统计量与抽样分布-太行之路网站-欢迎您！.pptx

统计量与抽样分布-太行之路网站-欢迎您！.pptx

《统计量与抽样分布-太行之路网站-欢迎您！.pptx》由会员分享，可在线阅读，更多相关《统计量与抽样分布-太行之路网站-欢迎您！.pptx（31页珍藏版）》请在冰豆网上搜索。

3.2统计量与抽样分布统计量与抽样分布统计量的定义统计量的定义.）,（,）,（,21212121计量计量是一个统是一个统则称则称不含未知参数不含未知参数中中若若的函数的函数是是的一个样本的一个样本是来自总体是来自总体设设nnnnXXXgfXXXXXXgXXXX是是不是不是例例1?

）,（,22321哪些不是哪些不是些是统计量些是统计量判断下列各式哪判断下列各式哪为未知为未知为已知为已知其中其中样本样本的一个的一个是来自总体是来自总体设设NXXX,11XT,3212XeXXT）,（313213XXXT）,max（3214XXXT,2215XXT）.（123222126XXXT.）,（）,（,21212121的观察值是则称的样本值是相应于样本设nnnnXXXfxxxfXXXxxx2.几个常用统计量几个常用统计量（样本矩样本矩）的的定义定义

（1）样本均值样本均值

（2）样本方差样本方差它反映了总体均值它反映了总体均值的信息的信息它反映了总体方差它反映了总体方差的信息的信息.,2121是这一样本的观察值是这一样本的观察值是来自总体的一个样本是来自总体的一个样本设设nnxxxXXX;11niiXnXniiXXnS122）（11（3）样本标准差样本标准差（4）样本样本k阶阶（原点原点）矩矩（5）样本样本k阶中心矩阶中心矩;11122niiXXnSSnikikXn11nikikXXn1）（12.2抽样分布抽样分布统计量是统计量是nn维随机变量维随机变量的函数，作为一个随机变量，它也有自己的函数，作为一个随机变量，它也有自己的概率分布。

通常把统计量的分布称为抽样的概率分布。

通常把统计量的分布称为抽样分布。

分布。

设总体设总体X的分布函数已知，如果对任意的分布函数已知，如果对任意容量为容量为n的样本，能求出给定的样本，能求出给定的统计量的分布函数，则的统计量的分布函数，则称该分布函数为的精确分布。

