We use latitude, longitude and magnitude data for foreshocks during 72 hours before the earthquake off the Pacific coast of Tohoku, Japan, a magnitude 9.0 (MW), occurred at 14 : 46 JST (05 : 46 UTC) on 11 March, 2011 with the epicenter 38.30 degrees for latitude and 142.37 degrees for longitude approximately 70 kilometers east of the coast. The data were taken from the website at http://earthquake.usgs.gov/earthquakes/eqarchives/epic/ epic global.php.
Graphical methods and a statistical test are used to detect change points in mean direction for turning angles between successive earthquakes epicenter. Model selection and fitting are studied for Jones and Pewsey’s (2005) distribution as a full model and cardioid, von Mises, and wrapped Cauchy distributions as submodels.
A distribution for magnitude M is introduced as the one whose transformed random variable R = exp{−(M − c)} is distributed as Kumaraswamy’s (1980) distribution, where c is a threshold value. The resulting distribution includes the exponential distribution as a special case. The paper studies joint distributions on the cylinder for magnitudes and successive angles with their fit to the data. It also discusses applicability of a modified Möbius distribution on the unit disc for transformed magnitudes and successive angles.

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An important theme in survival analysis is the investigation of prognosis factors that affect survival time. The tree-structured method has been applied to evaluate covariates; however, this method apparently has poor predictive outcomes. This problem may be improved by modeling many trees in a linear combination, as carried out in ensemble learning. The ensemble learning method has been actively studied in machine learning and statistics. Recently, several ensemble methods have been extended to ensure right-censored survival outcomes. Ishwaran et al. (2008) proposed the random survival forest method, which is constructed using a committee of many survival trees based on logrank statistics or Harrell’s C index. Ridgeway (2008) extended the multivariate additive regression trees (MART) method using the framework of the generalized linear model. Since these ensemble methods construct models having a “black box” nature, the models are difficult to intercept. Friedman and Popescu (2008) proposed the rule ensemble method, in which nodes of tree models are used as base learners. In this paper, we propose the newly developed rule ensemble method to analyze survival data, namely the survival rule ensemble method. The usefulness of the survival rule ensemble method is illustrated by a practical example in oncology data. By carrying out small-scale simulations, we found that the survival rule ensemble method showed better predictive performance compared with existing ensemble methods for survival outcomes.

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