A reformulation of the criteria for the independence of quadratic functions in normal variables

The Craig-Sakamoto theorem establishes a sufficient and necessary condition for the independence of two quadratic forms in normal variates, fascinating many statisticians and mathematicians, who continuously seek for simple and better proofs of the theorem and its extensions. In this article, we present a simple proof of a unified theorem on the independence of linear and quadratic functions in general normal variates.     

Symbolic cumulant calculations for frequency domain time series

With time series data, there is often the issue of finding accurate approximations for the variance of such quantities as the sample autocovariance function or spectral estimate. Smith and Field (J. Time. Ser. Anal 14: 381–395, 1993) proposed a variance estimate motivated by resampling in the frequency domain. In this paper we present some results on the cumulants of this and other frequency domain estimates obtained via symbolic computation. The statistics of interest are linear combinations of products of discrete Fourier transforms. We describe an operator which calculates the joint cumulants of such statistics, and use the operator to deepen our understanding of the behaviour of the resampling based variance estimate. The operator acts as a filter for a general purpose operator described in Andrews and Stafford (J.R. Statist. Soc. B55, 613–627).     

Weighted discrepancies and maximum likelihood estimation for discrete distributions

The paper shows that many estimation methods, including ML, moments, even-points, empirical c.f. and minimum chi-square, can be regarded as scoring procedures using weighted sums of the discrepancies between observed and expected frequencies The nature of the weights is investigated for many classes of distributions; the study of approximations to the weights clarifies the relationships between estimation methods, and also leads to useful formulae for initial values for ML iteration.     

A new class of weighted exponential distributions

Introducing a shape parameter to an exponential model is nothing new. There are many ways to introduce a shape parameter to an exponential distribution. The different methods may result in variety of weighted exponential (WE) distributions. In this article, we have introduced a shape parameter to an exponential model using the idea of Azzalini, which results in a new class of WE distributions. This new WE model has the probability density function (PDF) whose shape is very close to the shape of the PDFS of Weibull, gamma or generalized exponential distributions. Therefore, this model can be used as an alternative to any of these distributions. It is observed that this model can also be obtained as a hidden truncation model. Different properties of this new model have been discussed and compared with the corresponding properties of well-known distributions. Two data sets have been analysed for illustrative purposes and it is observed that in both the cases it fits better than Weibull, gamma or generalized exponential distributions.     

Approximate tests of hypotheses in regression models with grouped data

Techniques for testing hypotheses about parameters in the regression models under the situation of grouped data are provided. A test statistic similar to conventional F statistic is considered. A simulation study performed for a few cases shows that the proposed statistic has an approximate F distribution and is useful in applications.     

独立运行小型风力发电系统负载跟踪和充放电集成控制

本文分析了小型风力机的运行特性,提出了实现负载跟踪和充放电集成控制的系统结构,提取出系统的工作模式及工作模式之间的转换关系,给出了实现系统模式相应的控制策略.本文给出的负载跟踪和充放电集成控制方法有利于实现独立运行小型风力发电系统的优化及可靠运行.     

《醒世姻缘传》概数表示法研究

概数表示法对于语言表达的准确性和生动性具有重要的意义。产生于明末清初的通俗小说《醒世姻缘传》中的概数表示法种类多样，体现出山东方言中的一些特殊用法，反映了山东方言称数法由近代汉语向现代汉语过渡的特点。     

基于折衷原则的PID控制方案的寻优

在满意解原则基础上, 通过控制系统各性能指标之间的矛盾关系求取其相似关系,从而确定了一种折衷原则,并以实例验证了基于这种折衷原则控制方案的寻优方法的正确性和合理性,讨论了该折衷原则的特点及适用范围。     

Exact inference for the two-parameter exponential distribution under Type-II hybrid censoring

Epstein (1954) introduced the Type-I hybrid censoring scheme as a mixture of Type-I and Type-II censoring schemes. Childs et al. (2003) introduced the Type-II hybrid censoring scheme as an alternative to Type-I hybrid censoring scheme, and provided the exact distribution of the maximum likelihood estimator of the mean of a one-parameter exponential distribution based on Type-II hybrid censored samples. The associated confidence interval also has been provided. The main aim of this paper is to consider a two-parameter exponential distribution, and to derive the exact distribution of the maximum likelihood estimators of the unknown parameters based on Type-II hybrid censored samples. The marginal distributions and the exact confidence intervals are also provided. The results can be used to derive the exact distribution of the maximum likelihood estimator of the percentile point, and to construct the associated confidence interval. Different methods are compared using extensive simulations and one data analysis has been performed for illustrative purposes.     

The gamma-Lomax distribution

For any continuous baseline G distribution, Zografos and Balakrishnan [On families of beta- and generalized gamma-generated distributions and associated inference. Statist Methodol. 2009;6:344–362] proposed a generalized gamma-generated distribution with an extra positive parameter. A new three-parameter continuous distribution called the gamma-Lomax distribution, which extends the Lomax distribution is proposed and studied. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile functions, mean deviations and Rényi entropy. The estimation of the model parameters is performed by maximum likelihood. We also determine the observed information matrix. An application illustrates the usefulness of the proposed model.