称该分布函数为的精确分布。

）,（21nXXXg）,（21nXXX）,（21nXXX）,（21nXXXg）,（21nXXXg11样本均值的分样本均值的分布布正态总体的几个统计量的精确分布22分布分布33tt分布分布44FF分布分布21.样本均值的分布样本均值的分布设，是来自总体X的样本，由于正态变量的线性函数仍为正态变量，故，通常称为总体的标准误差总体的标准误差，记作）,（2NX）,（21nXXX）1,（2nNX）1,0（NnXUnX标准正态分布的上侧临界值标准正态分布的上侧临界值标准正态分布的双侧临界值标准正态分布的双侧临界值yxo图3-3yxo图3-4dteuUPtu2221）（）|（|2uUP2u2u22u2u22分布分布）.（,）1,0（）,（22222221221nnXXXNXXXnn记为记为布布分分的的服从自由度为服从自由度为则则的样本，的样本，是来自总体是来自总体设设2000）2（21）（2122xxexnxfxnn分布的上侧临界值图3-6oyx）（222）（）（）（ndxxfnnP）（2n2）（2n定理定理设是来自正态总体的样本，则1o样本均值与样本方差相互独立；2o）,（21nXXX）,（2NXX2S）1（）（）1（221222nXXSnnii性质性质1（此性质可以推广到多个随机变量的情形此性质可以推广到多个随机变量的情形）分布的性质分布的性质2）.（,）,（）,（2122221222122221221nnnn则则立立独独并且并且设设）（2分布的可加性分布的可加性）.（,）,2,1（）,（21212222mmiiiiinnnmin则则独立独立相互相互并且并且设设t分布又称分布又称学生氏学生氏（Student）分布分布.学生氏资料学生氏资料2.）.（,/,）,（）,1,0（2ntTtnnYXTYXnYNX记为记为分布分布的的服从自由度为服从自由度为则称随机变量则称随机变量独立独立且且设设定义定义tntnnnthn,1221）（212分布的概率密度函数为分布的概率密度函数为）（nt分布t当当n充分大时充分大时,其其图形类似于标准正图形类似于标准正态变量概率密度的态变量概率密度的图形图形.图图分布的概率密度曲线如分布的概率密度曲线如t.0对称的对称的显然图形是关于显然图形是关于t,21）（lim22tneth因为因为,）1,0（分布分布分布近似于分布近似于足够大时足够大时所以当所以当Ntn.）1,0（,分布相差很大分布相差很大分布与分布与但对于较小的但对于较小的Ntn定理定理2设是设是来自正态总体来自正态总体的样本，的样本，则统计量则统计量）,（21nXXX）,（2NX）1（/ntnSX定理定理3设和设和是来自是来自正态总体和正态总体和的样本，且两者相互独立，则的样本，且两者相互独立，则统计量统计量和分别为两和分别为两个总体的样本方差个总体的样本方差）,（21nXXX）,（221nYYY）,（211N）,（222N）2（11）（212121nntnnSYX2）1（）1（21222211nnSnSnS22S21S称为样本均值差的标准误，称为样本均值差的标准误，记作，即。

