K-S检验下的copula分布估计算法边缘分布的研究Research on Marginal Distribution in Copula Estimation of Distribution Algorithm Based on K-S test
赵慧,王丽芳,介婧,刘洁
摘要(Abstract):
借鉴K-S检验的思想,应用到copula分布估计算法边缘分布函数的选取中。在估计概率模型阶段,根据实际样本点来建立模型确定所服从的边缘分布函数,其中采用多种不同的分布函数(柯西分布、t分布和正态分布等)作为候选的边缘分布函数。在参数估计阶段,采用PMLE估计copula函数参数的方式进行仿真实验。根据所服从的不同的边缘分布分别进行采样,从而增加种群多样性,改善基于copula分布估计算法的执行效率。
关键词(KeyWords): copula分布估计算法;K-S检验;边缘分布函数
基金项目(Foundation): 山西省青年科学基金(2010021017-2);; 山西省高校产业化项目(2010015);; 山西省优秀研究生创新项目(20113121);; 太原科技大学博士基金(20122009);; 太原科技大学研究生创新项目(20125012)
作者(Author): 赵慧,王丽芳,介婧,刘洁
参考文献(References):
- [1]周树德,孙增圻.分布估计算法综述[J].自动化学报,2007,33(2):113-124.
- [2]LARRANAGA P,ETXEBERRIA R,LOZANO J A,et al.Optimization in Continuous Domains by Learning and Simulation ofGaussian Networks[C]∥Proceedings of the GECCO-2000 Workshop in Optimization by Building and Using Probabilistic Mod-els.San Francisco,2000:201-204.
- [3]王丽芳.Copula的分布估计算法[M].机械工业出版社,2012.
- [4]王丽芳,曾建潮,洪毅.利用Copula函数估计概率模型并采样的分布估计算法[J].控制与决策,2011,26(9):1333-1338.
- [5]杨兴民.Copula理论及其在相关分析中的应用[D].济南:山东大学,2007.
- [6]侯澍旻,李友荣,刘光临.K-S检验在轴承故障诊断中的应用[J].煤矿机械,2004(1):129-130.
- [7]吴喜之.非参数统计[M].北京:中国统计出版社,1992.
- [8]STEPHENS M A.“Tests based on EDF Statistics.”In Goodness-of-Fit Techniques[M].Macel Dekker,New York,1986:97-195.
- [9]杨茹.Clayton Copula分布估计算法中边缘分布的研究[D].太原:太原科技大学,2011.
- [10]WANG L,ZENG J,HONG Y.Estimation of Distribution Algorithm Based on Copula Theory[C]∥IEEE Congress on Evolution-ary Computation 2009.Trondheim,Norway,2009:1057-1063.
- [11]WANG L,ZENG J.Estimation of Distribution Based on Copula Theory[M]∥Exploitation of Linkage Learning in EvolutionaryAlgorithms.NY:Springer,2010:139-162.
- [12]WANG L,ZENG J,HONG Y.Estimation of Distribution Based on Archimedean Copulas[C]∥2009 World Summit on Geneticand Evolutionary Computation.Shanghai,China,2009:993-996.
- [13]SALINAS-GUTIERREZ R,HERNANDEZ-AGUIRRE A,VILLA-DIHARCE E R.Using Copulas in Estimation of DistributionAlgorithms[M]∥LNAI 5845,MICAI 2009.NY:Spring,2009:658-668.
- [14]WANG L,WANG Y,ZENG J,et al.An Estimation of Distribution Algorithm Based on Clayton Copula and Empirical Margin[C]∥Life System Modeling and Intelligent Computing,Communications in Computer and Information Science.Wuxi,China,2010,98(1):82-88.
- [15]WANG L,ZENG J,HONG Y.Using Gumbel Copula and Empirical Marginal Distribution in Estimation of Distribution Algo-rithm[C]∥2010 Third International Workshop on Advanced Computational Intelligence(IWACI 2010).Suzhou,China,2010:583-587.
- [16]WANG L,ZENG J,HONG Y,et al.Copula Estimation of Distribution Algorithm Sampling from Clayton Copula[J].Journal ofComputational Information Systems,2010,6(7):2431-2440
- [17]GUO X,WANG L,ZENG J,et al.Copula Estimation of Distribution Algorithm with PMLE[C]∥2011 7th International Confer-ence on Natural Computation.Shanhai,China,2011:1077-1081.
- [18]邱小霞,刘次华,吴娟.Copula函数中参数极大似然估计的性质[J].经济学,2008,25(2):212-215.