离散型随机变量高阶原点矩的一种新的递推计算方法

针对服从二项、泊松、几何、负二项、超几何、负超几何以及对数级数分布等离散型随机变量,给出了求其高阶原点矩的一个较为简单的递推计算方法.不仅非常容易地求出这些离散型随机变量的高阶原点矩,避免了计算阶乘矩或求导等复杂的运算,而且便于学生理解.论文还给出了这些离散型随机变量的3阶和4阶原点矩的表达式.     

求解幂级数型分布矩的一个注记

矩是概率论中的一个重要概念,有着广泛的应用.幂级数型分布包括了一些常见的概率分布,根据幂级数型分布解析表达式的特点,通过求导的方法,分别给出了原点矩和中心矩的递推公式,降低了求解高阶矩的计算难度.经过实例分析验证,该方法对幂级数类型的概率分布矩的计算是行之有效的方法.     

常用离散型随机变量的高阶原点矩

对离散型随机变量的高阶矩进行了研究,给出了几类离散型随机变量的高阶原点矩的统一递推公式,得到了离散型随机变量的高阶原点矩的形式特征.     

离散型随机变量k阶矩的计算

讨论了离散型随机变量k阶矩的计算问题·利用概率母函数和第一类Stirling数推导了k阶矩满足的统一递推表达式,并以常见的四种离散分布:二项分布、几何分布、泊松分布和负二项分布为例,借助数学计算软件mathematica给出了各自的前6阶矩的具体表达式.     

多元广义泊松分布的参数估计与诊断

广义泊松分布是普通泊松分布的自然推广,克服均值与方差相等的局限性.在计数数据中,常常会有多变量的情形,比如保险保单定价.因此文章考虑多元广义泊松分布的参数估计和假设检验问题,针对共协方差多元广义泊松模型提出两种参数估计的方法,矩估计方法和极大似然估计方法,并比较两种方法的优劣性.文章就多元广义泊松分布的假设检验问题,主要探讨了其退化检验及独立性检验,由于参数及变量较多,运用似然比检验方法构造服从卡方分布的检验统计量.最后,运用多元广义泊松理论分析不同地区森林发生火灾的次数,首先用文中提到的检验方法诊断数据是否可以用多元广义泊松分布,其次进行参数估计及实际问题的分析解释.     

Dividend payments in the perturbed compound poisson risk model with liquid reserve and interest

考虑一类资产盈余具有流动储备金和利率的带干扰的复合泊松风险模型的分红问题,得到了累积分红现值的矩母函数,n阶原点矩所满足的积分-微分方程及边界条件,并给出了索赔额为指数分布时相应积分-微分方程解的具体表达式.     

关于混合泊松分布之Willmot递推式的一个拓广

混合泊松分布的计算复杂与否视其结构分布而定.文章给出了结构分布密度函数满足一类一阶线性微分方程的混合泊松分布计算的递推式,它是Willmot递推式的一个拓广.     

非齐次泊松过程下的截断δ-冲击模型

本文研究了一类特殊的冲击模型-截断δ-冲击模型,利用可靠性理论得到了此类冲击模型系统寿命可靠度函数及其上界、矩存在的充分条件、失效率函数及寿命分布类,将截断δ-冲击模型由基础过程为齐次泊松过程情形推广到了非齐次泊松过程情形.     

基于离散枢轴量的泊松分布参数的精确最短置信区间

将泊松分布参数的充分统计量的离散型分布函数转化为生存伽马分布函数,以此为枢轴量构造了泊松分布参数的精确置信区间.通过数值模拟,选择合适的置信度组合,得到精确最短置信区间.讨论了大样本下泊松分布参数的近似置信区间的估计精度,验证了精确最短置信区间的计算结果.     

基于问题驱动的泊松分布教学设计

本文采用问题驱动的教学模式,探讨了对泊松分布的教学设计.从交通路口拥堵程度的评估问题入手,建立基于二项分布的概率模型,利用连续问题离散化的思想,引出泊松分布及泊松定理,最后计算交通路口拥堵的概率.     