记作，即。

分布的上侧临界值分布的上侧临界值分布的双侧临界值分布的双侧临界值2111nnS21XXS21XXS2111nnSt）（）（）（）（ntdttfntntP）（nt10t）（2nt）（|）（|（2ntntPyxo图图3-83-8yxo图图3-93-9）（nt2t2t服从第一自由度为，第二自由度为服从第一自由度为，第二自由度为的分布，记作的分布，记作3.F分布分布定义定义2122212212/,）,（）,（nYnXFYXnYnX则称随机变量则称随机变量独立独立且且设设）.,（21nnFF1n2nF分布的密度函数为分布的密度函数为F000）1（）（22112211xxxnnxCxfnnn22121211）（）2（）2（）2（nnnnnnnCF分布的分布的上侧临界值上侧临界值是指满足下式的是指满足下式的定理定理设，是正态总体设，是正态总体的样本容量和样本方差；，是正的样本容量和样本方差；，是正态总体态总体的样本容量和样本方差，且两个样本相互独的样本容量和样本方差，且两个样本相互独立，则统计量立，则统计量）,（21nnF）,（212121）（）,（）,（nnFdxxfnnFnnFP1n21S）,（211N2n22S）,（222N）1,1（2122212221nnFSS附表附表2-12-1标准正态分布表标准正态分布表z0.000.010.020.030.040.050.060.070.080.090.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.60.50000.53980.57930.61790.65540.69150.72570.75800.78810.81590.84130.86430.88490.90320.91920.93320.94520.50400.54380.58320.62170.65910.69500.72910.76110.79100.81860.84380.86650.88690.90490.92070.93450.94630.50800.54780.58710.62550.66280.69850.73240.76420.79390.82120.84610.86860.88880.90660.92220.93570.94740.51200.55170.59100.62930.66640.70190.73570.76730.79670.82380.84850.87080.89070.90820.92360.93700.94840.51600.55570.59480.63310.67000.70540.73890.77030.79950.82640.85080.87290.89250.90990.92510.93820.94950.51990.55960.59870.63680.67360.70880.74220.77340.80230.82890.85310.87490.89440.91150.92650.93940.95050.52390.56360.60260.64060.67720.71230.74540.77640.80510.83150.85540.87700.89620.91310.92780.94060.95150.52790.56750.60640.64430.68080.71570.74860.77940.80780.83400.85770.87900.89800.91470.92920.94180.95250.53190.57140.61030.64800.68440.71900.75170.78230.81060.83650.85990.88100.89970.91620.93060.94300.95350.53590.57530.61410.65170.68790.72240.75490.78520.81330.83890.86210.88300.90150.91770.93190.94410.95451.645附表附表2-22-2标准正态分布表标准正态分布表z0.000.010.020.030.040.050.060.070.080.091.61.71.81.92.02.12.22.32.42.52.62.72.82.93.00.94520.95540.96410.97130.97720.98210.98610.98930.99180.99380.99530.99650.99740.99810.99870.94630.95640.96480.97190.97780.98260.98640.98960.99200.99400.99550.99660.99750.99820.99900.94740.95730.96560.97260.97830.98300.98680.98980.99220.99410.99560.99670.99760.99820.99930.94840.95820.96640.97320.97880.98340.98710.99010.99250.99430.99570.99680.99770.99830.99950.94950.95910.96710.97380.97930.98380.98710.99040.99270.99450.99590.99690.99770.99840.99970.95050.95990.96780.97440.97980.98420.98780.99060.99290.99460.99600.99700.99780.99840.96980.95150.96080.96860.97500.98030.98460.98810.99090.99310.99480.99610.99710.99790.99850.99980.95250.96160.96930.97560.98080.98500.98840.99110.99320.99490.99620.99720.99790.99850.99990.95350.96250.97000.97620.98120.98540.98870.99130.99340.99510.99630.99730.99800.99860.99990.95450.96330.97060.97670.98170.98530.98900.99160.99360.99520.99640.99740.99810.99861.00001.96附表附表4-14-1=0.250.100.050.0250.010.005123456789101112131415161.3232.7734.1085.3856.6267.8419.03710.21911.38912.54913.70114.84515.98417.11718.24519.3692.7064.6056.2517.7799.23610.64512.01713.36214.68415.98717.27518.54919.81220.06422.30723.5423.8415.9917.8159.48811.07112.59214.06715.50716.91918.30719.67521.02622.36223.68524.99626.2965.0247.3789.34811.14312.83314.44916.01317.53519.02320.48321.92023.33724.73626.11927.48828.8456.6359.21011.34513.27715.08616.81218.47520.09021.66623.20924.72526.21727.68829.14130.57832.0007.87910.59712.83814.86016.75018.54820.27821.95523.58925.18826.75728.29929.89131.31932.80134.267分布表分布表17.535n2=0.9950.990.9750.950.900.75123456789101112131415160.0100.0720.2070.4120.6760.9891.3441.7352.1562.6033.0743.5654.0754.6015.1420.0200.1150.2970.5540.8721.2391.6462.0882.5583.0533.5714.1074.6605.2295.8120.0010.0510.2160.4840.8311.2371.6902.1802.7003.2473.8164.4045.0095.6296.2626.9080.0040.1030.3520.7111.1451.6352.1672.7333.3253.9404.5755.2265