完整版F分布的概念及表和查表方法.docx
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完整版F分布的概念及表和查表方法.docx
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完整版F分布的概念及表和查表方法
F分布
提出,并以其姓氏的第一个字母命名的。
A·1924F分布是年英国统计学家FisherR·分布有着广泛的应用,如在方差分它是一种非对称分布,有两个自由度,且位置不可互换。
F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
distributionF-
领域
统计学
提出者
R.A.Fisher
提出时间
1924
特性
非对称分布
目录1定义性质2
定义
,与若总体为来自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
[2]1图
若总体与总体独立,为来自X的一个样本,
的一个样本,则统计量Y为来自
,非中心参数为的非中心FF分布,记为服从自由度为和则称统计量
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
为来自X独立,与若总体:
性质6
的一个样本,则统计量Y为来自的一个样本,
F统计学附录表
Fα(0.005―0.10)—分布临界值表——
α=0.005
Fαk1k2
1
2
3
4
5
6
8
12
24
∞
12345678910
1112131415
1617
16211198.555.5531.3322.7818.6316.2414.6913.6112.8312.2311.7511.3711.0610.8010.5810.38
20000199.049.8026.2818.3114.4512.4011.0410.119.438.918.518.197.927.707.517.35
21615199.247.4724.2616.5312.9210.889.608.728.087.607.236.936.686.486.306.16
22500199.246.1923.1515.5612.0310.058.817.967.346.886.526.236.005.805.645.50
23056199.345.3922.4614.9411.469.528.307.476.876.426.075.795.565.375.215.07
23437199.344.8421.9714.5111.079.167.957.136.546.105.765.485.265.074.914.78
23925199.444.1321.3513.9610.578.687.506.696.125.685.355.084.864.674.524.39
24426199.443.3920.7013.3810.038.187.016.235.665.244.914.644.434.254.103.97
24940199.542.6220.0312.789.477.656.505.735.174.764.434.173.963.793.643.51
25465199.541.8319.3212.148.887.085.955.194.644.233.903.653.443.263.11
2.98
181920
2122232425
26272829304060120
10.2210.079.949.839.739.639.559.489.419.349.289.239.188.838.498.18
7.217.096.996.896.816.736.666.606.546.496.446.406.356.075.795.54
6.035.925.825.735.655.585.525.465.415.365.325.285.244.984.734.50
5.375.275.175.095.024.954.894.844.794.744.704.664.624.374.143.92
4.964.854.764.684.614.544.494.434.384.344.304.264.233.993.763.55
4.664.564.474.394.324.264.204.154.104.064.023.983.953.713.493.28
4.284.184.094.013.943.883.833.783.733.693.653.613.583.353.132.93
3.863.763.683.603.543.473.423.373.333.283.253.213.182.952.742.54
3.403.313.223.153.083.022.972.922.872.832.792.762.732.502.292.09
2.872.782.692.612.552.482.432.382.332.292.252.212.181.931.691.43
α=0.01
Fαk1k2
1
2
3
4
5
6
8
12
24
∞
12345
405298.4934.1221.2016.26
499999.0130.8118.0013.27
540399.1729.4616.6912.06
562599.2528.7115.9811.39
576499.3028.2415.5210.97
585999.3327.9115.2110.67
598199.3627.4914.8010.29
610699.4227.0514.379.89
623499.4626.6013.939.47
636699.5026.1213.469.02
678910
1112131415
1617181920
2122232425
26272829
13.7412.2511.2610.5610.049.659.339.078.868.688.538.408.288.188.108.027.947.887.827.777.727.687.647.60
10.929.558.658.027.567.206.936.706.516.366.236.116.015.935.855.785.725.665.615.575.535.495.455.42
9.788.457.596.996.556.225.955.745.565.425.295.185.095.014.944.874.824.764.724.684.644.604.574.54
9.157.857.016.425.995.675.415.205.034.894.774.674.584.504.434.374.314.264.224.184.144.114.074.04
8.757.466.636.065.645.325.064.864.694.564.444.344.254.174.104.043.993.943.903.863.823.783.753.73
8.477.196.375.805.395.074.824.624.464.324.204.104.013.943.873.813.763.713.673.633.593.563.533.50
8.106.846.035.475.064.744.504.304.144.003.893.793.713.633.563.513.453.413.363.323.293.263.233.20
7.726.475.675.114.714.404.163.963.803.673.553.453.373.303.233.173.123.073.032.992.962.932.902.87
7.316.075.284.734.334.023.783.593.433.293.183.083.002.922.862.802.752.702.662.622.582.552.522.49
6.885.654.864.313.913.603.363.163.002.872.752.652.572.492.422.362.312.262.212.172.132.102.06
2.03
30
4060120∞
7.567.317.086.856.64
5.395.184.984.794.60
4.514.314.133.953.78
4.023.833.653.483.32
3.703.513.343.173.02
3.473.293.122.962.80
3.172.992.822.662.51
2.842.662.502.342.18
