常用统计分布.ppt

单击此处编辑母版标题样式,常用统计分布,一、常见分布,二、概率分布的分位数,三、小结,一、常见分布,性质,1,(此性质可以推广到多个随机变量的情形),性质,2,证明,性质,3,同理,与,相互独立,2.,当,n,充分大时,其图形类似于标准正态变量概率密度的图形.,演 示,t,分布,具有下列性质：,性质5.6 设 ,则当 时有,性质5.7 设 ，是,T,的分布密度，,则,此性质说明，当 时，,T,分布的极限,分布是标准正态分布。,3.,其概率密度为,:,(1),(2),演 示,这说明,F,分布极限分布也是正态分布.,(3),二、概率分布的分位数,附表2-1,根据正态分布的对称性知,附表2-2,由分布的对称性知,附表3-1,附表3-2,附表4-1,附表4只详列到,n,=45,为止.,附表4-2,附表4-3,在,Matlab,中求解,例如,利用上公式,费,歇资料,费歇(,R.A.Fisher,),证明:,附表5-1,附表5-2,证明,三、小结,1.三大统计分布,的定义,性质.,2.,概率分布的分位数,附表2-1,标准正态分布表,z,0.00,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2,1.3,1.4,1.5,1.6,0.5000,0.5398,0.5793,0.6179,0.6554,0.6915,0.7257,0.7580,0.7881,0.8159,0.8413,0.8643,0.8849,0.9032,0.9192,0.9332,0.9452,0.5040,0.5438,0.5832,0.6217,0.6591,0.6950,0.7291,0.7611,0.7910,0.8186,0.8438,0.8665,0.8869,0.9049,0.9207,0.9345,0.9463,0.5080,0.5478,0.5871,0.6255,0.6628,0.6985,0.7324,0.7642,0.7939,0.8212,0.8461,0.8686,0.8888,0.9066,0.9222,0.9357,0.9474,0.5120,0.5517,0.5910,0.6293,0.6664,0.7019,0.7357,0.7673,0.7967,0.8238,0.8485,0.8708,0.8907,0.9082,0.9236,0.9370,0.9484,0.5160,0.5557,0.5948,0.6331,0.6700,0.7054,0.7389,0.7703,0.7995,0.8264,0.8508,0.8729,0.8925,0.9099,0.9251,0.9382,0.9495,0.5199,0.5596,0.5987,0.6368,0.6736,0.7088,0.7422,0.7734,0.8023,0.8289,0.8531,0.8749,0.8944,0.9115,0.9265,0.9394,0.9505,0.5239,0.5636,0.6026,0.6406,0.6772,0.7123,0.7454,0.7764,0.8051,0.8315,0.8554,0.8770,0.8962,0.9131,0.9278,0.9406,0.9515,0.5279,0.5675,0.6064,0.6443,0.6808,0.7157,0.7486,0.7794,0.8078,0.8340,0.8577,0.8790,0.8980,0.9147,0.9292,0.9418,0.9525,0.5319,0.5714,0.6103,0.6480,0.6844,0.7190,0.7517,0.7823,0.8106,0.8365,0.8599,0.8810,0.8997,0.9162,0.9306,0.9430,0.9535,0.5359,0.5753,0.6141,0.6517,0.6879,0.7224,0.7549,0.7852,0.8133,0.8389,0.8621,0.8830,0.9015,0.9177,0.9319,0.9441,0.9545,1.645,附表2-2,标准正态分布表,z,0.00,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,1.6,1.7,1.8,1.9,2.0,2.1,2.2,2.3,2.4,2.5,2.6,2.7,2.8,2.9,3.0,0.9452,0.9554,0.9641,0.9713,0.9772,0.9821,0.9861,0.9893,0.9918,0.9938,0.9953,0.9965,0.9974,0.9981,0.9987,0.9463,0.9564,0.9648,0.9719,0.9778,0.9826,0.9864,0.9896,0.9920,0.9940,0.9955,0.9966,0.9975,0.9982,0.9990,0.9474,0.9573,0.9656,0.9726,0.9783,0.9830,0.9868,0.9898,0.9922,0.9941,0.9956,0.9967,0.9976,0.9982,0.9993,0.9484,0.9582,0.9664,0.9732,0.9788,0.9834,0.9871,0.9901,0.9925,0.9943,0.9957,0.9968,0.9977,0.9983,0.9995,0.9495,0.9591,0.9671,0.9738,0.9793,0.9838,0.9871,0.9904,0.9927,0.9945,0.9959,0.9969,0.9977,0.9984,0.9997,0.9505,0.9599,0.9678,0.9744,0.9798,0.9842,0.9878,0.9906,0.9929,0.9946,0.9960,0.9970,0.9978,0.9984,0.9698,0.9515,0.9608,0.9686,0.9750,0.9803,0.9846,0.9881,0.9909,0.9931,0.9948,0.9961,0.9971,0.9979,0.9985,0.9998,0.9525,0.9616,0.9693,0.9756,0.9808,0.9850,0.9884,0.9911,0.9932,0.9949,0