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.     

Bounded risk estimation of a linear combination of location parameters in negative exponential distributions via three-stage sampling

The paper deals with the problem of bounded risk point estimation for a linear combination of location parameters of two negative exponential distributions. Isogai and Futschik considered the situation when the location and scale parameters are all unknown. They proposed purely sequential procedures and gave second order expansions of the average sample sizes and risks. In this paper we propose three-stage procedures and derive second order expansions of the average sample sizes and risks. Further, we compare the results with those from previous work.     

The beta generalized linear exponential distribution

In this paper, a new five-parameter lifetime distribution called beta generalized linear exponential distribution (BGLED) is introduced. It includes at least 17 popular sub-models as special cases such as the beta linear exponential, the beta generalized exponential, and the exponentiated generalized linear distributions. Mathematical and statistical properties of the proposed distribution are discussed in details. In particular, explicit expression for the density function, moments, asymptotics distributions for sample extreme statistics, and other statistical measures are obtained. The estimation of the parameters by the method of maximum-likelihood is discussed and the finite sample properties of the maximum-likelihood estimators (MLEs) are investigated numerically. A real data set is used to demonstrate its superior performance fit over several existing popular lifetime models.     

四川盆地雷口坡组层序岩相古地理

针对四川盆地各矿区雷口坡组地层划分方案不统一，且受早印支运动的影响，雷口坡组顶部岩溶带地层垮塌破坏，造成地层内幕划分及岩相古地理恢复困难的难题，以层序地层学理论与方法为指导，重新厘定了盆地内雷口坡组的地层划分方案，以四级层序为作图单元进行层序岩相古地理重建。高精度的层序岩相古地理研究表明，雷口坡期四川盆地处于局限–蒸发海环境，在川西北一带靠近松潘—甘孜海槽一带发育有台地边缘，台地内部颗粒滩和台地边缘颗粒滩构成了雷口坡组的勘探主体。岩相古地理的演化表明，雷口坡组沉积时期盆地底形发生了东倾向西倾“跷跷板”式的转换，在层序I 早期仍保持了早三叠世西高东低的地形格局，至层序III 沉积期东倾趋势消失，层序IVV 沉积时期盆地内隆凹格局略具雏形。伴随着构造挤压运动的加剧，从层序VI 开始盆地底形隆凹格局分异加剧，形成巨厚膏盐盆，膏盐盆沉积中心在层序VIX 沉积时期具有明显西移的趋势。     

All pairwise comparisons of exponential location parameters under type i censoring — equal scale parameter case

In this paper, procedures for all pairwise comparisons of location parameters of negative exponential populations are developed when the common scale parameter is known or unknown using large sample distributional approximations of the relevant random variables. The small sample performance of these procedures are then examined using Monte Carlo simulation.     

Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models

Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.     

70年代国外习得顺序研究综述(二)

本文回顾了70年代句子习得顺序的相关研究,主要涉及否定句、疑问句的习得顺序的相关研究,也提及70年代提出的关于关系从句的习得顺序的三大研究假设,最后指出70年代习得顺序研究的意义和不足之处以及之后该领域的主要研究动态。     

Asymptotocally nonparametric tests with censored paired data

A class of asymptotically nonparametric test with contains a test proposed by Wei(1980), is considered for testing the equality of two continuous distribution funcitons when paired observations are subject to arbitrary right censorship. It is shown that under the null hypothesis each test statistic converges in distribution to the standard normal random variable. Furthermore. the Monte Carlo simulation results indicate that some tests in this class are more powerful than Wei's test. A generalization to incomplete censored paired data is also included.     

Locally best invariant test for outliers in a gamma type distribution

It is shown that the locally best invariant test for the existence of outliers for scale parameters of the gamma distribution is given by Bartholomew's test for exponentiality which is the ratio of the sum of squares of the data to the square of the sample mean. The optimality robustness, including null and nonnull robustness of the test is shown. A small simulation study to compare the power among the other eight competitive tests for testing exponentiality is performed. It is seen that the locally best invariant test is not always best but is reasonably good. It is slightly better than Cochran's test and suffers less from the limiting masking effect.