关于NA列部分和上升的阶

本文在不使用随机有界或矩一致有界的条件下，给出了不同分布NA列部分和上升的阶的某种意义上的最佳估计，并给出了不同分布NA列服从Kolmogorov强大数律的某种意义上的充分必要条件，最后本文对一般随机变量讨论了类似的问题．     

PP Cramèr-von Mises统计量P值的近似计算

本文给出了PPCramer－vonMises统计量极限分布的一种近似计算方法，用一个г分布作为极限分布的近似．当总体分别服从圆周上均匀分布及二元正态分布时，通过模拟计算相应的P值，发现该近似计算办法合理可行．     

多元极值分布随机向量的抽样方法

本文考虑如何在计算机上模拟产生服从多元极值分布的随机向量，并给山一个精确且简单的算法．讨论主要限于Logistic模型及嵌套Logiotic模型．     

异常数据检验的屏蔽效应

本文对屏蔽效应的一系列定理进行了归纳和证明，针对极值分布或威布尔分布，讨论了文献[1]中提出的六种检验统计量的屏蔽效应，文中仅给出了对Dixon型和F型统计量的结果，说明F型统计量能避免屏蔽效应。     

多个独立同分布应力作用下的极值型─极值型(Ⅰ-Ⅲ)模式的结构可靠性估计

本文讨论了在多个独立同分布应力作用下的极值型－极值型（Ⅰ－Ⅲ）模式结构可靠性估计，给出了分布参数及结构可靠度的短估计．极大似然估计及量信下限．     

方差函数确定指数族的条件

本文以矩量问题的分布函数解为工具,给出了方差函数(V(m),M_0)确定REF(V(m),M)的充分必要条件.此外,作者还得到矩量问题有限支撑分布函数解存在的一个充分必要条件.     

两指标双F统计过程控制图

当产品质量指标服从二元正态分时,可用T2控制图与Λ控制图联合判断产品生产的过程是否处于受控状态。本文利用T2统计量与F统计量、Λ统计量与F统计量之间的关系,得到了两指标情形下两类基于F分布统计量的统计过程控制图,简称双F统计过程控制图,并给出了控制图应用实例。     

加权PP型Crmer-Von Mises统计量的极限分布及其展开式

给出了高维分布假设检验中的加权ＰＰ型Ｃｒａｍｅｒ－Ｖｏｎ Ｍｉｓｅｓ检验统计量，并在零假设为一般分布情形下获得其统计量的极限分布及其分布展开式．     

随机需求弹性及在经济分析中的应用

引入随机弹性的概念及随机弹性的相关性质，进而给出随机需求弹性．利用随机需求弹性分析了当消费群体的收入为随机变量时，其收入对需求量的变化和影响．给出了当收入服从某种分布时，需求量的弹性分布．     

极值分布和威布尔分布异常数据的检验方法

本文对威布尔分布的极值分布异常数据的检验给出了一系列的方法，首先，导入了极值分布下一般Ｄｉｘｏｎ型统计量的精确分布，同时还给出了改进的Ｇ型统计量，及它们的分位点表。最后本文提出了一个新的统计量；Ｆ型统计量，并用Ｍｏｎｔｅ－Ｃａｒｌｏ模拟的方法给出其分位点表，从而首次给出威布尔分布异常值的直接检验方法。本文进一步讨论了这些检验方法的功效，且表明Ｆ型检验是最优的。     

Some properties and generalizations of multivariate Eyraud-Gumbel-Morgenstern distributions

The admissible values of the coefficient in a bivariate Eyraud-Gumbel-Morgenstern (EGM) distribution are found. For multivariate EGM distributions necessary and sufficient conditions are given for its coefficients, and its conditional distributions are found and shown to belong to a family of distributions further extending the multivariate EGM family.     

A space of generalized distributions

In this paper we use a duality method to introduce a new space of generalized distributions. This method is exactly the same introduced by Schwartz for the distribution theory. Our space of generalized distributions contains all the Schwartz distributions and all the multipole series of physicists and is, in a certain sense, the smallest space containing all these series. To The Memory of Laurent Schwartz     

Quasi-stationarity and quasi-ergodicity of general Markov processes

In this paper, we study the quasi-stationarity and quasi-ergodicity of general Markov processes. We show, among other things, that if X is a standard Markov process admitting a dual with respect to a finite measure m and if X admits a strictly positive continuous transition density p(t, x, y) (with respect to m) which is bounded in (x, y) for every t > 0, then X has a unique quasi-stationary distribution and a unique quasi-ergodic distribution. We also present several classes of Markov processes satisfying the above conditions.     

Some Truncated Distributions

Long-tailed distributions arise in many areas of the sciences. These distributions, however, suffer from the weakness of not having finite moments of all orders and this weakness has restricted their use. In this note, we introduce truncated versions of five of the most commonly known long-tailed distributions—which possess finite moments of all orders and could therefore be better models. Explicit expressions for the moments are derived for each of the truncated distributions. Several applications are illustrated using real data.     

强次指数分布族S*(γ)的μ积分尾分布的卷积等价性

在Klüppelberg提出强次指数分布族并研究其积分尾分布的次指数性的基础上,推广Foss等关于强次指数分布族S*的μ积分尾分布的次指数性结果,得到S*(γ)的μ积分尾分布的卷积等价性.     

Waiting Time Distributions Associated with Runs of Fixed Length in Two-State Markov Chains

In the present article a general technique is developed for the evaluation of the exact distribution in a wide class of waiting time problems. As an application the waiting time for the r-th appearance of success runs of specified length in a sequence of outcomes evolving from a first order two-state Markov chain is systematically investigated and asymptotic results are established. Several extensions and generalisations are also discussed.     

Marshall and Olkin’s Distributions

A review is provided of the continuous and discrete distributions introduced by the eminent Professors Marshall and Olkin. The topics reviewed include: bivariate geometric distribution, extreme value behavior, bivariate negative binomial distribution, bivariate exponential distribution, concomitants, reliability, distributions of sums and ratios, Ryu’s bivariate exponential distribution, bivariate Pareto distribution and generalized exponential and Weibull distributions. Some hitherto unknown results about these distributions are also mentioned. This is a tribute to the work of Professors Marshall and Olkin.     

Vacuum expectation values of quantum fields

We propose a new system of vacuum expectation values for quantum fields. For finite series, these distributions satisfy the linear Wightman axioms. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 41–63, October, 2008.     

Decompounding poisson random sums: Recursively truncated estimates in the discrete case

Given a sample from a discrete compound Poisson distribution, we consider variants of plug-in and likelihood estimators for the corresponding base distribution. These proceed recursively with an intermediate truncation step. We discuss the asymptotic behaviour of the estimators and give some numerical examples. Both procedures compare favourably with the straightforward and the naively projected plug-in estimator that we introduced in Buchmann and Grübel (2003,The Annals of Statistics,31, 1054–1074).     

Distribution and moments of the vector of the maximum of two absolutely continuous random vectors

In this paper, we determine the exact distribution of the vector of the componentwise maximum of two absolutely continuous dependent random vectors and we show that it is a finite mixture of particular skew distributions studied in the literature. The results are detailed when the two vectors are elliptically distributed and some particular cases are discussed. The exact expression of the covariance matrix is obtained in the normal case.