.9962,0.9972,0.9979,0.9985,0.9999,0.9535,0.9625,0.9700,0.9762,0.9812,0.9854,0.9887,0.9913,0.9934,0.9951,0.9963,0.9973,0.9980,0.9986,0.9999,0.9545,0.9633,0.9706,0.9767,0.9817,0.9853,0.9890,0.9916,0.9936,0.9952,0.9964,0.9974,0.9981,0.9986,1.0000,1.96,附表4-1,=0.25,0.10,0.05,0.025,0.01,0.005,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1.323,2.773,4.108,5.385,6.626,7.841,9.037,10.219,11.389,12.549,13.701,14.845,15.984,17.117,18.245,19.369,2.706,4.605,6.251,7.779,9.236,10.645,12.017,13.362,14.684,15.987,17.275,18.549,19.812,20.064,22.307,23.542,3.841,5.991,7.815,9.488,11.071,12.592,14.067,15.507,16.919,18.307,19.675,21.026,22.362,23.685,24.996,26.296,5.024,7.378,9.348,11.143,12.833,14.449,16.013,17.535,19.023,20.483,21.920,23.337,24.736,26.119,27.488,28.845,6.635,9.210,11.345,13.277,15.086,16.812,18.475,20.090,21.666,23.209,24.725,26.217,27.688,29.141,30.578,32.000,7.879,10.597,12.838,14.860,16.750,18.548,20.278,21.955,23.589,25.188,26.757,28.299,29.891,31.319,32.801,34.267,分布表,17.535,=0.995,0.99,0.975,0.95,0.90,0.75,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0.010,0.072,0.207,0.412,0.676,0.989,1.344,1.735,2.156,2.603,3.074,3.565,4.075,4.601,5.142,0.020,0.115,0.297,0.554,0.872,1.239,1.646,2.088,2.558,3.053,3.571,4.107,4.660,5.229,5.812,0.001,0.051,0.216,0.484,0.831,1.237,1.690,2.180,2.700,3.247,3.816,4.404,5.009,5.629,6.262,6.908,0.004,0.103,0.352,0.711,1.145,1.635,2.167,2.733,3.325,3.940,4.575,5.226,5.892,6.571,7.261,7.962,0.016,0.211,0.584,1.064,1.610,2.204,2.833,3.490,4.168,4.865,5.578,6.304,7.042,7.790,8.547,9.312,0.102,0.575,1.213,1.923,2.675,3.455,4.255,5.071,5.899,6.737,7.584,8.438,9.299,10.165,11.037,11.912,3.247,附表4-,2,分布表,=0.25,0.10,0.05,0.025,0.01,0.005,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,20.489,21.605,22.718,23.828,24.935,26.039,27.141,28.241,29.339,30.435,31.528,32.620,33.711,34.800,35.887,36.973,24.769,25.989,27.204,28.412,29.615,30.813,32.007,33.196,34.382,35.563,36.741,37.916,39.087,40.256,41.422,42.585,27.587,28.869,30.144,31.410,32.671,33.924,35.172,36.415,37.652,38.885,40.113,41.337,42.557,43.773,44.985,46.194,30.191,31.526,32.852,34.170,35.479,36.781,38.076,39.364,40.646,41.923,43.194,44.461,45.712,46.979,48.232,49.480,33.409,34.805,36.191,37.566,38.932,40.289,41.638,42.980,44.314,45.642,46.963,48.278,49.588,50.892,52.191,53.486,35.718,37.156,38.582,39.997,41.401,42.796,44.181,45.559,46.928,48.290,49.645,50.993,52.336,53.672,55.003,56.328,34.382,附表4-,3,分布表,附表3-1,=0.25,0.10,0.05,0.025,0.01,0.005,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1.0000,0.8165,0.7649,0.7407,0.7267,0.7176,0.7111,0.7064,0.7027,0.6998,0.6974,0.6955,0.6938,0.6924,0.6912,0.6901,3.0777,1.8856,1.6377,1.5332,1.4759,1.4398