Asymptotic distributions of non-central studentized statistics

Let X1,...,Xn be independent and identically distributed random variables and Wn = Wn(X1,...,Xn) be an estimator of parameter θ.Denote Tn =(Wn - θ0)/sn,where sn2 is a variance estimator of Wn.In this paper a general result on the limiting distributions of the non-central studen-tized statistic Tn is given.Especially,when s2n is the jacknife estimate of variance,it is shown that the limit could be normal,a weighted χ2 distribution,a stable distribution,or a mixture of normal and stable distribution.Applicati...     

US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology

We study the problem of suitably locating US Coast Guard air stations to respond to emergency distress calls. Our goal is to identify robust locations in the presence of uncertainty in distress call locations. Our analysis differs from the literature primarily in the way we model this uncertainty. In our optimization and simulation based methodology, we develop a statistical model and demonstrate our procedure using a real data set of distress calls. In addition to guiding strategic decisions of placement of various stations, our methodology is also able to provide guidance on how the resources should be allocated across stations.     

样本区间的概率分布

设(X1，X2，…Xn)为服从I=[0,1]上均匀分布的容量为n的简单随机样本，它们将I=[0，1]分隔成(n 1)个样本区间(sample spacing)．记Y0,Y1，…Yn分别为这些样本区间的长度，又设Zx(x,ω)为包含点X∈I的唯一的左闭右开区间的长度．由于随机选取的点集被广泛运用于许多概率模型中．例如流行病学、遗传学、时间序列分析以及交通流理论等．因此，对Zn(x)及其相关统计量分布的研究也就引起了人们的广泛关注．本文利用顺序统计量的性质讨论了Yi(O≤i≤n)以及Zn(x，ω)的概率分布，有利于今后对上述理论的研究。     

二项分布下的一种贝叶斯可靠性验收试验方案

为了合理利用先验信息制定可靠性验收试验方案，以降低验收试验的费用，在进行可靠性定型试验的前提下，提出了一种先验信息加工方法，并根据生产与使用双方实际所关心的风险意义，制定了产品可靠性验收试验的一种贝叶斯方案。算例结果证实，该方案在保证了生产方与使用方利益的前提下，减少了试验量，降低了验收试验费用。说明所提出的先验信息利用方式是有效的。     

On the Statistics of Partial Quotients of Finite Continued Fractions

We refine the remainder estimate in the asymptotic formula, earlier obtained in a joint paper with V. A. Bykovskii, for Arnold's problem about Gauss-Kuzmin statistics.     

Rook theory and cycle-counting permutation statistics

A statistic is found to combinatorially generate the cycle-counting q-hit numbers, defined algebraically by Haglund [Adv. in Appl. Math. 17 (1996) 408–459]. We then define the notion of a cycle-Mahonian pair of statistics (generalizing that of a Mahonian statistic), and show that our newly discovered statistic is part of such a pair. Finally, we note a second example of a cycle-Mahonian pair of statistics which leads us to define the stronger property of being a cycle-Euler–Mahonian pair.     

An Algebraic Method for the Exact Solution of the Partition Function of the Canonical Ensemble in Nuclear Multifragmentation

We propose a unified method for deducing recursive relations for the canonical partition function of a system of noninteracting particles with charge conservation if the particles follow the Bose–Einstein, Fermi–Dirac, or Maxwell–Boltzmann statistics or parastatistics. For all these types of statistics, we find recursive relations for the partition function of a new statistical model of nuclear multifragmentation with electric charge and baryon number conservation, accounting for the internal degrees of freedom of the nuclear fragments.     

Multiple Window and Cluster Size Scan Procedures

Researchers apply scan statistics to test for unusually large clusters of events within a time window of specified length w, or alternatively an unusually small window w that contains a specified number of events. In some cases, the researcher is interested in testing for a range of specified window lengths, or a set of several specified number of events k (cluster sizes). In this paper, we derive accurate approximations for the joint distributions of scan statistics for a range of values of w, or of k, that can be used to set an experiment-wide level of significance that takes into account the multiple comparisons involved. We use these methods to compare different ways of choosing the window sizes for the different cluster sizes. One special case is a multiple comparison procedure based on a generalized likelihood ratio test (GLRT) for a range of window sizes. We compare the power of the GLRT with another method for allocating the window sizes. We find that the GLRT is sensitive for very small window sizes at the expense of moderate and larger window sizes. We illustrate these results on two examples, one involving clustering of translocation breakpoints in DNA, and the other involving disease clusters.     

Stability of invariant linearly sufficient statistics in the general Gauss-Markov model

Necessary and sufficient conditions are derived for the inclusions and to be fulfilled where are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models , respectively.     

血清唾液酸与动脉粥样硬化危险因素的多元统计分析

应用酶法快速检测盒测定１２１例患者血清唾液酸（ＳｉａｌｉｃＡｃｉｄ，即ＳＡ）浓度，用酶法及免疫扩散法同步测定血脂，载脂蛋白，其测定值经多元线性回归统计分析，结果发现血清平均唾液酸浓度与血浆总胆固醇（ＴＣ），甘油三脂（ＴＧ），致动脉粥样硬化指数（ＡＰＯＢ／ＡＰＯＡＩ）成正相关，与高密度脂蛋白胆固醇（ＨＤＬ—Ｃ）成负相关，提示血清唾液酸浓度受血脂的影响，可作为评估动脉粥样硬化危险因素的指标。