F分布的概念及表和查表方法文档格式.docx
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F分布的概念及表和查表方法文档格式.docx
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F分布的概念及表和查表方法分布的概念及表和查表方法F分布分布F分布是1924年英国统计学家RAFisher提出,并以其姓氏的第一个字母命名的。
@#@它是一种非对称分布,有两个自由度,且位置不可互换。
@#@F分布有着广泛的应用,如在方差分析、回归方程的显著性检验中都有着重要的地位。
@#@中文名F分布外文名F-distribution领域统计学提出者R.A.Fisher提出时间1924特性非对称分布1定义2性质定义若总体,与为来自X的两个独立样本,设统计量则称统计量F服从自由度和的F分布,记为分布的概率密度为分布的概率密度函数图像如图1所示图12若总体与总体独立,为来自X的一个样本,为来自Y的一个样本,则统计量则称统计量F服从自由度为和,非中心参数为的非中心F分布,记为性质性质性质1:
@#@性质2:
@#@设,则。
@#@性质3:
@#@设,则。
@#@性质4:
@#@分布的分布函数可用标准正态分布的分布函数来逼近。
@#@即其中,(,充分大)。
@#@性质5:
@#@若总体与独立,为来自X的一个样本,为来自Y的一个样本,为已知参数。
@#@则统计量性质6:
@#@若总体与独立,为来自X的一个样本,为来自Y的一个样本,则统计量F统计学附录表F分布临界值表(0.0050.10)=0.005Fk1k212345681224123456789101112131415161716211198.555.5531.3322.7818.6316.2414.6913.6112.8312.2311.7511.3720000199.049.8026.2818.3114.4512.4011.0410.119.438.918.518.1921615199.247.4724.2616.5312.9210.889.608.728.087.607.236.9322500199.246.1923.1515.5612.0310.058.817.967.346.886.526.2323056199.345.3922.4614.9411.469.528.307.476.876.426.075.7923437199.344.8421.9714.5111.079.167.957.136.546.105.765.4823925199.444.1321.3513.9610.578.687.506.696.125.685.355.0824426199.443.3920.7013.3810.038.187.016.235.665.244.914.6424940199.542.6220.0312.789.477.656.505.735.174.764.434.1725465199.541.8319.3212.148.887.085.955.194.644.233.903.6518192021222324252627282930406012011.0610.8010.5810.3810.2210.079.949.839.739.639.559.489.419.349.289.237.927.707.517.357.217.096.996.896.816.736.666.606.546.496.446.406.686.486.306.166.035.925.825.735.655.585.525.465.415.365.325.286.005.805.645.505.375.275.175.095.024.954.894.844.794.744.704.665.565.375.215.074.964.854.764.684.614.544.494.434.384.344.304.265.265.074.914.784.664.564.474.394.324.264.204.154.104.064.023.984.864.674.524.394.284.184.094.013.943.883.833.783.733.693.653.614.434.254.103.973.863.763.683.603.543.473.423.373.333.283.253.213.963.793.643.513.403.313.223.153.083.022.972.922.872.832.792.763.443.263.112.982.872.782.692.612.552.482.432.382.332.292.252.219.188.838.498.186.356.075.795.545.244.984.734.504.624.374.143.924.233.993.763.553.953.713.493.283.583.353.132.933.182.952.742.542.732.502.292.092.181.931.691.43=0.01Fk1k212345681224123456789101112405298.4934.1221.2016.2613.7412.2511.2610.56499999.0130.8118.0013.2710.929.558.658.02540399.1729.4616.6912.069.788.457.596.99562599.2528.7115.9811.399.157.857.016.42576499.3028.2415.5210.978.757.466.636.06585999.3327.9115.2110.678.477.196.375.80598199.3627.4914.8010.298.106.846.035.47610699.4227.0514.379.897.726.475.675.11623499.4626.6013.939.477.316.075.284.73636699.5026.1213.469.026.885.654.864.3113141516171819202122232425262728293010.049.659.339.078.868.688.538.408.288.188.108.027.947.887.827.777.567.206.936.706.516.366.236.116.015.935.855.785.725.665.615.576.556.225.955.745.565.425.295.185.095.014.944.874.824.764.724.685.995.675.415.205.034.894.774.674.584.504.434.374.314.264.224.185.645.325.064.864.694.564.444.344.254.174.104.043.993.943.903.865.395.074.824.624.464.324.204.104.013.943.873.813.763.713.673.635.064.744.504.304.144.003.893.793.713.633.563.513.453.413.363.324.714.404.163.963.803.673.553.453.373.303.233.173.123.073.032.994.334.023.783.593.433.293.183.083.002.922.862.802.752.702.662.623.913.603.363.163.002.872.752.652.572.492.422.362.312.262.212.1740601207.727.687.647.607.567.317.086.856.645.535.495.455.425.395.184.984.794.604.644.604.574.544.514.314.133.953.784.144.114.074.044.023.833.653.483.323.823.783.753.733.703.513.343.173.023.593.563.533.503.473.293.122.962.803.293.263.233.203.172.992.822.662.512.962.932.902.872.842.662.502.342.182.582.552.522.492.472.292.121.951.792.132.102.062.032.011.801.601.381.00=0.025Fk1k2123456812241234567647.838.5117.4412.22799.539.0016.0410.65864.239.1715.449.98899.639.2515.109.60921.839.3014.889.36937.139.3314.739.20956.739.3714.548.98976.739.4114.348.75997.239.4614.128.51101839.5013.908.26891011121314151617181920212223242510.018.818.077.577.216.946.726.556.416.306.206.126.045.985.925.878.437.266.546.065.715.465.265.104.974.864.774.694.624.564.514.467.766.605.895.425.084.834.634.474.354.244.154.084.013.953.903.867.396.235.525.054.724.474.284.124.003