,1.4149,1.3968,1.3830,1.3722,1.3634,1.3562,1.3502,1.3450,1.3406,1.3368,6.3138,2.9200,2.3534,2.1318,2.0150,1.9432,1.8946,1.8595,1.8331,1.8125,1.7959,1.7823,1.7709,1.7613,1.7531,1.7459,12.7062,4.3027,3.1824,2.7764,2.5706,2.4469,2.3646,2.3060,2.2622,2.2281,2.2010,2.1788,2.1604,2.1448,2.1315,2.1199,31.8207,6.9646,4.5407,3.7469,3.3649,3.1427,2.9980,2.8965,2.8214,2.7638,2.7181,2.6810,2.6503,2.6245,2.6025,2.5835,63.6574,9.9248,5.8409,4.6041,4.0322,3.7074,3.4995,3.3554,3.2498,3.1693,3.1058,3.0545,3.0123,2.9768,2.9467,2.9208,分布表,1.8125,附表3-2,=0.25,0.10,0.05,0.025,0.01,0.005,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1.0000,0.8165,0.7649,0.7407,0.7267,0.7176,0.7111,0.7064,0.7027,0.6998,0.6974,0.6955,0.6938,0.6924,0.6912,0.6901,3.0777,1.8856,1.6377,1.5332,1.4759,1.4398,1.4149,1.3968,1.3830,1.3722,1.3634,1.3562,1.3502,1.3450,1.3406,1.3368,6.3138,2.9200,2.3534,2.1318,2.0150,1.9432,1.8946,1.8595,1.8331,1.8125,1.7959,1.7823,1.7709,1.7613,1.7531,1.7459,12.7062,4.3027,3.1824,2.7764,2.5706,2.4469,2.3646,2.3060,2.2622,2.2281,2.2010,2.1788,2.1604,2.1448,2.1315,2.1199,31.8207,6.9646,4.5407,3.7469,3.3649,3.1427,2.9980,2.8965,2.8214,2.7638,2.7181,2.6810,2.6503,2.6245,2.6025,2.5835,63.6574,9.9248,5.8409,4.6041,4.0322,3.7074,3.4995,3.3554,3.2498,3.1693,3.1058,3.0545,3.0123,2.9768,2.9467,2.9208,2.1315,分布表,附表5-1,分布表,1,2,3,4,5,6,7,8,9,10,12,15,20,24,30,40,120,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,647.8,38.51,17.44,12.22,10.01,8.81,8.07,7.57,7.21,6.94,6.72,6.55,6.41,6.30,6.20,6.12,6.04,5.95,5.92,799.5,39.00,16.04,10.65,8.43,7.26,6.54,6.06,5.71,5.46,5.26,5.10,4.97,4.86,4.77,4.69,4.62,4.56,4.51,864.2,39.17,15.44,9.98,7.76,6.60,5.89,5.42,5.08,4.83,4.63,4.47,4.35,4.24,4.15,4.08,4.01,3.95,3.90,899.6,39.25,15.10,9.60,7.39,6.23,5.52,5.50,4.72,4.47,4.28,4.12,4.00,3.89,3.80,3.73,3.66,3.61,3.56,921.8,39.30,14.88,9.36,7.15,5.99,5.29,4.82,4.48,4.24,4.04,3.89,3.77,3.66,3.58,3.50,3.44,3.38,3.33,937.1,39.33,14.73,9.20,6.98,5.82,5.12,4.65,4.23,4.07,3.88,3.73,3.60,3.50,3.41,3.34,3.28,3.22,3.17,948.2,39.36,14.62,9.07,6.85,5.70,4.99,4.53,4.20,3.95,3.76,3.61,3.48,3.38,3.29,3.22,3.16,3.10,3.05,956.7,39.37,14.54,8.98,6.76,5.60,4.90,4.43,4.10,3.85,3.66,3.51,3.39,3.29,3.20,3.12,3.06,3.01,2.96,963.3,39.39,14.47,8.90,6.68,5.52,4.82,4.36,4.03,3.78,3.59,3.44,3.31,3.21,3.12,3.05,2.98,2.93,2.88,968.6,39.40,14.42,8.84,6.62,5.46,4.76,4.30,3.96,3.72,3.53,3.37,3.25,3.15,3.06,2.99,2.92,2.87,2.82,976.7,39.41,14.34,8.75,6.52,5.37,4.67,4.20,3.87,3.62,3.43,3.28,3.15,3.05,2.96,2.89,2.82,2.77,2.72,984.9,39.43,14.25,8.66,6.43,5.27,4.57,4.10,3.77,3.52,3.33,3.18,3.05,2.95,2.86,2.79,2.72,2.67,2.62,993.1,39.45,14.17,8.56,6.33,5.17,4.47,4.00,3.67,3.42,3.23,3.07,2.95,2.84,2.76,2.68,2.62,2.56,2.51