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I have data for a random variable and I wish to test whether it conforms to the Tracy-Widom distribution. However, the T-W distribution is hard to compute. Is there a readly available table of its values I can just download?

Marcel
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1 Answers1

1

You could try page 39-44 of Bejan (2005) which gives cumulative probabilities

You might do better with a statistical package, such as the dtw, ptw, qtw functions in the RMTstat package in R. If you looked for quantiles (inverse CDF) you might for example get

prob     beta=1      beta=2     beta=4
0.0001 -5.2495820 -4.74089672 -6.7129735
0.001  -4.6541988 -4.29223640 -6.1787028
0.01   -3.8954334 -3.72444595 -5.5075714
0.025  -3.5158544 -3.44232243 -5.1764296
0.05   -3.1803810 -3.19416673 -4.8865513
0.1    -2.7824291 -2.90135094 -4.5462788
0.2    -2.2831649 -2.53656270 -4.1251980
0.3    -1.9103817 -2.26618204 -3.8152020
0.4    -1.5827670 -2.03003998 -3.5459679
0.5    -1.2685777 -1.80491241 -3.2906149
0.6    -0.9463339 -1.57539738 -3.0316173
0.7    -0.5922924 -1.32485956 -2.7504213
0.8    -0.1653210 -1.02495779 -2.4158767
0.9     0.4501291 -0.59685130 -1.9420592
0.95    0.9792895 -0.23247447 -1.5420487
0.975   1.4537219  0.09155832 -1.1886740
0.99    2.0233353  0.47763604 -0.7702858
0.999   3.2712253  1.31441944  0.1279186
0.9999  4.3508226  2.03469150  0.8933440
Henry
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  • A small point to note: the numbers in my table for beta=1 and beta=2 are broadly consistent with Andrei Bejan's tables for $TW_1$ and $TW_2$. For my beta=4 and his $TW_4$ there seems to be a scaling factor of $\sqrt{2}$ difference: for example my table suggests a median of about $-3.29$ while his table suggests something just below $-2.33$ – Henry Sep 01 '17 at 20:33