Structural probability bounds for the strong Pareto law

By using the structural density function (Fraser 1979, Ch. 7) of the parameters of a Pareto distribution, the structural distribution function of the strong Pareto law is derived. Its fractiles have been evaluated numerically for special cases, and the results are displayed through graphs from which structural one-sided probability bounds may be found. It is shown that these graphs may also be used to find structural tolerance bounds for the Pareto distribution.     

英语阅读抑制视域的歧义容忍度研究

本文基于英语阅读抑制与歧义容忍度的心理学同构关系,从英语阅读抑制视域角度审视歧义容忍度的倾向反应,指导学习者正确面对英语阅读中的陌生语言现象,帮助广大英语教师利用抑制效率调控学生的歧义容忍度,达到降低阅读焦虑、辅助元认知训练以及有效设置歧义场景的教学目的,促进学生英语阅读能力的提升.     

阅读中模糊容忍度与口语质量的相关性研究

为了了解阅读中的模糊容忍度与其随后口语产出质量之间是否存在相关关系,采用问卷调查的方法,分析了阅读中模糊容忍度与口语产出质量之间的关系.结果表明：阅读中的模糊容忍度与随后口语产出质量之间存在显著正相关.模糊容忍度越高,其口语成绩也越高.模糊容忍度对口语的影响表现在流利性、完整性和准确性三方面上.对语音和交际能力没有影响.阅读中的模糊容忍度与随后口语产出之间的相关性存在性别差异.对于女生而言存在这种相关性,对于男生则不存在.     

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.     

Some Applications of Order Statistics to Multivariate Analysis II

ABSTRACT

Harter (1979) summarized applications of order statistics to multivariate analysis up through 1949. The present paper covers the period 1950–1959. References in the two papers were selected from the first and second volumes, respectively, of the author's chronological annotated bibliography on order statistics [Harter (1978, 1983)]. Tintner (1950a) established formal relations between four special types of multivariate analysis: (1) canonical correlation, (2) principal components, (3) weighted regression, and (4) discriminant analysis, all of which depend on ordered roots of determinantal equations. During the decade 1950–1959, numerous authors contributed to distribution theory and/or computational methods for ordered roots and their applications to multivariate analysis. Test criteria for (i) multivariate analysis of variance, (ii) comparison of variance–covariance matrices, and (iii) multiple independence of groups of variates when the parent population is multivariate normal were usually derived from the likelihood ratio principle until S. N. Roy (1953) formulated the union–intersection principles on which Roy & Bose (1953) based their simultaneous test and confidence procedure. Roy & Bargmann (1958) used an alternative procedure, called the step–down procedure, in deriving a test for problem (iii), and J. Roy (1958) applied the step–down procedure to problem (i) and (ii), Various authors developed and applied distribution theory for several multivariate distributions. Advances were also made on multivariate tolerance regions [Fraser & Wormleighton (1951), Fraser (1951, 1953), Fraser & Guttman (1956), Kemperman (1956), and Somerville (1958)], a criterion for rejection of multivariate outliers [Kudô (1957)], and linear estimators, from censored samples, of parameters of multivariate normal populations [Watterson (1958, 1959)]. Textbooks on multivariate analysis were published by Kendall (1957) and Anderson (1958), as well as a monograph by Roy (1957) and a book of tables by Pillai (1957).     

Tolerance regions for random vectors and best linear predictors

In the case that vectors X and Y have a joint multivariate normal distribution, tolerance regions are found for the best linear predictor of Y using X if samples are used to estimate the regression coeffierante. Tolerance regions are also found for Y. In addition, simultaneous tolerance intervals for all linear functions of Y or of the best linear predictor of Y using X are found.     

Sample-size requirements for confidence bounds of prescribed precision on multivariate normal quantiles

The problem of setting confidence bounds on a central multivariate normal quantile is considered. It is shown that for the setting of exact confidence bounds of specified closeness to the quantile,the required minimum size of a normal sample is large and rises rapidly with the number of variates considered.