THE EXISTENCE OF MOMENTS OF NONLINEAR AUTOREGRESSIVE MODEL

1.IntroductionConsiderthefollowingnonlinearautoregressivemodelwhere{E,}isasequenceofindependentidenticallydistributedrandomvariableswithacommonalmosteverywherepositivedensityandfinitefirstmoment.stisindependentofat--s)s21.op')isameasurablefunctionfromRP-- RI.Writewhere"T"standsfortransposeofamatrixoravector.Then(1)canberewritteninthevectorformX,=T(Xt--l) et'(2)Sinceweneedthestrictstationarity,ergodicityandtheexistenceofcertainmomentsintheestimationtheoryoftimeseries,thegeometricalergodicit…     

广义Pareto模型统计推断及其应用

广义Pareto分布能很好地拟合数据分布的尾部,广泛地应用于金融市场的风险管理、风险经营问题的研究。利用概率加权矩法得到了三参数广义Pareto模型的参数估计式,给出了阈值的选取方法和风险值的计算公式;利用计算机模拟,计算得出了KS检验统计量的临界值。     

Effective multipoles in random media

Abstract

In a homogeneous medium, the far field generated by a localized source can be expanded in terms of multipoles; the coefficients are determined by the moments of the localized charge distribution. We show that this structure survives to some extent for a random medium in the sense of quantitative stochastic homogenization: In three space dimensions, the effective dipole and quadrupole – but not the octupole – can be inferred without knowing the realization of the random medium far away from the (overall neutral) source and the point of interest. Mathematically, this is achieved by using the two-scale expansion to higher order to construct isomorphisms between the hetero- and homogeneous versions of spaces of harmonic functions that grow at a certain rate, or decay at a certain rate away from the singularity (near the origin); these isomorphisms crucially respect the natural pairing between growing and decaying harmonic functions given by the second Green’s formula. This not only yields effective multipoles (the quotient of the spaces of decaying functions) but also intrinsic moments (taken with respect to the elements of the spaces of growing functions). The construction of these rigid isomorphisms relies on a good (and dimension-dependent) control on the higher-order correctors and their flux potentials.     

On size-biased Consul distribution

In this paper, a size-biased Consul distribution (SBCOND) is defined. Recurrence relations for central moments and the moments about origin are obtained. Different estimation methods for the parameters of the model are discussed. A comparative analysis is done among the three different estimation methods and the proposed model is compared with the generalized logarithmic series distribution (GLSD) and simple Consul distribution.     

A higher-order moment method of the lattice Boltzmann model for the conservation law equation

In this paper, we proposed a higher-order moment method in the lattice Boltzmann model for the conservation law equation. In contrast to the lattice Bhatnagar–Gross–Krook (BGK) model, the higher-order moment method has a wide flexibility to select equilibrium distribution function. This method is based on so-called a series of partial differential equations obtained by using multi-scale technique and Chapman–Enskog expansion. According to Hirt’s heuristic stability theory, the stability of the scheme can be controlled by modulating some special moments to design the third-order dispersion term and the fourth-order dissipation term. As results, the conservation law equation is recovered with higher-order truncation error. The numerical examples show the higher-order moment method can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the conservation law equation.     

A lattice Boltzmann model for the eddy–stream equations in two-dimensional incompressible flows

A lattice Boltzmann model for two-dimensional incompressible flows with eddy–stream equations is proposed. By using two kinds of distribution functions and employing several higher-order moments of equilibrium distribution functions, the eddy equation and stream function equation with the second-order truncation error are obtained. In the numerical examples, we compared the numerical results of this scheme with those obtained by other classical method. The numerical results agree well with the classical ones.     

The Distribution of the Sojourn Time for the Brownian Excursion

The solutions of various problems in the theories of queuing processes, branching processes, random graphs and others require the determination of the distribution of the sojourn time (occupation time) for the Brownian excursion. However, no standard method is available to solve this problem. In this paper we approximate the Brownian excursion by a suitably chosen random walk process and determine the moments of the sojourn time explicitly. By using a limiting approach, we obtain the corresponding moments for the Brownian excursion. The moments uniquely determine the distribution, enabling us to derive an explicit formula.     

A heavy-traffic-limit formula for the moments of the stationary distribution in GI/G/1-type Markov chains

This paper studies the heavy-traffic limit of the moments of the stationary distribution in GI/G/1-type Markov chains. For these Markov chains, several researchers have derived heavy-traffic-limit formulas for the stationary distribution itself. However, for its moments, no such formulas have been reported in the literature. This paper presents a heavy-traffic-limit formula for the moments of the stationary distribution and a sufficient condition for the formula to hold, by using a characteristic function approach.     

风险非同质时索赔次数的分布拟合的估计与检验问题

在非寿险精算中 ,索赔次数的分布一般假设为泊松分布 P(λ) .风险非同质时 λ的分布称为混合分布 .本文考虑了混合分布为三参数伽玛分布时的参数估计以及位置参数的检验问题