Small sample distribution of the likelihood ratio test in the random effects model

In this paper we examine the small sample distribution of the likelihood ratio test in the random effects model which is often recommended for meta-analyses. We find that this distribution depends strongly on the true value of the heterogeneity parameter (between-study variance) of the model, and that the correct p-value may be quite different from its large sample approximation. We recommend that the dependence of the heterogeneity parameter be examined for the data at hand and suggest a (simulation) method for this. Our setup allows for explanatory variables on the study level (meta-regression) and we discuss other possible applications, too. Two data sets are analyzed and two simulation studies are performed for illustration.     

以公平为取向调整收入分配政策的思考

在我国收入分配制度改革过程中，出现收入差距过大的一个重要原因，就是我们在认识上把公平与效率对立，片面强调效率原则。公平与效率应当作为政府调控收入分配的两个不同的取向，不存在一劳永逸的优先，而应当是相机抉择。当收入差距拉大到人们无法承受时，公平取向是我们不做出的选择。     

A Bayesian model for ranking hazardous road sites

Summary.  Road safety has recently become a major concern in most modern societies. The identification of sites that are more dangerous than others (black spots) can help in better scheduling road safety policies. This paper proposes a methodology for ranking sites according to their level of hazard. The model is innovative in at least two respects. Firstly, it makes use of all relevant information per accident location, including the total number of accidents and the number of fatalities, as well as the number of slight and serious injuries. Secondly, the model includes the use of a cost function to rank the sites with respect to their total expected cost to society. Bayesian estimation for the model via a Markov chain Monte Carlo approach is proposed. Accident data from 519 intersections in Leuven (Belgium) are used to illustrate the methodology proposed. Furthermore, different cost functions are used to show the effect of the proposed method on the use of different costs per type of injury.     

高能重离子碰撞中的夸克物质信号

用流体动力学模型研究一维流体的集体效应和相变对末态粒子分布的影响，结果表明：在ＲＨＩＣ－ＬＨＣ能区有相变和无相变时的末态快度分布形状是很不相同的，预计快度分部的形状可作为夸克物质形成的信号。     

激光束空间能量分布的CCD测量方法

介绍了一种激光束空间能量分布的快速测量新方法，该方法采用电荷耦合器件（ＣＣＤ）作为探测器，并采用微型计算机进行数据采集和处理，具有自动、实时、准确、直观等优点。文中还给出了Ｈｅ－Ｎｅ激光束（０．６３２８μｍ）的实验结果。     

Some Bayesian lower bounds on reliability in the lognormal distribution

The two-parameter lognormal distribution with density function f(y: γ, σ²) = [(2πσ²)^1/2y] ¹exp[?(ln y ? γ)²/2σ²], y > 0, is important as a failure-time model in life testing. In this paper, Bayesian lower bounds for the reliability function R(t: γ, σ²) = ?[(γ ? ln t)/σ] are obtained for two cases. First, it is assumed that γ is known and σ² has either an inverted gamma or “general uniform” prior distribution. Then, for the case that both γ and σ² are unknown, the normal-gamma prior and Jeffreys' vague prior are considered. Some Monte Carlo simulations are given to indicate some of the properties of the Bayesian lower bounds.     

Large sample interval estimation for the logarithmic series distribution

It is assumed that a large random sample of fixed size n is drawn from a logarithmic series distribution with parameter $tH and that it is desired to estimate e by means of two-sided confidence interval. Using asymptotic results, charts of confidence intervals are prepared for n = 50, 100, 200, 500 and 1,000, and confidence coefficients 0.90 and 0.95.     

Tests for the multivariate two-sample problem based on empirical probability measures

Nonparametric tests are proposed for the equality of two unknown p-variate distributions. Empirical probability measures are defined from samples from the two distributions and used to construct test statistics as the supremum of the absolute differences between empirical probabilities, the supremum being taken over all possible events. The test statistics are truly multivariate in not requiring the artificial ranking of multivariate observations, and they are distribution-free in the general p-variate case. Asymptotic null distributions are obtained. Powers of the proposed tests and a competitor are examined by Monte Carlo techniques.     

ROBUST COMPARISON OF DISPERSIONS FOR SAMPLES OF DIRECTIONAL DATA

Robust methods are proposed for testing whether several directional distributions on the unit p-sphere have comparable dispersions. The families of distributions considered are the Langevin for random vectors, and the Generalised Scheidegger-Watson for random axes, with specific interest in the Fisher and Watson distributions on the sphere. The methods are analogues of Levene's procedure for comparing variances of normal distributions.     

ESTIMATION OF GUARANTEE TIME AND MEAN LIFE AFTER WARRANTY FOR TWO-PARAMETER EXPONENTIAL FAILURE MODEL

Suppose manufactured items have failure times distributed with the two-parameter exponential density function à-^le-(x-μ)/à (x≥μ≥0). The paper considers estimation of the guarantee time μ and mean life after warranty à. Properties of various estimators are given for both separate and simultaneous estimation of μ and à. Criteria for comparing estimators are entropy loss, LINEX loss, and (generalized) Pitman nearness.