.8926.5717.2617.9620.0160.2110.5841.0641.6102.2042.8333.4904.1684.8655.5786.3047.0427.7908.5479.3120.1020.5751.2131.9232.6753.4554.2555.0715.8996.7377.5848.4389.29910.16511.03711.9123.247附表附表4-24-2分布表分布表n2=0.250.100.050.0250.010.0051718192021222324252627282930313220.48921.60522.71823.82824.93526.03927.14128.24129.33930.43531.52832.62033.71134.80035.88736.97324.76925.98927.20428.41229.61530.81332.00733.19634.38235.56336.74137.91639.08740.25641.42242.58527.58728.86930.14431.41032.67133.92435.17236.41537.65238.88540.11341.33742.55743.77344.98546.19430.19131.52632.85234.17035.47936.78138.07639.36440.64641.92343.19444.46145.71246.97948.23249.48033.40934.80536.19137.56638.93240.28941.63842.98044.31445.64246.96348.27849.58850.89252.19153.48635.71837.15638.58239.99741.40142.79644.18145.55946.92848.29049.64550.99352.33653.67255.00356.32834.382附表附表4-34-3分布表分布表n2附表附表3-13-1=0.250.100.050.0250.010.005123456789101112131415161.00000.81650.76490.74070.72670.71760.71110.70640.70270.69980.69740.69550.69380.69240.69120.69013.07771.88561.63771.53321.47591.43981.41491.39681.38301.37221.36341.35621.35021.34501.34061.33686.31382.92002.35342.13182.01501.94321.89461.85951.83311.81251.79591.78231.77091.76131.75311.745912.70624.30273.18242.77642.57062.44692.36462.30602.26222.22812.20102.17882.16042.14482.13152.119931.82076.96464.54073.74693.36493.14272.99802.89652.82142.76382.71812.68102.65032.62452.60252.583563.65749.92485.84094.60414.03223.70743.49953.35543.24983.16933.10583.05453.01232.97682.94672.9208分布表分布表1.8125nt附表附表3-23-2=0.250.100.050.0250.010.005123456789101112131415161.00000.81650.76490.74070.72670.71760.71110.70640.70270.69980.69740.69550.69380.69240.69120.69013.07771.88561.63771.53321.47591.43981.41491.39681.38301.37221.36341.35621.35021.34501.34061.33686.31382.92002.35342.13182.01501.94321.89461.85951.83311.81251.79591.78231.77091.76131.75311.745912.70624.30273.18242.77642.57062.44692.36462.30602.26222.22812.20102.17882.16042.14482.13152.119931.82076.96464.54073.74693.36493.14272.99802.89652.82142.76382.71812.68102.65032.62452.60252.583563.65749.92485.84094.60414.03223.70743.49953.35543.24983.16933.10583.05453.01232.97682.94672.92082.1315分布表分布表nt附表附表5-15-1分布表分布表1234567891012152024304012012345678910111213141516171819647.838.5117.4412.2210.018.818.077.577.216.946.726.556.416.306.206.126.045.955.92799.539.0016.0410.658.437.266.546.065.715.465.265.104.974.864.774.694.624.564.51864.239.1715.449.987.766.605.895.425.084.834.634.474.354.244.154.084.013.953.90899.639.2515.109.607.396.235.525.504.724.474.284.124.003.893.803.733.663.613.56921.839.3014.889.367.155.995.294.824.484.244.043.893.773.663.583.503.443.383.33937.139.3314.739.206.985.825.124.654.234.073.883.733.603.503.413.343.283.223.17948.239.3614.629.076.855.704.994.534.203.953.763.613.483.383.293.223.163.103.05956.739.3714.548.986.765.604.904.434.103.853.663.513.393.293.203.123.063.012.96963.339.3914.478.906.685.524.824.364.033.783.593.443.313.213.123.052.982.932.88968.639.4014.428.846.625.464.764.303.963.723.533.373.253.153.062.992.922.872.82976.739.4114.348.756.525.374.674.203.873.623.433.283.153.052.962.892.822.772.72984.939.4314.258.666.435.274.574.103.773.523.333.183.052.952.862.792.722.672.62993.139.4514.178.566.335.174.474.003.673.423.233.072.952.842.762.682.622.562.51997.239.4614.128.516.285.124.423.593.613.373.173.022.892.792.702.632.562.502.45100139.4614.088.466.235.074.363.893.563.313.122.962.842.732.642.572.502.442.39100639.4714.048.416.185.014.313.843.513.263.062.912.782.672.592.512.442.382.33101439.4913.958.316.074.904.203.733.393.142.942.792.662.552.462.382.322.262.20101839.5013.908.266.024.854.143.673.333.082.882.722.602.492.402.322.252.192.134.90F025.0