An intuitive clustering algorithm for spherical data with application to extrasolar planets

This paper proposes an intuitive clustering algorithm capable of automatically self-organizing data groups based on the original data structure. Comparisons between the propopsed algorithm and EM [1 A. Banerjee, I.S. Dhillon, J. Ghosh, and S. Sra, Clustering on the unit hypersphere using von Mises–Fisher distribution, J. Mach. Learn. Res. 6 (2005), pp. 1–39. [Google Scholar]] and spherical k-means [7 I.S. Dhillon and D.S. Modha, Concept decompositions for large sparse text data using clustering, Mach. Learn. 42 (2001), pp. 143–175. doi: 10.1023/A:1007612920971[Crossref], [Web of Science ®] , [Google Scholar]] algorithms are given. These numerical results show the effectiveness of the proposed algorithm, using the correct classification rate and the adjusted Rand index as evaluation criteria [5 J.-M. Chiou and P.-L. Li, Functional clustering and identifying substructures of longitudinal data, J. R. Statist. Soc. Ser. B. 69 (2007), pp. 679–699. doi: 10.1111/j.1467-9868.2007.00605.x[Crossref] , [Google Scholar],6 J.-M. Chiou and P.-L. Li, Correlation-based functional clustering via subspace projection, J. Am. Statist. Assoc. 103 (2008), pp. 1684–1692. doi: 10.1198/016214508000000814[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. In 1995, Mayor and Queloz announced the detection of the first extrasolar planet (exoplanet) around a Sun-like star. Since then, observational efforts of astronomers have led to the detection of more than 1000 exoplanets. These discoveries may provide important information for understanding the formation and evolution of planetary systems. The proposed clustering algorithm is therefore used to study the data gathered on exoplanets. Two main implications are also suggested: (1) there are three major clusters, which correspond to the exoplanets in the regimes of disc, ongoing tidal and tidal interactions, respectively, and (2) the stellar metallicity does not play a key role in exoplanet migration.     

A cramer - von mises type goodness of fit test with asymmetric weight function

A goodness of fit test of the Cramer - von Mises type, which gives more weight to the upper (or to the lower) tail of the distribution, is proposed and studied. It is found the orthogonal representation of the test for the case of a simple null hypothesis. The characteristic function of the asymptotic null distribution is found and inverted to get percentage points. The asymptotic power of the test is obtained for the normal null hypothesis, against mean and variance shifts and more asymmetric alternatives.

Also the case of the exponential null hypothesis is studied. It is found that the test, which emphasizes the upper tail, has more power than those of Anderson - Darling and Cramer - von Mises, against alternatives which differ from the null hypothesis mainly in the upper tail, and less power when the main difference is in the lower tail of the distribution.     

罗尔斯正义原则刍议

在罗尔斯所提出的有关社会正义的两个基本原则中 ,强调“最少受惠者的最大利益”的“差别原则”乃是罗尔斯正义论的重大创新和显著特征 ,但其中所表现出来的企图通过补偿与再分配而使所有社会成员都处于一种平等地位的思想愿望 ,也带有某种理想化的平均主义倾向 ,理论上也有其不充分、不完善的地方     

PSC考前培训的原则与方法

普通话水平测试(PSC)工作的顺利开展,一方面需要不断提高测试员素质,另一方面要加强普通话考前培训。加强PSC考前培训辅导对真正意义上的普及和提高普通话有着重要的现实意义。本文着重就培训的意义原则和具体操作实施方法作一阐述。     

Improper use of the ordinary least squares estimator in the switching regression model

The paper considers the consequences of incorrectly using the ordinary least squares estimator, when the true but unknown model is a switching regression. Bias and mean square error express ons are given for slope and residual variance estimators. Except for in very specialized cases the estimators are biased. A numerical exarnple illustrates some of the issues raised and provides a conpelison between the ordinary least squares and maximum likelihood estimators.     

An extension of the von mises distribution

Directional distribution theory is very useful for the estimation of directional spectra needed for the analysis of time series data. A four parameter directional exponential family is discussed. Depending on the values of its parameters this distribution can be unimodal symmetric, bimodal symmetric, unimodal non-symmetric, or bimodal non-symmetric. The moments of this distribution are found, and equations leading to maximum-likelihood estimates of the parameters along with an outline on numerical procedures for solving these equations are given. FORTRAN subroutines implementing these procedures are available from the authors. Finally, some applications of the new directional density are given.     

水管式热水锅炉水循环故障分析

论述了热水锅炉最小循环流速计算,对SZL型锅炉水循环故障进行了分析.