Testing non-oblique hypotheses

This paper considers a likelihood ratio test for testing hypotheses defined by non-oblique closed convex cones, satisfying the so called iteration projection property, in a set of k normal means. We obtain the critical values of the test using the Chi-Bar-Squared distribution. The obtuse cones are introduced as a particular class of cones which are non-oblique with every one of their faces. Examples with the simple tree order cone and the total order cone are given to illustrate the results.     

On square ordinal contingency tables: a comparison of social class and income mobility for the same individuals

Summary.  Square contingency tables with matching ordinal rows and columns arise in particular as empirical transition matrices and the paper considers these in the context of social class and income mobility tables. Such tables relate the socio-economic position of parents to the socio-economic position of their child in adulthood. The level of association between parental and child socio-economic position is taken as a measure of mobility. Several approaches to analysis are described and illustrated by UK data in which interest focuses on comparisons of social class and income mobility tables that are derived from the same individuals. Account is taken of the use of the same individuals in the two tables. Additionally comparisons over time are considered.     

A Likelihood-Based Approximation to the Cumulative Distribution Function of the Noncentral t Distribution

Optimal designs for estimating the parameters and also the optimum factor combinations in multiresponse experiments have been considered by various authors. However, till date, in mixture experiments optimum designs have been studied only in the single response case. In this article, attempt has been made to investigate optimum designs for estimating optimum mixing proportions in a multiresponse mixture experiment.     

Inferences on the lognormal mean for complete samples

In many engineering problems it is necessary to draw statistical inferences on the mean of a lognormal distribution based on a complete sample of observations. Statistical demonstration of mean time to repair (MTTR) is one example. Although optimum confidence intervals and hypothesis tests for the lognormal mean have been developed, they are difficult to use, requiring extensive tables and/or a computer. In this paper, simplified conservative methods for calculating confidence intervals or hypothesis tests for the lognormal mean are presented. In this paper, “conservative” refers to confidence intervals (hypothesis tests) whose infimum coverage probability (supremum probability of rejecting the null hypothesis taken over parameter values under the null hypothesis) equals the nominal level. The term “conservative” has obvious implications to confidence intervals (they are “wider” in some sense than their optimum or exact counterparts). Applying the term “conservative” to hypothesis tests should not be confusing if it is remembered that this implies that their equivalent confidence intervals are conservative. No implication of optimality is intended for these conservative procedures. It is emphasized that these are direct statistical inference methods for the lognormal mean, as opposed to the already well-known methods for the parameters of the underlying normal distribution. The method currently employed in MIL-STD-471A for statistical demonstration of MTTR is analyzed and compared to the new method in terms of asymptotic relative efficiency. The new methods are also compared to the optimum methods derived by Land (1971, 1973).     

Estimation with right‐censored observations under a semi‐Markov model

The semi‐Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end‐point of the support of the censoring time is strictly less than the right end‐point of the support of the semi‐Markov kernel, the transition probability of the semi‐Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi‐Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study. The Canadian Journal of Statistics 41: 237–256; 2013 © 2013 Statistical Society of Canada     

An Easily Implemented Generalised Inverse Gaussian Generator

Using the ‘ratio’ method an easily implemented algorithm is derived for the generalised inverse Gaussian distribution. Computer timings and efficiency calculations show that the procedure is fast over a wide range of distribution parameter values.     

Optimal record-based statistical procedures for the two-parameter exponential distribution

There are a number of situations in which the experimental data observed are record statistics. In this paper, optimal confidence intervals as well as uniformly most powerful (MP) tests for one-sided alternatives are developed. Since a uniformly MP test for a two-sided alternative does not exist, generalized likelihood ratio and uniformly unbiased and invariant tests are derived for the two parameters of the exponential distribution based on record data. For illustrative purposes, a data set on the times between consecutive telephone calls to a company's switchboard is analysed using the proposed procedures. Finally, some open problems in this direction are pointed out.     

计算气井储量新方法

提出了采用弹性二相法结合物质平衡方程作为计算全井储量的新方法。弹性二相法主要用于气藏开发进入拟稳态以后，要求压力和产量的测量精确，气藏的工作制度对弹性二相法储量也有很大影响，其计算可靠程度已被矿场实际证实；物质平衡方程在开发初期计算精度不高。将弹性二相法与物质平衡法结合建立多目标优化函数，该方法既能很好地应用弹性二相法，又能体现物质平衡，使得该方法适用范围更广，计算结果更可靠，对致密气藏具有更好的推广应用价值。通过实例气井动态储量进行的验证对比表明，该方法在理论上是合理的，实际验证是可行的。     

明代男女比例的统计分析——根据地方志数据的分析

男女失衡是当前中国面临的一大社会问题,对于未来的发展有着重大的影响。对这一问题进行历史角度的分析无疑会对我们破解难题有所帮助。本文主要是对中国明代男女比例情况的研究。根据地方志上遗留的男女人口的统计数据,笔者计算了各地的男女比例,并分别对基本情况、变化过程、未成年人男女比例三个方面进行简单的统计分析。通过这一初步研究,笔者试图把握明代男女比例的大致情况和发展趋势。从统计结果来看,明代中国普遍存在男女比例失衡的问题,并已经达到了非常严峻的程度。     

菲茨杰拉德创作能力的变迁——基于词汇测度的统计分析

传统上,不同评论者对同一作家作品的好恶往往会导致对作家创作能力截然不同的评价,这种主观定性评判并没有考虑作品本身的内在特质。计算语言学发现幂律分布在各类文本的词汇测度中具有普遍性,这为定量刻画文学作品的内在特质提供了统计手段。因为作家的创作能力不是一成不变的,不同创作时期的作品反映了作家创作能力的波动,为检验这一论断,以菲茨杰拉德的四部小说为例,对包括类符形符比、词汇增长率和词汇相对熵等在内的词汇测度进行统计分析,发现这三个测度与文中的形符数之间服从幂律关系。故提出一种计算作家创作能力的新测度以及比较其创作能力变化的新方法。菲茨杰拉德作品的实证分析表明：该测度不仅能够有力地印证现有的定性评论观点,而且还能够有效地反映作家创作能力的巅峰与低谷状态。