How to build a chi-square distribution table

Question

I would like to generate a chi-square distribution table in python as a function of the probability level and degree of freedom.

How to calculate the probability, given a known chi-value and degree of freedom, is this:

In[44]: scipy.stats.chisqprob(5.991, 2)
Out[44]: 0.050011615026579088

However, what I know is the probability and the degree of freedom. Thus, I would like to compute the corresponding chi-value for a given probability.

The end result should look similar to something like this.

Answer 1

The value that you want can be computed with the isf (inverse survival function) method of the scipy.stats.chi2 distribution.

This method uses broadcasting, so you can create your table with just a couple lines of code:

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])

Make df an array with shape (n, 1), so it broadcasts with p to create a 2-d array of all the pairings:

In [63]: df = np.array(range(1, 30) + range(30, 101, 10)).reshape(-1, 1)

Now just call isf:

In [64]: table = chi2.isf(p, df)

Tweak the default print options of numpy to create a nicely formatted table:

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]])

By setting the print options, the output shows only three decimal places, but the actual full values are still in table. E.g.:

In [67]: table[0, 0]
Out[67]: 3.927042222052108e-05

In [68]: table[0, 8]
Out[68]: 6.6348966010212171