Plot[(xA(n/2-1)*Exp[-x/2]/2A(n/2)/Gamma[n/2])/.(n→1).(x,0,10)]0.30F0.25F0.20H0.15H0.10上0.05810246Plot[(x^(n/2-1)*Exp[-x/2]/2A(n/2)/Gamma[n/2])/.(n→10),(x,0,30)]0.080.06H0.040.0251015252030
root[o]TMath::Prob(1o.82.1)(D0ublet)1.00409489093039703e-03随机性的统计检验root[1]TMath::Prob(1o.83,1)(Doublet)9.98686379180259171e-04root[2] TMath::Prob(3.84.1)(Doublet)5.00435212487051889e-02。通常置信度水平选取为0.99或者0.95。为了反映均匀性分布的特性，k的取值不宜太小，但也不能太大。一般选取的k值，要能使每个子区间有若于个伪随机数时就比较合适。X?valuel19]Degreesoffreedom (df)10.060.150.461.071.640.0040.022.713.846.6410.8320.100.210.450.711.392.413.224.605.999.2113.8230.350.581.011.422.373.664.646.257.8211.3416.2740.711.061.652.203.364.885.997.789.4913.2818.4751.141.612.343.004.356.067.299.2411.0720.5215.0961.632.203.073.835.357.238.5610.6412.5922.4616.81712.022.172.833.824.676.358.389.8014.0718.4824.32813.362.733.494.595.537.349.5211.0315.5120.0926.1293.324.175.386.398.3410.6612.2414.6816.9221.6727.88107.273.944.876.189.3411.7813.4415.9918.3123.2129.590.950.900.800.700.500.300.200.100.050.010.001Pvalue(Probability)theprobabilityofobservingateststatisticatleastasextremeinachi-squareddistribution
随机性的统计检验 the probability of observing a test statistic at least as extreme in a chi-squared distribution
随机数产生算法的表现示例：平均值；方差；chi2(0.2886)4.121
随机数产生算法的表现 示例： 平均值； 方差； chi2
随机性的统计检验独立性检验：O游程检。独立性检验的方法也有若干，如有列联表检验，相关系数检验，验。这里介绍列联表检验。如果把[0.1]上的伪随机序列{$1.S2....$2N分成两组：S1,S3.....E2N-1E2, E4.....2N第一组作为随机变量的取值，第二组作为随机变量y的取值在x-y平面内的单位正方形域[0≤α≤1,0≤y≤1]上，分别以平行于坐标轴的平行线，将正方形域分成k×k个相同面积的小正方形网格。落在每个网格内的随机数的实际频数nij应当近似等于理论频数mij=是由此可以算出为：A(nij-mi)2V二miji,j=1同样，×2应满足×2（（k一1)2）的分布。据此可以采用与均匀性检验的2方法，假定出显著性水平来进行检验
随机性的统计检验
https://indico.ihep.ac.cn/event/4902/contribution/15/material/slides/0.pdfStatistical Methods for Particle PhysicsLecture l: intro, parameter estimation, testshttp://indico.ihep.ac.cn/event/49o2/五业万年iSTEP 2015Shandong University, JinanAugust 11-19, 2015GlenCowan（谷林·科恩）Physics DepartmentROYALRoyal Holloway, University of LondonHOLLOWAYg.cowan@rhul.ac.ukUNIVERSITYOFLONDONwww.pp.rhul.ac.uk/~cowan
https://indico.ihep.ac.cn/event/4902/contribution/15/material/slides/0.pdf