Tables of the Negative Binomial Probability Distribution

An age replacement policy requires that a unit be replaced when it attains a specified age, or at failure, whichever occurs first. The mathematical solution to the problem of what is the optimal age for replacement is well known. This paper adapts this general mathematical solution to the cases when a truncated normal, Gamma, or Weibull distribution can be assumed. Graphs are presented from which one can readily ascertain the optimal solutions for these models.     

Tables for Obtaining the Best Linear Invariant Estimates of Parameters of the Weibull Distribution

A censored life-test situation is considered and the assumption of a Weibull distribution for failure times is made. Tables are given for estimating log reliable life, where the estimator is best among linear estimators with expected loss invariant under translations. These best linear invariant (BLI) estimators have uniformly smaller expected loss than the Gauss-Markov best linear unbiased (BLU) estimators and are simple linear functions of the BLU estimators. The preliminary discussion involves a comparison of the BLI estimators with other widely used estimators.     

Certain Studies on the Structure and Statistics of the Logarithmic Series Distribution and Related Tables

The objective of this paper is to present a method of detection of spuriosity using a Bayesian approach. The model used is very specific—all observations are hopefully generated independently from the same normal source, N(μ, σ²), but it is feared that one of these may come from a spurious source, that of N(μ + a, σ²). The posterior of the “shift parameter a” is obtained, and it is shown to be a weighted combination of (Univariate) generalized t-distributions. The weights are very interesting and give much information, as do the separate generalized t-distributions. Examples are given to illustrate the use of the posterior of a, and the weights, etc. The procedure generalizes easily to the multivariate case, i.e., where the observations are hopefully generated independently from N(, ), but the fear exists that one of the observations is spurious from N( + a, ). A brief summary of results for this case is given.     

Upper Bounds for the Power of Invariant Tests for the Exponential Distribution with Weibull Alternatives

The problem of testing for the exponential distribution (with scale, or both location and scale parameters unknown) against Weibull alternatives is considered. Upper bounds for the power of any invariant test are presented. Tests based upon the maximum likelihood estimator of the shape parameter, or a modification of it, are given which virtually achieve these bounds.     

Tables of a Truncated Standard Normal Distribution: A Doubly Truncated Case

As an extension to the singly truncated case, this article further examines a doubly truncated normal distribution. In this article, we consider both symmetric and asymmetric cases with two truncation points on the left and the right, and develop the tables of a truncated mean, a truncated variance, and a cumulative probability.     

Tables of a Truncated Standard Normal Distribution: A Singly Truncated Case

A normal distribution has a unique position in many engineering fields, and the standard normal distribution table has been widely used for more than a century. There are many situations, however, in which a truncated normal distribution needs to be considered. Although the theoretical foundations of the truncated normal distribution are well established, there has been little work on tabulating the characteristics associated with the truncated normal distribution, such as a cumulative probability, a truncated mean, and a truncated variance. In this article, we provide tables for a singly truncated normal distribution, which may be useful for quality practitioners.     

Approximately Somewhere Most Powerful Tests for Marginal Homogeneity of a Square Table Under Restricted Alternatives

For testing marginal homogeneity of a square contingency table under the restricted alternative that either is stochastically larger than the other, approximately somewhere most powerful tests are studied. The Mann-Whitney test is included in them. Among the approximately somewhere most powerful tests, an optimal one is derived by the most stringent principle and compared with the Mann-Whitney test and the Stuart’s test with respect to their asymptotic powers. Simulation study indicates that the Mann-Whitney and most stringent tests both have consistently higher powers, compared with the Stuart’s test for detecting the locational shifts when a bivariate continuous distribution is assumed as an underlying distribution. It is indicated that the Mann-Whitney test competes well with the approximately most stringent somewhere most powerful test, but the latter is more reliable than the former.

     

An Association Model for Trivariate Contingency Tables and The Underlying Trivariate Normal Distribution

This paper compares an association model for trivariate contingency tables with the trivariate normal distribution. First, similarity between the two models is discussed. Second, it is proved that the association model approximates the discretized trivariate normal distribution. An aritificial illustration shows the degrees of the approximations in small tables. Third, estimation of the correlation coefficients of the underlying trivariate normal distribution is discussed. The present approach is illustrated by use of numerical examples.

     

Approximations to the Distribution of the Sample Coefficient Alpha Under Nonnormality

Approximate distributions of the sample coefficient alpha under nonnormality as well as normality are derived by using the single- and two-term Edgeworth expansions up to the term of order 1/n. The case of the standardized coefficient alpha including the weights for the components of a test is also considered. From the numerical illustration with simulation using the normal and typical nonnormal distributions with different types/degrees of nonnormality, it is shown that the variances of the sample coefficient alpha under nonnormality can be grossly different from those under normality. The corresponding biases and skewnesses are shown to be negative under various conditions. The method of developing confidence intervals of the population coefficient alpha using the Cornish-Fisher expansion with sample cumulants is presented.

     

Alternatives of Energy Absorption Element Design Parameters for an Armored Combat Vehicle Seat Under Explosive Loading

Strength of Materials - The principle of operation of a proposed energy absorption element alternative consists in conversion of ambush mine explosion-gained kinetic energy into the plastic strain...     

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。     

Tables for Normal Sampling with Unknown Variance-the Student Distribution and Economically Optimal Sampling Plans

Industrial scientists and engineers often use experimental designs in which all degrees of freedom are used to estimate effects and consequently no classical estimate of the error is possible. Robust scale estimates provide an alternative measure of the error. In this study, several such scale estimators are evaluated based on the power or related significance tests. The pseudo standard error method of Lenth provides the best overall performance. Lenth's t approximation for critical values was found to be inaccurate, however, so new tables are provided. Additional recommendations are made according to the experimenter's prior belief in the number of likely important factors.     

Handbook of Statistical Tables

The Student's test of H ₀: μ = μ₀ against H ₁: μ ≠ μ₀ of the location parameter μ of the normal, logistic and Cauchy distributions when the scale parameter σ is unknown based on a few selected sample percentiles is considered. Tables facilitating the computation of the testing statistic are provided and the effects of the biases of the linear estimates involved on the test are investigated.     

不同触头压力下真空灭弧室温升分布研究

开关设备作为线路的供电单元,各部分的温度不得超过允许值,作为真空开关及断路器的核心元件,真空灭弧室的温升性能主要取决于回路电阻大小。真空灭弧室的回路电阻主要由动静触头本身电阻值及接触电阻值组成。断路器合闸时,灭弧室动静触头接触,但表面仍然会存在间隙,间隙面以金属桥的形式导电形成接触电阻。不同的触头压力及接触面粗糙度不同时,动静触头的间隙也不同,从而影响真空灭弧室的回路电阻及其性能。本文通过对灭弧室不同触头压力及接触面不同粗糙度时灭弧室动静导电杆温升的研究,分析触头压力及触头接触面粗糙度对灭弧室温升的影响,得到不同触头压力及触头表面粗糙度下温升变化趋势,为真空灭弧室设计中触头材料及表面粗糙度的选择、形状的设计提供理论基础。     

删失数据下密度核估计的误差分布的强逼近

在随机右删失数据下构造了概率密度函数的核估计和随机加权估计，得到了核估计的误差分布的正态逼近速度和随机加权逼近速度，改进了孙六权和朱力行(1999)的主要结果。     

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.