密度分布非均匀的反馈控制Logistic单种群模型平衡态的稳定性

本文对种群密度在非均匀分布情形下,考虑了具反馈控制的滞后 Logistic 生态模型平衡位置的稳定性;分别给出了在常时滞和弱连续时滞以及强连续时滞情况下的稳定性条件;其结果是对 Gopalsamy 在密度均匀分布情形下相应结果的推广.     

The EPA Health Risk Assessment of Methylcyclopentadienyl Manganese Tricarbonyl (MMT)

This paper describes the U.S. Environmental Protection Agency's assessment of potential health risks associated with the possible widespread use of a manganese (Mn)-based fuel additive, methylcyclopentadienyl manganese tricarbonyl (MMT). This assessment was significant in several respects and may be instructive in identifying certain methodological issues of general relevance to risk assessment. A major feature of the inhalation health risk assessment was the derivation of Mn inhalation reference concentration (RfC) estimates using various statistical approaches, including benchmark dose and Bayesian analyses. The exposure assessment component used data from the Particle Total Exposure Assessment Methodology (PTEAM) study and other sources to estimate personal exposure levels of particulate Mn attributable to the permitted use of MMT in leaded gasoline in Riverside, CA, at the time of the PTEAM study; on this basis it was then possible to predict a distribution of possible future exposure levels associated with the use of MMT in all unleaded gasoline. Qualitative as well as quantitative aspects of the risk characterization are summarized, along with inherent uncertainties due to data limitations.     

A Trivariate Distribution for the Height,Weight, and Fat of Adult Men*

Using exploratory data analysis, probability plots, scatterplots, and computer animations to rotate and visualize the data, we fit a trivariate Normal distribution to data for the height, the natural logarithm of body weight, and the body fat for 646 men between the ages of 50 and 80 years as reported by the medical staff of the U.S. Veterans Administration's “Normative Aging Study” in Boston, MA. Although these data do not include any children, women, or young men, the measurements represent the best data that we could find through a 4-year search. We believe that these data are well measured and reliable for men in the specified age range and that these data reveal an interesting statistical pattern for use in probabilistic PBPK models.     

由1971—2011年诺贝尔文学奖获奖情况反思中国文学

针对当前现状,以1971—2011年的诺贝尔文学奖四十年来的获奖情况为研究对象,从获奖作家所属的不同的国家分布、作家性别比例及和获奖作品风格与主旨这三个大的方面入手进行分析,探究诺贝尔文学奖的发展态势,概括和反思目前中国文学的发展状况,剖析中国作家莫言的获奖原因,由此提出对于中国作家要在诺贝尔文学奖中占有更多席位需要完善方面的建议和看法。     

Likelihood Factorizations for Mixed Discrete and Continuous Variables

Some general remarks are made about likelihood factorizations, distinguishing parameter-based factorizations and concentration-graph factorizations. Two parametric families of distributions for mixed discrete and continuous variables are discussed. Conditions on graphs are given for the circumstances under which their joint analysis can be split into separate analyses, each involving a reduced set of component variables and parameters. The result shows marked differences between the two families although both involve the same necessary condition on prime graphs. This condition is both necessary and sufficient for simplified estimation in Gaussian and for discrete log linear models.     

Weighted Approximations to Continuous Time Martingales with Applications

A weighted approximation to a sequence of continuous time martingales by a time transformed Wiener process is established. The basic tool of proof is the Skorohod imbedding for martingale difference sequences. As an application of the main result a useful weighted approximation to the randomly weighted uniform empirical process is derived. A number of other applications are also discussed.     

Random Bernstein Polynomials

Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1] which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non-parametric inference. In the second part of the paper, we study the posterior from a Bernstein–Dirichlet prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a changing dimension parameter space.     

Kernel Density Estimation with Generalized Binning

We propose kernel density estimators based on prebinned data. We use generalized binning schemes based on the quantiles points of a certain auxiliary distribution function. Therein the uniform distribution corresponds to usual binning. The statistical accuracy of the resulting kernel estimators is studied, i.e. we derive mean squared error results for the closeness of these estimators to both the true function and the kernel estimator based on the original data set. Our results show the influence of the choice of the auxiliary density on the binned kernel estimators and they reveal that non-uniform binning can be worthwhile.     

Beta-Bernstein Smoothing for Regression Curves with Compact Support

ABSTRACT. The problem of boundary bias is associated with kernel estimation for regression curves with compact support. This paper proposes a simple and uni(r)ed approach for remedying boundary bias in non-parametric regression, without dividing the compact support into interior and boundary areas and without applying explicitly different smoothing treatments separately. The approach uses the beta family of density functions as kernels. The shapes of the kernels vary according to the position where the curve estimate is made. Theyare symmetric at the middle of the support interval, and become more and more asymmetric nearer the boundary points. The kernels never put any weight outside the data support interval, and thus avoid boundary bias. The method is a generalization of classical Bernstein polynomials, one of the earliest methods of statistical smoothing. The proposed estimator has optimal mean integrated squared error at an order of magnitude n ^−4/5, equivalent to that of standard kernel estimators when the curve has an unbounded support.     

A Goodness-of-fit Test for Exponentiality Based on the Memoryless Property

In this investigation a test of goodness of fit for exponentiality is proposed. This procedure applies equally whether the scale and/or the location parameters of the distribution are known or not. The limiting null and non-null distributions of the test statistic are normal under minimal conditions. Monte Carlo critical values for small sample sizes are given and the power of the test is calculated for various alternatives showing that it compares favourably relatively to other more complicated published procedures.