2022年F分布的概念及表和查表方法_共6页.pdf

F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特性非对称分布目录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 1 2若总体与总体独立，为来自 X 的一个样本，精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 1 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 1 页，共 12 页 - - - - - - - - -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 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精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 2 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 2 页，共 12 页 - - - - - - - - -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（0.005 0.10） =0.005Fk1k21234568 12241234567891016211198.555.5531.3322.7818.6316.2414.6913.6112.8320000199.049.8026.2818.3114.4512.4011.0410.119.4321615199.247.4724.2616.5312.9210.889.608.728.0822500199.246.1923.1515.5612.0310.058.817.967.3423056199.345.3922.4614.9411.469.528.307.476.8723437199.344.8421.9714.5111.079.167.957.136.5423925199.444.1321.3513.9610.578.687.506.696.1224426199.443.3920.7013.3810.038.187.016.235.6624940199.542.6220.0312.789.477.656.505.735.1725465199.541.8319.3212.148.887.085.955.194.64精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 3 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 3 页，共 12 页 - - - - - - - - -1112131415161718192021222324252627282930406012012.2311.7511.3711.0610.8010.5810.3810.2210.079.949.839.739.639.559.489.419.349.289.239.188.838.498.188.918.518.197.927.707.517.357.217.096.996.896.816.736.666.606.546.496.446.406.356.075.795.547.607.236.936.686.486.306.166.035.925.825.735.655.585.525.465.415.365.325.285.244.984.734.506.886.526.236.005.805.645.505.375.275.175.095.024.954.894.844.794.744.704.664.624.374.143.926.426.075.795.565.375.215.074.964.854.764.684.614.544.494.434.384.344.304.264.233.993.763.556.105.765.485.265.074.914.784.664.564.474.394.324.264.204.154.104.064.023.983.953.713.493.285.685.355.084.864.674.524.394.284.184.094.013.943.883.833.783.733.693.653.613.583.353.132.935.244.914.644.434.254.103.973.863.763.683.603.543.473.423.373.333.283.253.213.182.952.742.544.764.434.173.963.793.643.513.403.313.223.153.083.022.972.922.872.832.792.762.732.502.292.094.233.903.653.443.263.112.982.872.782.692.612.552.482.432.382.332.292.252.212.181.931.691.43精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 4 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 4 页，共 12 页 - - - - - - - - -=0.01Fk1k21234568122412345678910111213141516171819405298.4934.1221.2016.2613.7412.2511.2610.5610.049.659.339.078.868.688.538.408.288.18499999.0130.8118.0013.2710.929.558.658.027.567.206.936.706.516.366.236.116.015.93540399.1729.4616.6912.069.788.457.596.996.556.225.955.745.565.425.295.185.095.01562599.2528.7115.9811.399.157.857.016.425.995.675.415.205.034.894.774.674.584.50576499.3028.2415.5210.978.757.466.636.065.645.325.064.864.694.564.444.344.254.17585999.3327.9115.2110.678.477.196.375.805.395.074.824.624.464.324.204.104.013.94598199.3627.4914.8010.298.106.846.035.475.064.744.504.304.144.003.893.793.713.63610699.4227.0514.379.897.726.475.675.114.714.404.163.963.803.673.553.453.373.30623499.4626.6013.939.477.316.075.284.734.334.023.783.593.433.293.183.083.002.92636699.5026.1213.469.026.885.654.864.313.913.603.363.163.002.872.752.652.572.49精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 5 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 5 页，共 12 页 - - - - - - - - -202122232425262728293040601208.108.027.947.887.827.777.727.687.647.607.567.317.086.856.645.855.785.725.665.615.575.535.495.455.425.395.184.984.794.604.944.874.824.764.724.684.644.604.574.544.514.314.133.953.784.434.374.314.264.224.184.144.114.074.044.023.833.653.483.324.104.043.993.943.903.863.823.783.753.733.703.513.343.173.023.873.813.763.713.673.633.593.563.533.503.473.293.122.962.803.563.513.453.413.363.323.293.263.233.203.172.992.822.662.513.233.173.123.073.032.992.962.932.902.872.842.662.502.342.182.862.802.752.702.662.622.582.552.522.492.472.292.121.951.792.422.362.312.262.212.172.132.102.062.032.011.801.601.381.00=0.025Fk1k212345681224精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 6 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 6 页，共 12 页 - - - - - - - - -1234567891011121314151617181920212223647.838.5117.4412.2210.018.818.077.577.216.946.726.556.416.306.206.126.045.985.925.875.835.795.75799.539.0016.0410.658.437.266.546.065.715.465.265.104.974.864.774.694.624.564.514.464.424.384.35864.239.1715.449.987.766.605.895.425.084.834.634.474.354.244.154.084.013.953.903.863.823.783.75899.639.2515.109.607.396.235.525.054.724.474.284.124.003.893.803.733.663.613.563.513.483.443.41921.839.3014.889.367.155.995.294.824.484.244.043.893.773.663.583.503.443.383.333.293.253.223.18937.139.3314.739.206.985.825.124.654.324.073.883.733.603.503.413.343.283.223.173.133.093.053.02956.739.3714.。