,997.2,39.46,14.12,8.51,6.28,5.12,4.42,3.59,3.61,3.37,3.17,3.02,2.89,2.79,2.70,2.63,2.56,2.50,2.45,1001,39.46,14.08,8.46,6.23,5.07,4.36,3.89,3.56,3.31,3.12,2.96,2.84,2.73,2.64,2.57,2.50,2.44,2.39,1006,39.47,14.04,8.41,6.18,5.01,4.31,3.84,3.51,3.26,3.06,2.91,2.78,2.67,2.59,2.51,2.44,2.38,2.33,1014,39.49,13.95,8.31,6.07,4.90,4.20,3.73,3.39,3.14,2.94,2.79,2.66,2.55,2.46,2.38,2.32,2.26,2.20,1018,39.50,13.90,8.26,6.02,4.85,4.14,3.67,3.33,3.08,2.88,2.72,2.60,2.49,2.40,2.32,2.25,2.19,2.13,4.90,1,2,3,4,5,6,7,8,9,10,15,20,24,30,40,60,120,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,161.4,18.51,10.13,7.71,6.61,5.99,5.59,5.32,3.12,4.96,4.84,4.75,4.67,4.60,4.54,4.49,4.45,4.41,4.38,199.5,19.00,9.55,6.94,5.79,5.14,4.74,4.46,4.26,4.10,3.98,3.89,3.81,3.74,3.68,3.63,3.59,5.55,3.52,215.7,19.16,9.28,6.59,5.41,4.76,4.35,4.07,3.81,3.71,3.59,3.49,3.41,3.34,3.29,3.24,3.20,3.16,3.13,224.6,19.25,9.12,6.39,5.19,4.53,4.12,3.84,3.63,3.48,3.36,3.26,3.18,3.11,3.06,3.01,2.96,2.93,2.90,230.2,19.30,9.01,6.26,5.05,4.39,3.97,3.69,3.48,3.33,3.20,3.11,3.03,2.96,2.90,2.85,2.81,2.77,2.74,234.0,19.33,8.94,6.16,4.95,4.28,3.87,3.58,3.37,3.22,3.09,3.00,2.92,2.85,2.79,2.74,2.70,2.66,2.63,236.8,19.35,8.89,6.09,4.88,4.21,3.79,3.50,3.29,3.14,3.01,2.91,2.83,2.76,2.71,2.66,2.61,2.58,2.54,238.9,19.37,8.85,6.04,4.82,4.15,3.73,3.44,3.23,3.07,2.95,2.85,2.77,2.70,2.64,2.59,2.55,2.51,2.48,24.05,19.38,8.81,6.00,4.77,4.10,3.68,3.39,3.18,3.02,2.90,2.80,2.71,2.65,2.59,2.54,2.49,2.46,2.42,241.9,19.40,8.79,5.96,4.74,4.06,3.64,3.35,3.14,2.98,2.85,2.75,2.67,2.60,2.54,2.49,2.45,2.41,2.38,245.9,19.43,8.70,5.86,4.62,3.94,2.51,3.22,3.01,2.85,2.72,2.62,2.53,2.46,2.40,2.35,2.31,2.27,2.23,248.0,19.45,8.66,5.80,4.56,3.87,3.44,3.15,2.94,2.77,2.65,2.54,2.46,2.39,2.33,2.28,2.23,2.19,2.16,249.1,19.45,8.64,5.77,4.53,3.84,3.41,3.12,2.90,2.74,2.61,2.51,2.42,2.35,2.29,2.24,2.19,2.15,2.11,250.1,19.46,8.62,5.75,4.50,3.81,3.38,3.08,2.86,2.70,2.57,5.47,2.38,2.31,2.25,2.19,2.15,2.11,2.07,151.1,19.47,8.59,5.72,4.46,3.77,3.34,3.04,2.83,2.66,2.53,2.43,2.34,2.27,2.20,2.15,2.10,2.06,2.03,252.2,19.48,8.57,5.69,4.43,3.74,3.30,3.01,2.79,2.62,2.49,2.38,2.30,2.22,2.16,2.11,2.06,2.02,1.98,253.3,19.49,8.55,5.66,4.40,3.70,3.27,2.97,2.75,2.58,2.45,2.34,2.25,2.18,2.11,2.06,2.01,1.97,1.93,254.3,19.50,8.53,5.63,4.36,3.67,3.23,2.93,2.71,2.54,2.40,2.30,2.21,2.13,2.07,2.01,1.96,1.92,1.88,2.31,附表5-,2,分布表,费歇资料,Ronald Aylmer Fisher,Born:,17 Feb 1890 in London,England,Died:,29 July 1962 in Adelaide,Australia,学生氏资料,Born:,13 June 1876 in Canterbury,England,Died:,16 Oct 1937 in Beaconsfield,England,William,Sealey,Gosset,格里汶科资料,Boris,Vladimirovich,Gnedenko,Born:,1 Jan 1912 in,Simbirsk,(now,Ulyanovskaya,),Russia,Died:,27 Dec 1995 in Moscow,Russia,