Asymptotic Expansions of the Distribution of the Estimator for the Generalized Partial Correlation Under Nonnormality

The generalized partial correlation is denned as a correlation between two variables, where the linear effects of common and unique third variables are partialed out from the two variables. The generalized partial correlation includes simple, partial, part/semipartial and bipartial correlations as special cases. The Edgeworth expansion of the distribution of the standardized sample coefficient for the generalized partial correlation is obtained up to order O(1/n) under nonnormality. Also asymptotic expansions of the distribution of the Studentized estimator are obtained using the Edgeworth expansion, Cornish-Fisher expansion and Hall’s method with variable transformation. As extensions, the results of multivariate cases or generalized partial set-correlations are given.

     

Some Approximations for the Noncentral-F Distribution

Among the various approximations for the noncentral-F distribution. the best known are the computationally simpler approximation due to Severo and Zelen [18] and Laubscher [9], which requires only the normal distribution, and a more accurate approximation due to Tiku [21], which requires the F distribution. Thcsr approximations are systematically evaluated. Some variations of these approximations are considered and found to he of comparable accuracy. An Edgeworth-acries approximation, which requires only the normal distribution, is developed and sren to be superior in accuracy. A FORTRAN-subroutine for the Edgeworth-series approximation is given.     

Coefficient Alpha: An Engineer's Interpretation of Test Reliability

Reliability is a fundamental concept of test construction. The most common measure of reliability, coefficient alpha, is frequently used without an understanding of its behavior. This article contributes to the understanding of test reliability by demonstrating that questions which lower reliability are inconsistent with the bulk of the test, being prone to test‐taking tricks and guessing. These qualitative characteristics, obtained from focus groups, provide possible causes of lower reliability such as poorly written questions (e.g., the correct answer looks different from the incorrect answers), questions where students must guess (e.g., the topic is too advanced), and questions where recalling a definition is crucial. Quantitative findings confirm that questions lower reliability when students who answer correctly have lower overall scores than students who answer incorrectly. This phenomenon is quantified by the “gap” between these students' overall scores, which is shown to be highly correlated with other item metrics. An increasing number of concept inventory tests are being developed to assess student learning in engineering. Scores and student comments from the Statistics Concept Inventory are used to make these judgments.     

An Inequality for the Sample Coefficient of Variation and an Application to Variables Sampling

The problem of time trends is frequently present in chemical processes. Experimental designs which can be used in these situations have been developed by several workers. The designs of D. R. Cox are restricted to a few levels and can be used with both qualitative or quantitative variables. The randomly oriented designs of G. E. P. Box are useful when all of the variables are quantitative. Both of these types of designs presuppose the fitting of a first-order model to the data. Combinations of these designs can be made which allow the study of both qualitative and quantitative variables in the same experiment. Designs which permit the fitting of a polynomial response are available for one variable problem. Problems involving two variables can be handled by the proper combination of randomly oriented firstorder designs. Satisfactory designs for situations involving more than two independent variables and a polynomial response of second order or higher are not presently available. Further work in this area will be of interest to experimenters in the physical sciences.     

Two Sample Tests in the Weibull Distribution

A test based on maximum likelihood estimators is given for testing the equality of the shape parameters in two Weibull distributions with the scale parameters unknown. Tests for the equality of the scale parameters are also presented along with a procedure for selecting the Weibull process with the larger mean life.     

Estimation of the Parameters of the Gamma Distribution by Sample Quantiles

This paper deals with large sample estimation of the location parameter (α₁ and the scale parameter α₂ in the gamma distribution with known shape parameter. Best linear unbiased estimates based on k sample quantiles are used. For a given k, the optimum spacings of the sample quantiles can be replaced by simpler “nearly optimum” spacings at virtually no loss of asymptotic efficiency. The theory behind the nearly optimum spacings is briefly reviewed. The major part of the paper concerns estimation of α₂ when α₂ is known. Nearly optimum spacings together with the coefficients to be used in computing the estimates are presented in a number of tables for k = 1(1) 10, and various values of the shape parameter. The paper also contains brief discussions of estimation of α₁, when α₂ is known, and simultaneous estimation of α₁ and α₂.     

Approximations to the Non-Central t,with Applications

A mildly conservative but very rapid calculation technique is proposed for problems requiring the use of the Non-central t distribution. Examples and a brief table are provided.     

