风险模型基础上,研究了保险公司保费收入和索赔均服从复合泊松过程的双复合泊松风险模型,针对最优投资策略和求解破产时刻惩罚金期望折现函数的问题,利用重期望公式和马氏性得到期望折现函数满足的带边界条件的二阶积分微分方程,通过高效的Sinc数值方法求出折现函数的近似数值解,从而由图像分析破产概率变化的趋势.     

Computation of the Optimal Policy for the Control of a Compound Immigration Process through Total Catastrophes

In this paper we consider a Markov decision model introduced by Economou (2003), in which it was proved that the optimal policy in the problem of controlling a compound immigration process through total catastrophes is of control-limit type. We show that the average cost of a control-limit policy is unimodal as a function of the critical point. This result enables us to design very efficient algorithms for the computation of the optimal policy as the bisection procedure and a special-purpose policy iteration algorithm that operates on the class of control-limit policies.AMS 2000 Subject Classification: Primary 9OC40; Secondary 6OJ25     

增长网络的形成机理和度分布计算

关于增长网络的形成机理,着重介绍由线性增长与择优连接组成的BA模型, 以及加速增长模型.此外,我们提出了一个含反择优概率删除旧连线的模型,这个模型能自组织演化成scale-free(SF)网络.关于计算SF网络的度分布,简要介绍文献上常用的基于连续性理论的动力学方法(包括平均场和率方程)和基于概率理论的主方程方法.另外,我们基于马尔可夫链理论还首次尝试了数值计算方法.这一方法避免了复杂方程的求解困难,所以较有普适性,因此可用于研究更为复杂的网络模型.我们用这种数值计算方法研究了一个具有对数增长的加速增长模型,这个模型也能自组织演化成SF网络.     

血型分布规律初探

以马氏链为工具对人类 ABO血型的分布规律做了初步探讨 .用群体遗传学的理论对所建数学模型进行了解释和论证 .提出了一个新的检验稳定 (即平衡 )的方法 .     

Comparison of the Bayesian and Randomised Decision Tree Ensembles within an Uncertainty Envelope Technique

Multiple Classifier Systems (MCSs) allow evaluation of the uncertainty of classification outcomes that is of crucial importance for safety critical applications. The uncertainty of classification is determined by a trade-off between the amount of data available for training, the classifier diversity and the required performance. The interpretability of MCSs can also give useful information for experts responsible for making reliable classifications. For this reason Decision Trees (DTs) seem to be attractive classification models for experts. The required diversity of MCSs exploiting such classification models can be achieved by using two techniques, the Bayesian model averaging and the randomised DT ensemble. Both techniques have revealed promising results when applied to real-world problems. In this paper we experimentally compare the classification uncertainty of the Bayesian model averaging with a restarting strategy and the randomised DT ensemble on a synthetic dataset and some domain problems commonly used in the machine learning community. To make the Bayesian DT averaging feasible, we use a Markov Chain Monte Carlo technique. The classification uncertainty is evaluated within an Uncertainty Envelope technique dealing with the class posterior distribution and a given confidence probability. Exploring a full posterior distribution, this technique produces realistic estimates which can be easily interpreted in statistical terms. In our experiments we found out that the Bayesian DTs are superior to the randomised DT ensembles within the Uncertainty Envelope technique.     

The Spectrum of the Independent Metropolis–Hastings Algorithm

In this paper we perform a spectral analysis for the kernel operator associated with the transition kernel for the Metropolis–Hastings algorithm that uses a fixed, location independent proposal distribution. Our main result is to establish the spectrum of the kernel operator T in the continuous case, thereby generalizing the results obtained by Liu in (Statist. Comput. 6, 113–119 1996) for the finite case.     

用有限差分—Chebyshev Tau方法求Poisson方程的准确解

提出了一种求解二维Poisson方程的新方法－有限差分－Chebyshev Tau方法,并给出了一些有关的数值结果,结果表明,这一方法是令人满意的,且与其它方法相容。     

Model‐based quantification of the volatility of options at transaction level with extended count regression models

In this paper, we elaborate how Poisson regression models of different complexity can be used in order to model absolute transaction price changes of an exchange‐traded security. When combined with an adequate autoregressive conditional duration model, our modelling approach can be used to construct a complete modelling framework for a security's absolute returns at transaction level, and thus for a model‐based quantification of intraday volatility and risk. We apply our approach to absolute price changes of an option on the XETRA DAX index based on quote‐by‐quote data from the EUREX exchange and find that within our Bayesian framework a Poisson generalized linear model (GLM) with a latent AR(1) process in the mean is the best model for our data according to the deviance information criterion (DIC). While, according to our modelling results, the price development of the underlying, the intrinsic value of the option at the time of the trade, the number of new quotations between two price changes, the time between two price changes and the Bid–Ask spread have significant effects on the size of the price changes, this is not the case for the remaining time to maturity of the option. Copyright © 2006 John Wiley & Sons, Ltd.     

Joint Distributions of Numbers of Success-runs Until the First Consecutive k Successes in a Higher-Order Two-State Markov Chain

Let X-m+1, X-m+2,.., X0, X1, X2,.., be a time-homogeneous {0, 1}-valued m-th order Markov chain. Joint distributions of the numbers of trials, failures and successes, of the numbers of trials and success-runs of length l (m l k) and of the numbers of trials and success-runs of length l (l m k) until the first consecutive k successes are obtained in the sequence X1, X2,.., There are some ways of counting numbers of runs of length l. This paper studies the joint distributions based on four ways of counting numbers of runs, i.e., the number of non-overlapping runs of length l, the number of runs of length greater than or equal to l, the number of overlapping runs of length l and the number of runs of length exactly l. Marginal distributions of them can be obtained immediately, and surprisingly their distributions are very simple.