Estimation under modified Weibull distribution based on right censored generalized order statistics

In this paper, the maximum likelihood (ML) and Bayes, by using Markov chain Monte Carlo (MCMC), methods are considered to estimate the parameters of three-parameter modified Weibull distribution (MWD(β, τ, λ)) based on a right censored sample of generalized order statistics (gos). Simulation experiments are conducted to demonstrate the efficiency of the proposed methods. Some comparisons are carried out between the ML and Bayes methods by computing the mean squared errors (MSEs), Akaike's information criteria (AIC) and Bayesian information criteria (BIC) of the estimates to illustrate the paper. Three real data sets from Weibull(α, β) distribution are introduced and analyzed using the MWD(β, τ, λ) and also using the Weibull(α, β) distribution. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic, {AIC and BIC} to emphasize that the MWD(β, τ, λ) fits the data better than the other distribution. All parameters are estimated based on type-II censored sample, censored upper record values and progressively type-II censored sample which are generated from the real data sets.     

A course in constructing effective displays of data for pharmaceutical research personnel

Interpreting data and communicating effectively through graphs and tables are requisite skills for statisticians and non‐statisticians in the pharmaceutical industry. However, the quality of visual displays of data in the medical and pharmaceutical literature and at scientific conferences is severely lacking. We describe an interactive, workshop‐driven, 2‐day short course that we constructed for pharmaceutical research personnel to learn these skills. The examples in the course and the workshop datasets source from our professional experiences, the scientific literature, and the mass media. During the course, the participants are exposed to and gain hands‐on experience with the principles of visual and graphical perception, design, and construction of both graphic and tabular displays of quantitative and qualitative information. After completing the course, with a critical eye, the participants are able to construct, revise, critique, and interpret graphic and tabular displays according to an extensive set of guidelines. Copyright © 2013 John Wiley & Sons, Ltd.     

On the use of different metrics for assessing complex pattern reproductions

Nowadays, there is an increasing interest in multi-point models and their applications in Earth sciences. However, users not only ask for multi-point methods able to capture the uncertainties of complex structures and to reproduce the properties of a training image, but also they need quantitative tools for assessing whether a set of realizations have the properties required. Moreover, it is crucial to study the sensitivity of the realizations to the size of the data template and to analyze how fast realization-based statistics converge on average toward training-based statistics. In this paper, some similarity measures and convergence indexes, based on some physically measurable quantities and cumulants of high-order, are presented. In the case study, multi-point simulations of the spatial distribution of coarse-grained limestone and calcareous rock, generated by using three templates of different sizes, are compared and convergence toward training-based statistics is analyzed by taking into account increasing numbers of realizations.     

On a bounded bimodal two-sided distribution fitted to the Old-Faithful geyser data

In this paper, we shall develop a novel family of bimodal univariate distributions (also allowing for unimodal shapes) and demonstrate its use utilizing the well-known and almost classical data set involving durations and waiting times of eruptions of the Old-Faithful geyser in Yellowstone park. Specifically, we shall analyze the Old-Faithful data set with 272 data points provided in Dekking et al. [3]. In the process, we develop a bivariate distribution using a copula technique and compare its fit to a mixture of bivariate normal distributions also fitted to the same bivariate data set. We believe the fit-analysis and comparison is primarily illustrative from an educational perspective for distribution theory modelers, since in the process a variety of statistical techniques are demonstrated. We do not claim one model as preferred over the other.     

网络舆论倾向性的动态跟踪方法及实证研究

从统计学视角审视网络舆论倾向性的监测问题,提出了以粗糙分类器为基础建立舆论倾向性分类模型,将复杂的预警指标体系简化为单一直观的跟踪统计量,并通过跟踪统计量动态跟踪舆论倾向性变化轨迹的研究方法。实证研究以2011年郭美美事件相关新闻跟帖为对象。分析表明,网络舆论的消极倾向性在整个事件发展过程中呈持续增长,与基本事实相符,证实了方法的可行性和适用性。     

从统计学史解析“自由度”概念

自由度是统计学中一个十分重要而又长期没有被圆满解释的概念。对此,从统计学史角度,对皮尔逊、费歇尔有关自由度问题争论原始文献细致考察,彻底澄清了自由度概念的内涵及与其相关的统计思想,弥补了Fienberg、Stigler与陈希孺已有解释的缺陷。研究表明：皮尔逊关于卡方检验中无论总体分布已知还是其来自于样本推断统计量都具有同一分布的错误判断,导致卡方检验的准确性出现偏差,这种偏差虽被同时代少数几个统计学家察觉但他们却无法解释其根源。费歇尔提出自由度概念并结合n维几何、假设检验与最大似然方法的论证不仅修正了皮尔逊的错误,也完善了从样本统计量估计总体参数的数理逻辑。     

A Recursive Formula for the Probability of Occurrence of at Least m out of N Events

A recursive same-sign relation is derived that reduces the probability of occurrence of at least m out of N independent events to the probability of occurrence of at least m out of N ? 1 of these N events.     

Multiple Comparison Procedures: The Practical Solution

A practicing statistician looks at the multiple comparison controversy and related issues through the eyes of the users. The concept of consistency is introduced and discussed in relation to five of the more common multiple comparison procedures. All of the procedures are found to be inconsistent except the simplest procedure, the unrestricted least significant difference (LSD) procedure (or multiple t test). For this and other reasons the unrestricted LSD procedure is recommended for general use, with the proviso that it should be viewed as a hypothesis generator rather than as a method for simultaneous hypothesis generation and testing. The implications for Scheffé's test for general contrasts are also discussed, and a new recommendation is made.     

Progressive type II censored order statistics from exponential distributions

In the model of progressive type II censoring, point and interval estimation as well as relations for single and product moments are considered. Based on two-parameter exponential distributions, maximum likelihood estimators (MLEs), uniformly minimum variance unbiased estimators (UMVUEs) and best linear unbiased estimators (BLUEs) are derived for both location and scale parameters. Some properties of these estimators are shown. Moreover, results for single and product moments of progressive type II censored order statistics are presented to obtain recurrence relations from exponential and truncated exponential distributions. These relations may then be used to compute all the means, variances and covariances of progressive type II censored order statistics based on exponential distributions for arbitrary censoring schemes. The presented recurrence relations simplify those given by Aggarwala and Balakrishnan (1996)     

Generalized exponential distribution: Moments of order statistics

In this paper, we consider the generalized exponential distribution (GED) with shape parameter α. We establish several recurrence relations satisfied by the single and the product moments for order statistics from the GED. The relationships can be written in terms of polygamma and hypergeometric functions and used in a simple recursive manner in order to compute the single and the product moments of all order statistics for all sample sizes.