python - How to build a chi-square distribution table -

i generate chi-square distribution table in python function of probability level , degree of freedom.

how calculate probability, given known chi-value , degree of freedom, this:

in[44]: scipy.stats.chisqprob(5.991, 2) out[44]: 0.050011615026579088 

however, know probability , degree of freedom. thus, compute corresponding chi-value given probability.

the end result should similar something this.

the value want can computed isf (inverse survival function) method of scipy.stats.chi2 distribution.

this method uses broadcasting, can create table couple lines of code:

in [61]: 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 array shape (n, 1), broadcasts p create 2-d array of pairings:

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

now call isf:

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

tweak default print options of numpy create 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 print options, output shows 3 decimal places, actual full values still in table. e.g.:

in [67]: table[0, 0] out[67]: 3.927042222052108e-05  in [68]: table[0, 8] out[68]: 6.6348966010212171