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应用数学学报  2012, Vol. Issue (6): 984-1002    DOI:
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对称的ι1-球分布:性质与应用
余君武
湖南科技大学数学与计算科学学院, 湘潭 411201
Symmetric ι1-spherical Distributions: Properties and Applications
YU Junwu
School of Mathematics and Computation Science, Hunan University of Science and Technology, Xiangtan, 411201
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摘要 本文研究了一个有用的nι1-球分布族LSn和对称的ι1-球分布的 某些重要的性质. 导出了z(z∈ LSn)的边际分布、条件分布、生存函数、双边指数分布的尺度混合分布类(被表示为 LSn, ∞), 讨论了它们的独立性、刻画和稳健性. 并应用在非参数预测和数论网的产生中. 最后, 在模型诊断与异常值检验中, 用蒙特卡罗方法, 获得了非常有用的某些检验统计量的分位数.
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余君武
关键词刻画   双边指数分布   拉普拉斯分布   ι1-球分布   稳健性     
Abstract: In this paper, we study a useful family of n-dimensionalι1-spherical distributions (denoted as LSn). Although the symmetric ι1-spherical distribution has long been known to be a special case of the more general ιp-spherical distribution, some of its important properties have not yet been explored. We first derive the marginal and conditional distributions of z ∈ LSn when the joint density function of z does not exist. We also present the survival function for LSn. We then investigate the class of scale mixtures of a random vector with independently and identically distributed double exponential components (denoted by LSn, ∞) and its relationship with LSn. Other properties such as independency, characterization and robustness are also studied. Applications in nonparametric prediction and generation of number-theoretic nets will be presented. Monte Carlo methods are utilized to obtain the quantiles of some test statistics which are useful in model diagnostics and outlier detection.
Key wordscharacterization   double exponential distribution   Laplace distribution   ιp-spherical distribution   robustness   
收稿日期: 2012-04-06;
基金资助:

国家社会科学基金(09BTJ012)和湖南省科技厅计划(11JB1176)资助项目.

引用本文:   
余君武. 对称的ι1-球分布:性质与应用[J]. 应用数学学报, 2012, (6): 984-1002.
YU Junwu. Symmetric ι1-spherical Distributions: Properties and Applications[J]. Acta Mathematicae Applicatae Sinica, 2012, (6): 984-1002.
 
[1] Ng K W, Tian G L. Characteristic Functions ofι1-spherical and ι1-norm Symmetric Distributions and their Applications. J. Multi. Anal., 76: 192-213 (2001)
[2] Johnson N L, Kotz S. Distribution in Statistics: Continuous Univariate Distribution-1, Vol.2, New York, Wiley, 1970
[3] Liang Y, Leung K S. Genetic Algorithm with Adaptive Elitist-population Strategies for Multimodal Function Optimization. Appl. Soft Compu., 2011, 11: 2017-2034
[4] Plucinska A. On Certain Problems Connected with a Division of a Normal Population into Parts. Zastosowania Matematyki, 1965, 8: 117-125 (in Polish)
[5] Fang K T, Wang Y. Number-theoretic Methods in Statistics. London: Chapman & Hall, 1994
[6] Cai W W, Ewing D J, Ma L. Investigation of Temperature Parallel Simulated Annealing for Optimizing Continuous Functions with Application to Hyperspectral Tomography. Appl. Math. Comput., 2011, 217: 5754-5767
[7] Takemura A, Kuriki S. Theory of Cross Sectionally Contoured Distributions and its Applications. Institute of the Japanese Economy, University of Tokyo, 1996
[8] Thangaraj R, Pant M, Abraham A, Bouvry P. Particle Swarm Optimization: Hybridization Perspectives and Experimental Illustrations. Applied Mathematics and Computation, 2011, 217: 5208-5226
[9] Chmielewski M A. Elliptically Symmetric Distributions: a Review and Bibliography. Inter. Statist. Review, 1981, 49: 67-74
[10] Xiao J, Li L. A Hybrid Ant Colony Optimization for Continuous Domains. Expert Syst. Appl., 2011, doi: 10. 1016/j.eswa.2011.02.151
[11] Gupta R D, Richards D St P. Multivariate Liouville Distributions. J. Multi. Anal., 1987, 23: 233-256
[12] 李晓磊, 邵之江, 钱积新. 一种基于动物自治体的寻优模式: 鱼群算法. 系统工程理论与实践, 2002, 22(11): 32-38 (Li Xiaolei, Shao Zhijiang, Qian Jixin. An Optimizing Method Based on Autonomous Animats: Fish-swarm Algorithm. Systems Engineering Theory and Practice, 2002, 22(11): 32-38)
[13] Karaboga D. An Idea Based on Honey Bee Swarm for Numerical Optimization. Kayseri: Erciyes University, 2005
[14] Cambanis S, Keener R, Simons G. On α-symmetric Distributions. J. Multi. Anal., 1983, 13: 213-233
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