摘要
本文研究了一个有用的n维e_1-球分布族LS_n和对称的e_1-球分布的某些重要的性质.导出了z(z∈LS_n)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LS_(n,∞)),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.
In this paper, we study a useful family of n-dimensional l1-spherical distribu- tions （denoted as LSn. Although the symmetric l1-spherical distribution has long been known to be a special case of the more general lp-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.
出处
《应用数学学报》
CSCD
北大核心
2012年第6期984-1002,共19页
Acta Mathematicae Applicatae Sinica
基金
国家社会科学基金(09BTJ012)
湖南省科技厅计划(11JB1176)资助项目
关键词
刻画
双边指数分布
拉普拉斯分布
e_1-球分布
稳健性
characterization
double exponential distribution
Laplace distribution
lp-spherical distribution
robustness