.893.803.733.663.613.563.517.155.995.294.824.484.244.043.893.773.663.583.503.443.383.333.296.985.825.124.654.324.073.883.733.603.503.413.343.283.223.173.136.765.604.904.434.103.853.663.513.393.293.203.123.063.012.962.916.525.374.674.203.873.623.433.283.153.052.962.892.822.772.722.686.285.124.423.953.613.373.173.022.892.792.702.632.562.502.452.416.024.854.143.673.333.082.882.722.602.492.402.322.252.192.132.09262728293040601205.835.795.755.725.695.665.635.615.595.575.425.295.155.024.424.384.354.324.294.274.244.224.204.184.053.933.803.693.823.783.753.723.693.673.653.633.613.593.463.343.233.123.483.443.413.383.353.333.313.293.273.253.133.012.892.793.253.223.183.153.133.103.083.063.043.032.902.792.672.573.093.053.022.992.972.942.922.902.882.872.742.632.522.412.872.842.812.782.752.732.712.692.672.652.532.412.302.192.642.602.572.542.512.492.472.452.432.412.292.172.051.942.372.332.302.272.242.222.192.172.152.142.011.881.761.642.042.001.971.941.911.881.851.831.811.791.641.481.311.00=0.05F12345681224k1k212345678910111213141516171819161.418.5110.137.716.615.995.595.325.124.964.844.754.674.604.54199.519.009.556.945.795.144.744.464.264.103.983.883.803.743.68215.719.169.286.595.414.764.354.073.863.713.593.493.413.343.29224.619.259.126.395.194.534.123.843.633.483.363.263.183.113.06230.219.309.016.265.054.393.973.693.483.333.203.113.022.962.90234.019.338.946.164.954.283.873.583.373.223.093.002.922.852.79238.919.378.846.044.824.153.733.443.233.072.952.852.772.702.64243.919.418.745.914.684.003.573.283.072.912.792.692.602.532.48249.019.458.645.774.533.843.413.122.902.742.612.502.422.352.29254.319.508.535.634.363.673.232.932.712.542.402.302.212.132.07202122232425262728293040601204.494.454.414.384.354.324.304.284.264.244.224.214.204.184.174.083.633.593.553.523.493.473.443.423.403.383.373.353.343.333.323.233.243.203.163.133.103.073.053.033.012.992.982.962.952.932.922.843.012.962.932.902.872.842.822.802.782.762.742.732.712.702.692.612.852.812.772.742.712.682.662.642.622.602.592.572.562.542.532.452.742.702.662.632.602.572.552.532.512.492.472.462.442.432.422.342.592.552.512.482.452.422.402.382.362.342.322.302.292.282.272.182.422.382.342.312.282.252.232.202.182.162.152.132.122.102.092.002.242.192.152.112.082.052.032.001.981.961.951.931.911.901.891.792.011.961.921.881.841.811.781.761.731.711.691.671.651.641.621.514.003.923.843.153.072.992.762.682.602.522.452.372.372.292.212.252.172.092.102.021.941.921.831.751.701.611.521.391.251.00=0.10Fk1k212345681224123456789101112131439.868.535.544.544.063.783.593.463.363.2949.509.005.464.323.783.463.263.113.012.9253.599.165.364.193.623.293.072.922.812.7355.839.245.324.113.523.182.962.812.692.6157.249.295.314.053.453.112.882.732.612.5258.209.335.284.013.403.052.832.672.552.4659.449.375.253.953.342.982.752.592.472.3860.719.415.223.903.272.902.672.502.382.2862.009.455.183.833.192.822.582.402.282.1863.339.495.133.763.102.722.472.292.162.061516171819202122232425262728293040603.233.183.143.103.073.053.033.012.992.972.962.952.942.932.922.912.862.812.762.732.702.672.642.622.612.592.572.562.552.542.532.522.662.612.562.522.492.462.442.422.402.382.362.352.342.332.322.312.542.482.432.392.362.332.312.292.272.252.232.222.212.192.182.172.452.392.352.312.272.242.222.202.182.162.142.132.112.102.092.082.392.332.282.242.212.182.152.132.112.092.082.062.052.042.022.012.302.242.202.152.122.092.062.042.022.001.981.971.951.941.931.922.212.152.102.052.021.991.961.931.911.891.871.861.841.831.821.812.102.041.981.941.901.871.841.811.791.771.751.731.721.701.691.681.971.901.851.801.761.721.691.661.631.611.591.571.551.531.521.501202.902.892.892.882.842.792.752.712.512.502.502.492.442.392.352.302.302.292.282.282.232.182.132.082.172.162.152.142.092.041.991.942.072.062.062.052.001.951.901.852.002.001.991.981.931.871.821.171.911.901.891.881.831.771.721.671.801.791.781.771.711.661.601.551.671.661.651.641.571.511.451.381.491.481.471.461.381.291.191.00注:
@#@三大抽样分布一般是指卡方分布(2分布)、t分布和F分布,是来自正态总体的三个常用的分布。
@#@说明:
@#@F分布表横坐标是x,纵坐标是y(如下图),一个分位点一张表,根据公式中的分子自由度(表第一行数字,k1)和分母自由度(表第一列数字,k2);@#@它是一种非对称分布,有两个自由度,且位置不可互换。
@#@f分布表查询方法例:
@#@1.首先需要了解自由度是多
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