医药数理统计第3章：参数估计

单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,单击此处编辑母版标题样式,*,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,单击此处编辑母版标题样式,*,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,单击此处编辑母版标题样式,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,医药数理统计第3章：参数估计,第,3,章：参数估计,4,1,2,3,总体、样本、统计量,抽样分布,参数点估计,参数区间估计,3.1,总体、样本和统计量,总体,:,对某一问题的研究对象全体称为总体,。,个体,:,组成总体的每个观察单元，称为个体,。,总体可以是具体事物的集合，如一批产品,。,也可以是关于事物的度量数据集合，如长度测量,。,总体可以包含有限个个体，也可以包含无限个个体,。,总体中的个体，应当有共同的可观察的特征。该特征与研究目的有关,。,总体的参数,:,总体的数字特征即总体指标,。,一、总体与样本,当总体数量很大时，只能从中抽取部分个体进行究。,从总体中取出的若干个体，称为样本,。,样本中所含个体的个数，称为样本容量,。,简单随机抽样,:,总体中每个个体被抽取的可能性,是均等的,而且每抽取一个个体时总体分布不变,.,(1),独立性,：,(2),代表性,:,与总体,X,相同的概率分布,。,例如,:,在研究广州市民的年收入时,随机抽取广州市民,100,名来进行调查,.,请问总体、样本、样本容量、随机变量、总体参数分别是什么？,在随机抽样中,样本 应具有,:,相互独立,.,注意：统计量完全依赖于样本。由于样本是随机变量，故统计量也是随机变量,。,常用的统计量主要有：,二、统计量,3.2,抽样分布,抽样分布：是指统计量作为随机变量所服从的概率分布。,我们主要学习常用统计量样本均值与样本方差相关的常用抽样分布。而在大多数情形，统计量服从正态分布或以正态分布为渐近分布，所以正态分布是最常用抽样分布。后面我们还要学习同样起着重要作用的 分布、,t,分布、,F,分布。,一、样本均值 分布与中心极限定理,即样本均值的抽样分布仍为正态分布，且,样本均值 标准化后,定理的结果可转化为,:,定理,3.2(,中心极限定理,),在实际实用时,当总体分布未知时,对大样本情形,(n30),就可用中心极限定理,.,定义,（其中,n,称为自由度,表示相互独立的标准正态变量的个数）。,二、样本方差的分布与 分布,我们将服从的分布 称为自由度是,n,的,(,卡方,),分布,并将服从,(,卡方,),的随机变量为 变量,.,.,2,分布的,密度函数,f(y),曲线,分位点 ： 设,X, ,2,(n),，若对于：,01,，,存在,满足,则称,为,分布的上侧,分位数。,临界值,附表,4-1,附表,5,只详列到,n,=45,为止,.,附表,4-2,附表,4-3,定理,3.3,1.,构造,若,XN(0, 1), Y,2,(n), X,与,Y,独立，则,t(n),称为自由度为,n,的,t,分布。,t,分布,三、,t,统计量与,t,分布,2. t,(n),的概率密度曲线为,2.,基本性质,:,(1) f(t),关于,t=0,(,纵轴,),对称。,(2) f(t),的极限为,N(0,，,1),的密度函数，即,3.,分位点,设,T,t(n),，若对,:00,， 满足,PTt,(n)=,，,则称,t,(n),为,t(n),的上侧分位点,临界值,附表,3-1,附表,3-2,注,:,定理,3.4,t(n-1),我们将所服从的,t(n-1),分布称为自由度是,(n-1),的,t,分布或学生分布,并将服从,t,分布的随机变量为,T,。,三、,t,统计量与,t,分布,四、两个样本方差比的分布与,F,分布,1.,构造,若,X,1,2,(n,1,),，,X,2,2,(n,2,),，,X,1,，,X,2,独立,，,则,称为第一自由度为,n,1,，第二自由度为,n,2,的,F,分布。,2. F,分布的分位点,对于,：,00,，满足,PFF,(n,1,n,2,)=,，,则称,F,(n,1,n,2,),为,F(n,1,n,2,),的上侧,分位点；,注：,附表,5-1,附表,5-2,附加,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,