On some special birth processes in biology

This paper presents some theorems on distributions associated with some special birth processes in biology.     

期货市场有效性理论与实证检验

本文以我国期货市场选取的六种期货的价格行为为对象,利用单位根检验与自相关检验的结合,并同时利用方差比检验和多重方差比检验来随机游走假设进行实证研究,目的在于探讨国内铜、大豆、小麦等六大期货市场是否呈有效态势。结果显示:各种检验方法得出的结论不尽一致,除上天胶外,各大期货市场的对数期货价格序列不能拒绝弱式有效市场假设。     

Some Limit Results for Pareto Random Variables

We sample m (m ≥ 1) i.i.d. Pareto random variables with the density function x ^?2 (x ≥ 1) and establish two large deviations for the partial sums. In addition, the maxima of sums of the two-tailed Pareto random variables is discussed and some asymptotical forms are obtained also.     

语用失误与大学英语教学

本文探讨大学英语教学中如何利用语用学来指导大学英语教学。     

网络弧生长对网络可靠性的影响

人们普遍认为,对于一般的网络图而言,当网络弧在生长时将有益于网络可靠性的增强。然而事实证明该论断并不完全正确。对于某些注重最短路径长度的网络而言:(1) 当网络>G受到随机攻击时,以网络最短路熵作为网络可靠性的判断依据,分别计算在增加一条弧前后网络结点或网络弧受到攻击而失效时的网络最短路熵,比较网络最短路熵的大小,熵值越大,可靠性越弱;(2) 当网络G受到恶意攻击时,根据悲观原则定义了一种新的可靠性指标,该指标值越大,网络可靠性越强。结果表明:(1) 当G与G'的最短路径长度相等时,G'的可靠性不弱于G;(2)当G与G'的最短路径长度不相等时,G与G'的可靠性相对大小关系不唯一。对该问题的研究有助于人们清楚的认识到网络弧生长对网络可靠性的影响。最后用简化的江苏省城市间高速公路网络图为例来说明该研究的有效性与实用性。     

A novel portfolio selection model in a hybrid uncertain environment

The future returns of each securities cannot be correctly reflected by the securities data in the past, therefore the statistical techniques and the experts’ judgement and experience are combined together to estimate the security returns in the future. In this paper, the returns of each securities are assumed to be fuzzy random variables, then following the ideas of mean variance model a new portfolio selection model in a hybrid uncertain environment is proposed. Moreover, the λ-mean variance efficient frontiers and λ-mean variance efficient portfolios are defined, and the properties of λ-mean variance efficient portfolios located on different λ-mean variance efficient frontiers are discussed. Finally, a numerical example is presented to illustrate the proposed portfolio selection model. On the basis of the results, we can conclude that the proposed model can provide the more flexible results.     

A sequential procedure for testing the existence of a random walk model in finite samples

Given the random walk model, we show, for the traditional unrestricted regression used in testing stationarity, that no matter what the initial value of the random walk is or its drift or its error standard deviation, the sampling distributions of certain statistics remain unchanged. Using Monte Carlo simulations, we estimate, for different finite samples, the sampling distributions of these statistics. After smoothing the percentiles of the empirical sampling distributions, we come up with a new set of critical values for testing the existence of a random walk, if each statistic is being used on an individual base. Combining the new sets of critical values, we finally suggest a general methodology for testing for a random walk model.     

TEST FOR TREATMENT EFFECT BASED ON BINARY DATA WITH RANDOM SAMPLE SIZES

The problem of testing for treatment effect based on binary response data is considered, assuming that the sample size for each experimental unit and treatment combination is random. It is assumed that the sample size follows a distribution that belongs to a parametric family. The uniformly most powerful unbiased tests, which are equivalent to the likelihood ratio tests, are obtained when the probability of the sample size being zero is positive. For the situation where the sample sizes are always positive, the likelihood ratio tests are derived. These test procedures, which are unconditional on the random sample sizes, are useful even when the random sample sizes are not observed. Some examples are presented as illustration.     

A Limit Theorem for Solutions of Inequalities

Let H ( p ) be the set { x ∈ X : h ( x ) ≤ p } where h is a real-valued lower semicontinuous function on a locally compact separable metric space X . This paper presents a general limit theorem for the sequence of random sets H _n ( p ) = { x ∈ X : h _n ( x ) ≤ p } n ≥ 1, where h _n , n ≥ 1, are functions that estimate h     

The Analysis of Methadone Clinic Data Using Marginal and Conditional Logistic Models with Mixture or Random Effects

The paper develops methods for the statistical analysis of outcomes of methadone maintenance treatment (MMT). Subjects for this study were a cohort of patients entering MMT in Sydney in 1986. Urine drug tests on these subjects were performed weekly during MMT, and were reported as either positive or negative for morphine, the marker of recent heroin use. To allow correlation between the repeated binary measurements, a marginal logistic model was fitted using the generalized estimating equation (GEE) approach and the alternating logistic regression approach. Conditional logistic models are also considered. Results of separate fitting to each patient and score tests suggest that there is substantial between-patient variation in response to MMT. To account for the population heterogeneity and to facilitate subject-specific inference, the conditional logistic model is extended by introducing random intercepts. The two, three and four group mixture models are also investigated. The model of best fit is a three group mixture model, in which about a quarter of the subjects have a poor response to MMT, with continued heroin use independent of daily dose of methadone; about a quarter of the subjects have a very good response, with little or no heroin use, again independent of dose; and about half the subjects responded in a dose-dependent fashion, with reduced heroin use while receiving higher doses of methadone. These findings are consistent with clinical experience. There is also an association between reduced drug use and increased duration in treatment. The mixture model is recommended since it is quite tractable in terms of estimation and model selection as well as being supported by clinical experience.