The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.     

Testing for Serial Independence: Beyond the Portmanteau Approach

Portmanteau tests are typically used to test serial independence even if, by construction, they are generally powerful only in presence of pairwise dependence between lagged variables. In this article, we present a simple statistic defining a new serial independence test, which is able to detect more general forms of dependence. In particular, differently from the Portmanteau tests, the resulting test is powerful also under a dependent process characterized by pairwise independence. A diagram, based on p-values from the proposed test, is introduced to investigate serial dependence. Finally, the effectiveness of the proposal is evaluated in a simulation study and with an application on financial data. Both show that the new test, used in synergy with the existing ones, helps in the identification of the true data-generating process. Supplementary materials for this article are available online.     

Likelihood ratio order of parallel systems under multiple-outlier models

This paper studies the likelihood ratio ordering of parallel systems under multiple-outlier models. We introduce a partial order, the so-called θ-order, and show that the θ-order between the parameter vectors of the parallel systems implies the likelihood ratio order between the systems.     

慈善与慈善组织的秩序维度与政策选择

人是生活在秩序维度的，人的生命的价值，尤其是劳动力的价值，与处于不同秩序维度有关系。公共慈善也是如此。它有原始秩序的维度，也有扩展秩序的维度，在不同的维度里，有不同的价值。从特朗普家族慈善基金会的命运，可以见出慈善和慈善组织涉及到的不同维度秩序的冲突。更好地发展慈善和慈善组织，需要解决冲突，在不同的秩序维度里，处理好各个方面的关系。     

词序像似性研究及实例分析

像似性是相对任意性而言的。语言像似性是指语言形式或结构与其所表达的概念之间存在对应关系,而词序像似性是指词的组织形式和人的认知结构之间有某种对应关系,主要受四个原则支配:顺序像似原则、距离像似原则、与说话人接近原则和文化规约像似原则。正确理解词序像似性的概念和原则,对目标语的学习有重要的指导意义。     

The generalized odd half-Cauchy family of distributions: Properties and applications

We introduce and study general mathematical properties of a new generator of continuous distributions with one extra parameter called the generalized odd half-Cauchy family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear mixture of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the flexibility of the new family by means of two real data sets.     

The Kumaraswamy GEV distribution

The popular generalized extreme value (GEV) distribution has not been a flexible model for extreme values in many areas. We propose a generalization – referred to as the Kumaraswamy GEV distribution – and provide a comprehensive treatment of its mathematical properties. We estimate its parameters by the method of maximum likelihood and provide the observed information matrix. An application to some real data illustrates flexibility of the new model. Finally, some bivariate generalizations of the model are proposed.     

Stochastic comparisons between extreme order statistics from scale models

Stochastic ordering relations between extreme order statistics from exponential, Weibull and gamma distributions have been studied extensively by many researchers in recent years. In this work, we obtain various ordering results for the comparisons of two extreme order statistics from scale models when one set of scale parameters majorizes the other. The new results obtained here are applied when the baseline distributions are exponentiated Weibull or generalized gamma distributions. In this way, we generalize and extend some results established recently in the literature.     

数量体现述式的系统功能语法研究

系统功能语言学中的系统语法是体现性语法，语言被视为意义资源系统，而非封闭自足的规则系统。系统语法和阶与范畴语法的一个变化就是体现述式的引入，体现述式是对层际或层内体现关系的一种建模由操作项和操作符构成。系统功能语法主要识别了插入、排序、重合、扩展、预选等五种体现述式，本文基于系统功能语法对数量在体现过程中的体现述式进行跨语言的探索研究。      

Pitman closeness,monotonicity and consistency of best linear unbiased and invariant estimators for exponential distribution under Type II censoring

Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last 50 years since the ground breaking work of Lloyd [E.H. Lloyd, Least squares estimation of location and scale parameters using order statistics, Biometrika 39 (1952), pp. 88–95]. These comparisons have been made under many different criteria across different parametric families of distributions. A noteworthy one is by Nagaraja [H.N. Nagaraja, Comparison of estimators and predictors from two-parameter exponential distribution, Sankhyā Ser. B 48 (1986), pp. 10–18], who made a comparison of best linear unbiased (BLUE) and best linear invariant (BLIE) estimators in the case of exponential distribution. In this paper, continuing along the same lines by assuming a Type II right censored sample from a scaled-exponential distribution, we first compare BLUE and BLIE of the exponential mean parameter in terms of Pitman closeness (nearness) criterion. We show that the BLUE is always Pitman closer than the BLIE. Next, we introduce the notions of Pitman monotonicity and Pitman consistency, and then establish that both BLUE and BLIE possess these two properties.