Distribution-Free Runs Test for Conditional Symmetry

A distribution-free runs test for conditional symmetry is proposed. The null distribution of the test statistics is derived. Intensive simulation is conducted to examine the power of the proposed test for different sample sizes and different alternatives. Data on the bilirubin level of babies in neonatal intensive care is used to illustrate the method.     

Detection of symmetry or lack of 11 and applications

Developed is a method for using a random sample to select between the model of symmetry of the sampled distribution and the model of skewness to the right. The technique is meant to be used as a preliminary step, in the analysis of data, which is to be followed by other inferential procedures. Two examples of this use, which pertain to robust regression and quantile estimation, are discussed.     

Tests of symmetry derived as components of pearson's phi-squared distance measure

Rank statistics which arise as estimates of the first and third components of a frequency decomposition of Pearson's phi-squared distance measure, introduced by Eubank, LaRiccia, and Rosenstein (1987), are examined for their usefulness as tests of symmetry about a known median against various asymmetric alternatives, Pitman asymptotic relative efficiencies are used to compare the efficacies of the new statistics with classical test procedures, and empirical powers of the new tests are compared via simulation for a variety of asymmetric distributions. Statistics which arise from components based on Legendre polynomials are of particular interest. The first component is the familiar Wilcoxon signed rank statistic. The third component, which is a new statistic for this problem, exhibits a high level of sensitivity to a variety of asymmetric alternatives both asymptotically and in small sample studies.     

从对称到群的定义

群是“抽象代数”中重要的代数系统,有广泛的应用。文章由三种感知上的对称——平面图形的对称、数域的对称和多项式的对称,引出了抽象群的定义,并将抽象群和对称群进行了比较,通过对比,可以看出由对称引出群这一做法形象直观,通俗易懂。     

物理、伦理、管理与对称化管理——信息人社会与势科学理论研究之四

以信息作用为核心,从物理、伦理、管理的内在联系和比较演绎中,结合人性和自然界普遍存在的“二律背反”规律和物质作用与信息作用中体现的对称性机制,提出了“对称化管理”;在相对论引力不均匀的引力空间弯曲与信息化社会信息不均匀的信息空间弯曲的分形规律即标度对称支配的可比较机制中,演绎了局域对称化管理以及从有形走向无形、从有界走向连续的文化场管理。而对称性产生、发展及演化的机制则是势科学机制。     

均匀电磁场的探讨

均匀电磁场可谓电磁场的特例,在科研及生产中应用甚广。本文就均匀电磁场的判别、常见的均匀电磁场、均匀电磁场的形成及提高其空间特性等诸方面进行了论述。     

Two envelopes

“You have been given either envelopeA orB. B contains either one-half or twice the money inA. Do you want to switch? Now you open your envelope? Are you still happy to stand pat?” Answers depend on whether you think there is an upper bound to the money inA. You should no longer be indifferent if you think there is not an upper bound, but, if you think there is a certain upper boundU, you should want to switch or not depending on whether your envelope holds less thanU. Expected monetary values are extended to acts with infinitely many equally possible monetary values. It is maintained that though strong dominance under infinite partitions does not in the absence of an upper bound for values imply greater expected value, ‘univocal strong dominance’ is even then properly decisive for choice.     

空间图形的对称性初探

本文推广了现行《空间解析几何》教材中空间图形关于“坐标原点,坐标平面,坐标轴”对称图形的特殊结论,给出了空间图形关于“点、平面、直线”对称图形的一般性定理,并举例说明其应用。     

A deterministic event tree approach to uncertainty,randomness and probability in individual chance processes

Both Popper and Good have noted that a deterministic microscopic physical approach to probability requires subjective assumptions about the statistical distribution of initial conditions. However, they did not use such a fact for defining an a priori probability, but rather recurred to the standard observation of repetitive events. This observational probability may be hard to assess for real-life decision problems under uncertainty that very often are - strictly speaking - non-repetitive, one-time events. This may be a reason for the popularity of subjective probability in decision models. Unfortunately, such subjective probabilities often merely reflect attitudes towards risk, and not the underlying physical processes.In order to get as objective as possible a definition of probability for one-time events, this paper identifies the origin of randomness in individual chance processes. By focusing on the dynamics of the process, rather than on the (static) device, it is found that any process contains two components: observer-independent (= objective) and observer-dependent (= subjective). Randomness, if present, arises from the subjective definition of the rules of the game, and is not - as in Popper's propensity - a physical property of the chance device. In this way, the classical definition of probability is no longer a primitive notion based upon equally possible cases, but is derived from the underlying microscopic processes, plus a subjective, clearly identified, estimate of the branching ratios in an event tree. That is, equipossibility is not an intrinsic property of the system object/subject but is forced upon the system via the rules of the game/measurement.Also, the typically undefined concept of symmetry in games of chance is broken down into objective and subjective components. It is found that macroscopic symmetry may hold under microscopic asymmetry. A similar analysis of urn drawings shows no conceptual difference with other games of chance (contrary to Allais' opinion). Finally, the randomness in Lande's knife problem is not due to objective fortuity (as in Popper's view) but to the rules of the game (the theoretical difficulties arise from intermingling microscopic trajectories and macroscopic events).Dedicated to Professor Maurice Allais on the occasion of the Nobel Prize in Economics awarded December, 1988.