Correlation-Type Goodness of Fit Test for Extreme Value Distribution Based on Simultaneous Closeness

In reliability studies, one typically would assume a lifetime distribution for the units under study and then carry out the required analysis. One popular choice for the lifetime distribution is the family of two-parameter Weibull distributions (with scale and shape parameters) which, through a logarithmic transformation, can be transformed to the family of two-parameter extreme value distributions (with location and scale parameters). In carrying out a parametric analysis of this type, it is highly desirable to be able to test the validity of such a model assumption. A basic tool that is useful for this purpose is a quantile–quantile (QQ) plot, but in its use, the issue of the choice of plotting position arises. Here, by adopting the optimal plotting points based on Pitman closeness criterion proposed recently by Balakrishnan et al. (2010b Balakrishnan , N. , Davies , K. F. , Keating , J. P. , Mason , R. L. ( 2010b ). Computation of optimal plotting points based on Pitman Closeness with an application to goodness of fit for location-scale families. Submitted to Computational Statistics & Data Analysis.  [Google Scholar]), and referred to as simultaneous closeness probability (SCP) plotting points, we propose a correlation-type goodness of fit test for the extreme value distribution. We compute the SCP plotting points for various sample sizes and use them to determine the mean, standard deviation and critical values for the proposed correlation-type test statistic. Using these critical values, we carry out a power study, similar to the one carried out by Kinnison (1989 Kinnison , R. ( 1989 ). Correlation coefficient goodness of fit test for extreme value distribution . The American Statistician 43 : 98 – 100 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), through which we demonstrate that the use of SCP plotting points results in better power than with the use of mean ranks as plotting points and nearly the same power as with the use of median ranks. We then demonstrate the use of the SCP plotting points and the associated correlation-type test for Weibull analysis with an illustrative example. Finally, for the sake of comparison, we also adapt two statistics proposed by Gan and Koehler (1990 Gan , F. F. , Koehler , K. J. ( 1990 ). Goodness of fit based on P-P probability plots . Technometrics 32 : 289 – 303 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), in the context of probability–probability (PP) plots, based on SCP plotting points and compare their performance to those based on mean ranks. The empirical study also reveals that the tests from the QQ plot have better power than those from the PP plot.     

Further Results on Order Statistics Generated by Two Simulation Methods

Uniform order statistics generated by two simulation methods are compared by means of Pitman’s measure of closeness. This measure, as a probability, is shown to be asymptotically 1/2. Some results are also established for fixed points of the cumulative distribution function (CDF) for a uniform order statistic. These fixed points are important for calculations involving the joint distribution of these order statistics.     

A Viable Alternative to Resorting to Statistical Tables

It is shown in this article that, given the moments of a distribution, any percentage point can be accurately determined from an approximation of the corresponding density function in terms of the product of an appropriate baseline density and a polynomial adjustment. This approach, which is based on a moment-matching technique, is not only conceptually simple but easy to implement. As illustrated by several applications, the percentiles so obtained are in excellent agreement with the tabulated values. Whereas statistical tables, if at all available or accessible, can hardly ever cover all the potentially useful combinations of the parameters associated with a random quantity of interest, the proposed methodology has no such limitation.     

Estimating mixtures of normal distributions via empirical characteristic function

This paper uses the empirical characteristic function (ECF) procedure to estimate the parameters of mixtures of normal distributions. Since the characteristic function is uniformly bounded, the procedure gives estimates that are numerically stable. It is shown that, using Monte Carlo simulation, the finite sample properties of th ECF estimator are very good, even in the case where the popular maximum likelihood estimator fails to exist. An empirical application is illustrated using the monthl excess return of the Nyse value-weighted index.     

小型回转点云的配准研究

针对回转半径较大的小型回转点云配准时其回转特征不明显问题,提出一种先利用最小二乘法计算出点云的拟合平面并将所有点投影到该平面上,再利用滚球算法计算该二维点云数据的边界,并对边界点云进行3次B样条拟合,最后根据B样条曲线的变化特点,找出特征点,并利用特征点进行配准。对于回转半径较大且尺寸较小的回转点云,由 于其回转特性不是非常明显,因此完全依靠其回转特性进行配准,会有一定的难度,所以需要利用其他一些特征进行配准。最后通过三坐标扫描仪获取物体的外表面形状数据,然后进行配合验证,结果表明可以准确获取特征点。该方法可以有效地对小型点云进行配准。     

论《了不起的盖茨比》的"奇特化"艺术

菲茨杰拉德在其代表作《了不起的盖茨比》中对“奇特化”艺术手法的运用极为出色,主要表现为题材的奇特化、奇特化的场景和奇特化的叙述视角等几种形态,从而把一个平淡无奇的三角恋爱故事题材雕刻成了一部充满了被扭曲的浪漫情调的悲剧性作品。     

Mobilizing on Campus: Conservative Movements and Today’s College Students1

Social movement scholars have known for some time that students, and particularly college students, play an important role in modern social movements. Yet the full extent of conservative mobilizing, both today and in the past, is frequently overlooked. This article highlights the critical role college campuses have played in the rise of conservative movements in the United States over the last 40 years. In doing so, it develops a concept of transition points to help explain the mechanisms responsible for the longstanding finding that college students form an important core of many social movements. Transition points are marked by both changes in routines and changes in social network configuration. The utility of the transition point concept is explored through ethnographic and interview data from the American pro‐life movement.