Easy-to-construct confidence bands for comparing two simple linear regression lines

This paper shows how to construct confidence bands for the difference between two simple linear regression lines. These confidence bands provide directly the information on the magnitude of the difference between the regression lines over an interval of interest and, as a by-product, can be used as a formal test of the difference between the two regression lines. Various different shapes of confidence bands are illustrated, and particular attention is paid towards confidence bands whose construction only involves critical points from standard distributions so that they are consequently easy to construct.     

Testing for ordered failure rates under general progressive censoring

For exponentially distributed failure times under general progressive censoring schemes, testing procedures for ordered failure rates are proposed using the likelihood ratio principle. Constrained maximum likelihood estimators of the failure rates are found. The asymptotic distributions of the test statistics are shown to be mixtures of chi-square distributions. When testing the equality of the failure rates, a simulation study shows that the proposed test with restricted alternative has improved power over the usual chi-square statistic with an unrestricted alternative. The proposed methods are illustrated using data of survival times of patients with squamous carcinoma of the oropharynx.     

Maximum log-likelihood ratio test for a change in three parameter Weibull distribution

Asymptotic behavior of a log-likelihood ratio statistic for testing a change in a three parameter Weibull distribution is studied. It is shown that if a shape parameter α>2$\alpha >2$ the law of iterated logarithm for maximum-likelihood estimators is still valid and the log-likelihood testing statistic is asymptotically distributed (after an appropriate normalization) according to a Gumbel distribution.     

Some theory and practical uses of trimmed L-moments

Trimmed L-moments, defined by Elamir and Seheult [2003. Trimmed L-moments. Comput. Statist. Data Anal. 43, 299–314], summarize the shape of probability distributions or data samples in a way that remains viable for heavy-tailed distributions, even those for which the mean may not exist. We derive some further theoretical results concerning trimmed L-moments: a relation with the expansion of the quantile function as a weighted sum of Jacobi polynomials; the bounds that must be satisfied by trimmed L-moments; recurrences between trimmed L-moments with different degrees of trimming; and the asymptotic distributions of sample estimators of trimmed L-moments. We also give examples of how trimmed L-moments can be used, analogously to L-moments, in the analysis of heavy-tailed data. Examples include identification of distributions using a trimmed L-moment ratio diagram, shape parameter estimation for the generalized Pareto distribution, and fitting generalized Pareto distributions to a heavy-tailed data sample of computer network traffic.     

Stochastic Modelling of Times to Temperature for Furnaces Supplying Titanium Blooms to a Rolling Mill at TIMET

In conjunction with TIMET at Waunarlwydd (Swansea, UK) a model has been developed that will optimise the scheduling of various blooms to their eight furnaces so as to minimise the time taken to roll these blooms into the finished mill products. This production scheduling model requires reliable data on times taken for the various furnaces that heat the slabs and blooms to reach the temperatures required for rolling. These times to temperature are stochastic in nature and this paper identifies the distributional form for these times using the generalised F distribution as a modelling framework. The times to temperature were found to be similarly distributed over all furnaces. The identified distributional forms were incorporated into the scheduling model to optimise a particular campaign that was run at TIMET Swansea. Amongst other conclusion it was found that, compared to the actual campaign, the model produced a schedule that reduced the makespan by some 35%.     

Power of the Neyman Smooth Test for Evaluating Multivariate Forecast Densities

We compare and investigate Neyman's smooth test, its components, and the Kolmogorov-Smirnov (KS) goodness-of-fit test for testing the uniformity of multivariate forecast densities. Simulations indicate that the KS test lacks power when the forecast distributions are misspecified, especially for correlated sequences of random variables. Neyman's smooth test and its components work well in samples of size typically available, although there sometimes are size distortions. The components provide directed diagnosis regarding the kind of departure from the null. For illustration, the tests are applied to forecast densities obtained from a bivariate threshold model fitted to high-frequency financial data.     

Statistical Inference Based on Pooled Data: A Moment-Based Estimating Equation Approach

We consider statistical inference on parameters of a distribution when only pooled data are observed. A moment-based estimating equation approach is proposed to deal with situations where likelihood functions based on pooled data are difficult to work with. We outline the method to obtain estimates and test statistics of the parameters of interest in the general setting. We demonstrate the approach on the family of distributions generated by the Box-Cox transformation model, and, in the process, construct tests for goodness of fit based on the pooled data.     

Censored Kullback-Leibler Information and Goodness-of-Fit Test with Type II Censored Data

The Kulback-Leibler information has been considered for establishing goodness-of-fit test statistics, which have been shown to perform very well (Arizono & Ohta, 1989; Ebrahimi et al., 1992, etc). In this paper, we propose censored Kullback-Leibler information to generalize the discussion of the Kullback-Leibler information to the censored case. Then we establish a goodness-of-fit test statistic based on the censored Kullback-Leibler information with the type 2 censored data, and compare the test statistics with some existing test statistics for the exponential and normal distributions.     

几种传输线的场分布

求开放平板线、外正三角形內圆同轴线、外方內圆同轴线、外正六边形內圆同轴线的特性阻抗而建立的精确保角变换的基础上,本文进一步讨论了显式逆变换函数,从而求得了这几种传输线的场分布的闭合表达式。由于所用保角变换的精确性,所得的显式场分布在内导体和外导体的内接圆尺寸之比小于0.5in。基本上是准确的,在这个尺寸比稍大些时也可作为参考。这些场分布对于了解传输线的功率容量,计算衰减常数,考虑功率耦合,设计有关的有源器件等都是必不可少的。文中获得的几种传输线的场分布的显著特点是计算方便,在一般实用范围內有足够的精度。     

电磁导弹的波瓣特性

首次在球坐标系统下研究了电磁导弹有趣的波瓣特性。研究表明:当天线口径、距离一定时,电磁导弹的波瓣随波形参量减小而变窄;当天线口径、波形参量一定时,电磁导弹的波瓣随距离增加而变窄;当波形参量、距离一定时,电磁导弹的波瓣随天线口径增加而变宽;电磁导弹不存在副瓣;电磁导弹的能量在远轴时仍按球面波方式衰减。这些结论有助于理解电磁导弹的实质。