我想在 python 中生成卡方分布表作为概率水平和自由度的函数。
在给定卡值和自由度的情况下，如何计算概率是这样的:
In[44]: scipy.stats.chisqprob(5.991, 2)
Out[44]: 0.050011615026579088
不过，我知道的是概率和自由度。因此，我想计算给定概率对应的卡值。
最终结果应该类似于 something like this .
最佳答案
可以使用 scipy.stats.chi2 的 isf(逆生存函数)方法计算您想要的值分布。
此方法使用广播，因此您只需几行代码即可创建表格:
In [61]: from scipy.stats import chi2
In [62]: p = np.array([0.995, 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, 0.01, 0.005])
使 df 成为形状为 (n, 1) 的数组，因此它使用 p 进行广播以创建一个包含所有元素的二维数组配对:
In [63]: df = np.array(range(1, 30) + range(30, 101, 10)).reshape(-1, 1)
现在调用isf:
In [64]: table = chi2.isf(p, df)
调整 numpy 的默认打印选项以创建格式良好的表格:
In [65]: np.set_printoptions(linewidth=130, formatter=dict(float=lambda x: "%7.3f" % x))
In [66]: table
Out[66]:
array([[ 0.000, 0.000, 0.001, 0.004, 0.016, 2.706, 3.841, 5.024, 6.635, 7.879],
[ 0.010, 0.020, 0.051, 0.103, 0.211, 4.605, 5.991, 7.378, 9.210, 10.597],
[ 0.072, 0.115, 0.216, 0.352, 0.584, 6.251, 7.815, 9.348, 11.345, 12.838],
[ 0.207, 0.297, 0.484, 0.711, 1.064, 7.779, 9.488, 11.143, 13.277, 14.860],
[ 0.412, 0.554, 0.831, 1.145, 1.610, 9.236, 11.070, 12.833, 15.086, 16.750],
[ 0.676, 0.872, 1.237, 1.635, 2.204, 10.645, 12.592, 14.449, 16.812, 18.548],
[ 0.989, 1.239, 1.690, 2.167, 2.833, 12.017, 14.067, 16.013, 18.475, 20.278],
[ 1.344, 1.646, 2.180, 2.733, 3.490, 13.362, 15.507, 17.535, 20.090, 21.955],
[ 1.735, 2.088, 2.700, 3.325, 4.168, 14.684, 16.919, 19.023, 21.666, 23.589],
[ 2.156, 2.558, 3.247, 3.940, 4.865, 15.987, 18.307, 20.483, 23.209, 25.188],
[ 2.603, 3.053, 3.816, 4.575, 5.578, 17.275, 19.675, 21.920, 24.725, 26.757],
[ 3.074, 3.571, 4.404, 5.226, 6.304, 18.549, 21.026, 23.337, 26.217, 28.300],
[ 3.565, 4.107, 5.009, 5.892, 7.042, 19.812, 22.362, 24.736, 27.688, 29.819],
[ 4.075, 4.660, 5.629, 6.571, 7.790, 21.064, 23.685, 26.119, 29.141, 31.319],
[ 4.601, 5.229, 6.262, 7.261, 8.547, 22.307, 24.996, 27.488, 30.578, 32.801],
[ 5.142, 5.812, 6.908, 7.962, 9.312, 23.542, 26.296, 28.845, 32.000, 34.267],
[ 5.697, 6.408, 7.564, 8.672, 10.085, 24.769, 27.587, 30.191, 33.409, 35.718],
[ 6.265, 7.015, 8.231, 9.390, 10.865, 25.989, 28.869, 31.526, 34.805, 37.156],
[ 6.844, 7.633, 8.907, 10.117, 11.651, 27.204, 30.144, 32.852, 36.191, 38.582],
[ 7.434, 8.260, 9.591, 10.851, 12.443, 28.412, 31.410, 34.170, 37.566, 39.997],
[ 8.034, 8.897, 10.283, 11.591, 13.240, 29.615, 32.671, 35.479, 38.932, 41.401],
[ 8.643, 9.542, 10.982, 12.338, 14.041, 30.813, 33.924, 36.781, 40.289, 42.796],
[ 9.260, 10.196, 11.689, 13.091, 14.848, 32.007, 35.172, 38.076, 41.638, 44.181],
[ 9.886, 10.856, 12.401, 13.848, 15.659, 33.196, 36.415, 39.364, 42.980, 45.559],
[ 10.520, 11.524, 13.120, 14.611, 16.473, 34.382, 37.652, 40.646, 44.314, 46.928],
[ 11.160, 12.198, 13.844, 15.379, 17.292, 35.563, 38.885, 41.923, 45.642, 48.290],
[ 11.808, 12.879, 14.573, 16.151, 18.114, 36.741, 40.113, 43.195, 46.963, 49.645],
[ 12.461, 13.565, 15.308, 16.928, 18.939, 37.916, 41.337, 44.461, 48.278, 50.993],
[ 13.121, 14.256, 16.047, 17.708, 19.768, 39.087, 42.557, 45.722, 49.588, 52.336],
[ 13.787, 14.953, 16.791, 18.493, 20.599, 40.256, 43.773, 46.979, 50.892, 53.672],
[ 20.707, 22.164, 24.433, 26.509, 29.051, 51.805, 55.758, 59.342, 63.691, 66.766],
[ 27.991, 29.707, 32.357, 34.764, 37.689, 63.167, 67.505, 71.420, 76.154, 79.490],
[ 35.534, 37.485, 40.482, 43.188, 46.459, 74.397, 79.082, 83.298, 88.379, 91.952],
[ 43.275, 45.442, 48.758, 51.739, 55.329, 85.527, 90.531, 95.023, 100.425, 104.215],
[ 51.172, 53.540, 57.153, 60.391, 64.278, 96.578, 101.879, 106.629, 112.329, 116.321],
[ 59.196, 61.754, 65.647, 69.126, 73.291, 107.565, 113.145, 118.136, 124.116, 128.299],
[ 67.328, 70.065, 74.222, 77.929, 82.358, 118.498, 124.342, 129.561, 135.807, 140.169]])
通过设置打印选项，输出只显示三位小数，但实际的完整值仍在表中。例如:
In [67]: table[0, 0]
Out[67]: 3.927042222052108e-05
In [68]: table[0, 8]
Out[68]: 6.6348966010212171
关于python - 如何建立卡方分布表，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/32301698/