2.472.292.121.951.79
2.011.801.601.381.00
α=0.025
Fαk1
k2
1
2
3
4
5
6
8
12
24
∞
123456789101112131415
647.838.5117.4412.2210.018.818.077.577.216.946.726.556.416.306.20
799.539.0016.0410.658.437.266.546.065.715.465.265.104.974.864.77
864.239.1715.449.987.766.605.895.425.084.834.634.474.354.244.15
899.639.2515.109.607.396.235.525.054.724.474.284.124.003.893.80
921.839.3014.889.367.155.995.294.824.484.244.043.893.773.663.58
937.139.3314.739.206.985.825.124.654.324.073.883.733.603.503.41
956.739.3714.548.986.765.604.904.434.103.853.663.513.393.293.20
976.739.4114.348.756.525.374.674.203.873.623.433.283.153.052.96
997.239.4614.128.516.285.124.423.953.613.373.173.022.892.792.70
101839.5013.908.266.024.854.143.673.333.082.882.722.602.492.40
16171819202122232425
26272829304060120∞
6.126.045.985.925.875.835.795.755.725.695.665.635.615.595.575.425.295.155.02
4.694.624.564.514.464.424.384.354.324.294.274.244.224.204.184.053.933.803.69
4.084.013.953.903.863.823.783.753.723.693.673.653.633.613.593.463.343.233.12
3.733.663.613.563.513.483.443.413.383.353.333.313.293.273.253.133.012.892.79
3.503.443.383.333.293.253.223.183.153.133.103.083.063.043.032.902.792.672.57
3.343.283.223.173.133.093.053.022.992.972.942.922.902.882.872.742.632.522.41
3.123.063.012.962.912.872.842.812.782.752.732.712.692.672.652.532.412.302.19
2.892.822.772.722.682.642.602.572.542.512.492.472.452.432.412.292.172.051.94
2.632.562.502.452.412.372.332.302.272.242.222.192.172.152.142.011.881.761.64
2.322.252.192.132.092.042.001.971.941.911.881.851.831.811.791.641.481.311.00
α=0.05
Fαk1k2
1
2
3
4
5
6
8
12
24
∞
1
161.4
199.5
215.7
224.6
230.2
234.0
238.9
243.9
249.0
254.3
2345678910
1112131415
16171819202122232425
18.5110.137.716.615.995.595.325.124.964.844.754.674.604.544.494.454.414.384.354.324.304.284.264.24
19.009.556.945.795.144.744.464.264.103.983.883.803.743.683.633.593.553.523.493.473.443.423.403.38
19.169.286.595.414.764.354.073.863.713.593.493.413.343.293.243.203.163.133.103.073.053.033.012.99
19.259.126.395.194.534.123.843.633.483.363.263.183.113.063.012.962.932.902.872.842.822.802.782.76
19.309.016.265.054.393.973.693.483.333.203.113.022.962.902.852.812.772.742.712.682.662.642.622.60
19.338.946.164.954.283.873.583.373.223.093.002.922.852.792.742.702.662.632.602.572.552.532.512.49
19.378.846.044.824.153.733.443.233.072.952.852.772.702.642.592.552.512.482.452.422.402.382.362.34
19.418.745.914.684.003.573.283.072.912.792.692.602.532.482.422.382.342.312.282.252.232.202.182.16
19.458.645.774.533.843.413.122.902.742.612.502.422.352.292.242.192.152.112.082.052.032.001.981.96
19.508.535.634.363.673.232.932.712.542.402.302.212.132.072.011.961.921.881.841.811.781.761.731.71
2627282930
4060120∞
4.224.214.204.184.174.084.003.923.84
3.373.353.343.333.323.233.153.072.99
2.982.962.952.932.922.842.762.682.60
2.742.732.712.702.692.612.522.452.37
2.592.572.562.542.532.452.372.292.21
2.472.462.442.432.422.342.252.172.09
2.322.302.292.282.272.182.102.021.94
2.152.132.122.102.092.001.921.831.75
1.951.931.911.901.891.791.701.611.52
1.691.671.651.641.621.511.391.251.00
α=0.10
Fαk1k2
1
2
3
4
5
6
8
12
24
∞
12345
678910
1112
39.868.535.544.544.063.783.593.463.363.293.233.18
49.509.005.464.323.783.463.263.113.012.922.862.81
53.599.165.364.193.623.293.072.922.812.732.662.61
55.839.245.324.113.523.182.962.812.692.612.542.48
57.249.295.314.053.453.112.882.732.612.522.452.39
58.209.335.284.013.403.052.832.672.552.462.392.33
59.449.375.253.953.342.982.752.592.472.382.302.24
60.719.415.223.903.272.902.672.502.382.282.212.15
62.009.455.183.833.192.822.582.402.282.182.102.04
63.339.495.133.763.102.722.472.292.162.06
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