Some aspects of probability forecasting

The problems of assessing, comparing and combining probability forecasts for a binary events sequence are considered. A Gaussian threshold model (analytically of closed form) is introduced which allows generation of different probability forecast sequences valid for the same events. Chi - squared type test statistics, and also a marginal-conditional method are proposed for the assessment problem, and an asymptotic normality result is given. A graphical method is developed for the comparison problem, based upon decomposing arbitrary proper scoring rules into certain elementary scoring functions. The special role of the logarithmic scoring rule is examined in the context of Neyman - Pearson theory.     

Computation of finite population parameters and approximate probability values for multi-response randomized block permutation procedures (mrbp)

An algorithm is presented for computing the finite population parameters and the approximate probability values associated with a recently-developed class of statistical inference techniques termed multi-response randomized block permutation procedures (MRBP).     

Editor's Report

There are two common methods for statistical inference on 2 × 2 contingency tables. One is the widely taught Pearson chi-square test, which uses the well-known χ²statistic. The chi-square test is appropriate for large sample inference, and it is equivalent to the Z-test that uses the difference between the two sample proportions for the 2 × 2 case. Another method is Fisher’s exact test, which evaluates the likelihood of each table with the same marginal totals. This article mathematically justifies that these two methods for determining extreme do not completely agree with each other. Our analysis obtains one-sided and two-sided conditions under which a disagreement in determining extreme between the two tests could occur. We also address the question whether or not their discrepancy in determining extreme would make them draw different conclusions when testing homogeneity or independence. Our examination of the two tests casts light on which test should be trusted when the two tests draw different conclusions.     

从统计学史解析“自由度”概念

自由度是统计学中一个十分重要而又长期没有被圆满解释的概念。对此,从统计学史角度,对皮尔逊、费歇尔有关自由度问题争论原始文献细致考察,彻底澄清了自由度概念的内涵及与其相关的统计思想,弥补了Fienberg、Stigler与陈希孺已有解释的缺陷。研究表明：皮尔逊关于卡方检验中无论总体分布已知还是其来自于样本推断统计量都具有同一分布的错误判断,导致卡方检验的准确性出现偏差,这种偏差虽被同时代少数几个统计学家察觉但他们却无法解释其根源。费歇尔提出自由度概念并结合n维几何、假设检验与最大似然方法的论证不仅修正了皮尔逊的错误,也完善了从样本统计量估计总体参数的数理逻辑。     

SOME REMARKS ON THE MEAN, MEDIAN, MODE AND SKEWNESS

Many sufficient conditions for inequalities about the mean, median, mode and skewness have been obtained. The paper presents a theorem that unifies already known results, gives some counter-examples, and considers the cases of Pearson distributions.     

A Decomposition of Pearson–Fisher and Dzhaparidze–Nikulin Statistics and Some Ideas for a More Powerful Test Construction

An explicit decomposition on asymptotically independent distributed as chi-squared with one degree of freedom components of the Pearson–Fisher and Dzhaparidze–Nikulin tests is presented. The decomposition is formally the same for both tests and is valid for any partitioning of a sample space. Vector-valued tests, components of which can be not only different scalar tests based on the same sample, but also scalar tests based on components or groups of components of the same statistic are considered. Numerical examples illustrating the idea are presented.     

A Simple Approximate Procedure for Constructing Binomial and Poisson Tolerance Intervals

The problems of constructing tolerance intervals for the binomial and Poisson distributions are considered. Closed-form approximate equal-tailed tolerance intervals (that control percentages in both tails) are proposed for both distributions. Exact coverage probabilities and expected widths are evaluated for the proposed equal-tailed tolerance intervals and the existing intervals. Furthermore, an adjustment to the nominal confidence level is suggested so that an equal-tailed tolerance interval can be used as a tolerance interval which includes a specified proportion of the population, but does not necessarily control percentages in both tails. Comparison of such coverage-adjusted tolerance intervals with respect to coverage probabilities and expected widths indicates that the closed-form approximate tolerance intervals are comparable with others, and less conservative, with minimum coverage probabilities close to the nominal level in most cases. The approximate tolerance intervals are simple and easy to compute using a calculator, and they can be recommended for practical applications. The methods are illustrated using two practical examples.     

On the use of curve fitting to model the error of the Cornish-Fisher expansion of the pearson type-VI distribution

The Cornish-Fisher expansion of the Pearson type VI distribution is known to be reasonably accurate when both degrees of freedom are relatively large (say greater than or equal to 5). However, when either or both degrees of freedom are less than 5, the accuracy of the computed percentage point begins to suffer; in some cases severely. To correct for this, the error surface in the degrees of freedom plane is modeled by least squares curve fitting for selected levels of tail probability (.025, .05, and .10) which can be used to adjust the percentage point obtained from the usual Cornish-Fisher expansion. This adjustment procedure produces a computing algorithm that computes percentage points of the Pearson type VI distribution at the above probability levels, accurate to at least + 1 in 3 digits in approximately 11 milliseconds per subroutine call on an IBM 370/145. This adjusted routine is valid for both degrees of freedom greater than or equal to 1.     

企业伦理气候、组织承诺与组织公民行为的关系——以温州民营企业为例

企业社会责任等方面存在的问题是造成温州民营企业“民工荒”的重要原因。通过问卷调查,发现员工对企业伦理气候中的法规导向最为认可且看法比较一致,对组织承诺中的情感承诺最为认可且对道德承诺的看法相对一致,对组织公民行为中的组织公益最为认可且看法比较一致。员工对组织承诺、组织公民行为的主张是正向积极的,未发现企业伦理气候、组织承诺对组织公民行为有强烈的正向影响。提出温州民营企业摆脱困境的思路：重视企业伦理气候建设,形成正确的企业文化,增强员工的向心力;强化员工的组织承诺;鼓励员工的组织公民行为。     

Baker- Lin-Huang Type Bivariate Distributions Based on Order Statistics

Baker (2008 Baker, R. (2008). An order-statistics-based method for constructing multivariate distributions with fixed marginals. J. Multivariate Anal. 99: 23122327.[Crossref], [Web of Science ®] , [Google Scholar]) introduced a new class of bivariate distributions based on distributions of order statistics from two independent samples of size n. Lin and Huang (2010 Lin, G.D., Huang, J.S. (2010). A note on the maximum correlation for Baker’s bivariate distributions with fixed marginals. J. Multivariate Anal. 101: 22272233.[Crossref], [Web of Science ®] , [Google Scholar]) discovered an important property of Baker’s distribution and showed that the Pearson’s correlation coefficient for this distribution converges to maximum attainable value, i.e., the correlation coefficient of the Fréchet upper bound, as n increases to infinity. Bairamov and Bayramoglu (2013 Bairamov, I., Bayramoglu, K. (2013). From Huang-Kotz distribution to Baker’s distribution. J. Multivariate Anal. 113: 106115.[Crossref], [Web of Science ®] , [Google Scholar]) investigated a new class of bivariate distributions constructed by using Baker’s model and distributions of order statistics from dependent random variables, allowing higher correlation than that of Baker’s distribution. In this article, a new class of Baker’s type bivariate distributions with high correlation are constructed based on distributions of order statistics by using an arbitrary continuous copula instead of the product copula.