摩擦系数对齿轮接触应力分布的影响

从J—C公式(两平行圆柱体同时受到法向和切向赫芝压强时的应力分布)出发,在计算机上用优化方法计算了不同摩擦系数下,最大切应力τ_(max),等效应力σ_e和正交切应力τ_(XZ)的极大值位置。结果表明,当摩擦系数分别为0.18和0.24时,τ_(max)和σ_e的最大值位置到达表面。当z>b时,摩擦系数的变化对τ_(max)和σ_e的分布没有显著影响。当摩擦系数增大时,动态的正交切应力τ_(XZ)由对称循环状态向脉动循环状态过渡,而τ_(XZ)的极大值位置的x坐标及应力变程没有显著变化。还在计算结果的基础上对接触疲劳破坏的力学条件进行了讨论。     

Application of a Pyrometer and Standard Sample to Determine The Surface Temperature of Materials Under Study

Measurement Techniques - The methodology of determining the surface temperature of composite materials with unknown emissivity is studied. The methodology is implemented by using a standard sample...     

Approximations to the Mean and Standard Deviation of Reciprocals of Observations

Instrument performance evaluation is generally based on accuracy and repeatability, with the test process consisting of observations of known or standard events. The data are then reduced by various manipulations. This paper will show how to simplify such manipulations when the observation is the reciprocal of the desired event. In addition, it will show that the error introduced is negligible under certain easily tested conditions.     

Tables of the Distribution of the Mann-Whitney-Wilcoxon U-Statistic Under Lehmann Alternatives

A simple recursive formula is used to generate the distribution of the MWW U-statistic under alternatives of the form K ₁: G – F ^k ,1 ≠ k < 0, and K ₂: G – 1? (1 ? F) ^k , 1 ≠ k > 0, and it is pointed out that many of these alternatives are of interest in life testing, reliability testing and related fields. Tables are given for the case G = 1 – (1 ? F) ^k for 4 ≤ n, m ≤ 8 and k = 2,3,4,6,9,12 and it is shown that these tables can also be used when G = F ^k and when 0 < k < 1.     

Selection of the Blur Coefficient for Probability Density Kernel Estimates Under Conditions of Large Samples

Measurement Techniques - A fast algorithm is proposed for choosing the blur factors of kernel functions of a non-parametric probability density estimate under conditions of large-scale statistical...     

电子商务下基于协同配送的配送中心选址研究

针对电子商务中的配送中心选址问题,综合考虑配送中心的运输成本、时间窗约束等要素并结合协同策略对该问题展开研究,提出了一种基于协同策略的配送中心选址模型。该模型以协同策略为基础,可以更加有效地对配送中心选址的各种要素进行优化。实验结果表明本文所提出的选址模型能够较好地验证在电子商务条件下,有一定时效要求且配送成本低廉的配送中心选址方案。     

Approximations to the Average Run Length in Cumulative Sum Control Charts

An approximation to the average run length for cumulative sum control charts is derived using the analogy between this procedure and the sequential probability ratio test for normal observations. This approximation is also derived by using a Brownian motion approximation to the cumulative sum. The Brownian motion approximation does not require the normality assumption. The analytical expression for the average run length obtained from the approximation is then used to determine the optimal choice of parameters to minimize the average run length at a specified deviation flom control, subject to a fixed average run length when in control.     

On the Phase-Type Approximations of General Distributions

In this paper the approximation of general distributions, with known squared coefficient of variation, by phase-type distributions using the first three moments is studied. The phase-type distributions presented in this paper can be fitted to observed data sets and also can be used to approximate general distributions to be used in analytical models as well as in simulation. Formulas for the approximating distributions are presented and examples are given to show the approximations.     

How to Choose the Proper Sample Size

Two simple proof-load testing procedures are suggested to estimate the correlation between two variables that can individually only be determined destructively. The first procedure assumes that the means and variances of the variables are known. The second testing procedure is more flexible and requires no prior information. By assuming that the variables have a bivariate normal distribution and considering only the number of units that fail at each proof-load, we determine the maximum likelihood estimate for the correlation coefficient. Theoretical and simulation results compare favorably with previously suggested more complicated procedures and guide the practitioner in appropriate choices for the proof-load levels.     

Interval Estimation of the Parameters of a Distribution from a Sample of a Random Quantity

A program is developed for solving the problem of making an interval estimation of the parameters of a distribution from a single sample of a random quantity, based on a statistical modeling method. The results of a solution of the problem for certain symmetric and asymmetric distributions are presented. The average error in estimating the confidence intervals and their limits is 4–15% in the range of values of the confidence level of 0.8 P 0.998 for a sample volume of N = 500–1000.