两广义Gaussian分布之间的最小Kullback-Leibler距离
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摘要
在Kullback-Leibler距离的基础上,对Kullback-Leibler距离进行了改进,给出了最小的Kullback-Leibler距离,并讨论了它的性质.探讨了两个不同概率密度函数的差异程度,得到了广义Gaussian分布最小的Kullback-Leibler距离,并作为特例得到了Laplacian分布和Gaussian分布最小的Kullback-Leibler距离.
In this paper,it gives the exact definition of the minimum Kullback-Leibler distance between two different distribution functions. The properties of the minimum Kullback-Leibler distance are discussed. The difference degree of two different probability density function are discussed. The minimum Kullback-Leibler distance between two different generalized Gaussian distribution are obtained. The minimum Kullback-Leibler distance of Laplacian distribution,Gaussian distribution are derived.
In this paper,it gives the exact definition of the minimum Kullback-Leibler distance between two different distribution functions. The properties of the minimum Kullback-Leibler distance are discussed. The difference degree of two different probability density function are discussed. The minimum Kullback-Leibler distance between two different generalized Gaussian distribution are obtained. The minimum Kullback-Leibler distance of Laplacian distribution,Gaussian distribution are derived.
引文
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[10]李开灿.Pearson-χ2距离的若干性质[J].数学的实践与认识,2003,33(1):49-53.
[11]李开灿,孟朝玲.χ2分布、t分布和F分布的一致渐进正态性[J].北京印刷学院学报,2004,12(3):30-33.
[2]Joshi R J,Fischer T R.Comparison of generalized Gaussian and laplacian modeling in DCT image coding[J].IEEE Trans,on signal processing letters,1995,2(5):81-82.
[3]Do M N,Vetteli M.Wavelet-based texture retrieval using generalized Gaussian density and Kullback-leibler distance[J].IEEE Trans,2002,11(2):146-158.
[4]Walden A T,Hosken J W J.The nature of the non-Gaussianity of primary reflection coefficients and its significance for deconvolution[R].The 47th meeting of the EAEG,Budapest,1985,1038-1066.
[5]Robert G O,Shau S K.Updating Schemes,Correlation Structure,Blocking and Parameterization for the Gibbs Sampler[J].J R Statist Soc B,1997(59):291-317.
[6]Liu S J,Wong W H,Kong A.Correlation Structure and Convergence Rate of the Gibbs Sampler with Various Scans[J].J R Statist Soc B,1995(57):157-169
[7]Reiss R D.Approximate Distributions of Order Statistics[M].New York:Springer,1980.
[8]金秀岩.广义Gaussian分布Pearson-χ2距离及其渐近性[J].西南师范大学学报,2007,33(5):1040-1045.
[9]蔡择林,李开灿.常见分布的最大Kullback-Leibler距离[J].武汉大学学报,2007,53(5):513-517.
[10]李开灿.Pearson-χ2距离的若干性质[J].数学的实践与认识,2003,33(1):49-53.
[11]李开灿,孟朝玲.χ2分布、t分布和F分布的一致渐进正态性[J].北京印刷学院学报,2004,12(3):30-33.