RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.91 16.7527 0.528762
2 to 25 15.68 19.3448 0.690899
3 to 26 15.91 31.3057 0.981672
4 to 27 15.65 25.7643 0.921137
5 to 28 15.52 18.5224 0.643374
6 to 29 15.59 20.5655 0.753669
7 to 30 16.04 14.6281 0.377748
8 to 31 16.10 25.9314 0.924281
9 to 32 15.82 12.1153 0.206891
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.126114
Tough bday spacings test for dh-ranFile-2018-07-08_09:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 11 29 77 87 98 79 67 28 16 7 1
(O-E)^2/E 0.4 1.6 0.2 1.2 0.0 0.0 4.3 0.1 0.1 0.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 10.116, p= 0.570
RESULTS OF GCD FOR dh-ranFile-2018-07-08_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.284084
p-value, dist. of gcd's: 0.420784
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.480 0.388 0.012 0.328 0.174 0.467 0.231 0.964
Bits 8 to 15---> 0.845 0.245 0.893 0.130 0.592 0.290 0.718 0.480
Bits 16 to 23---> 0.942 0.292 0.960 0.011 0.921 0.962 0.003 0.940
Bits 24 to 31---> 0.476 0.615 0.842 0.764 0.759 0.563 0.509 0.970
KS test for the above 32 p values: 0.828
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_09:31,
p-values for 5 runs: 0.6830, 0.1034, 0.5229, 0.0286, 0.2860
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 226 211.4 1.006 1.006
r= 29 5120 5134.0 0.038 1.044
r= 30 23200 23103.0 0.407 1.451
r= 31 11454 11551.5 0.823 2.274
chi-square = 2.274 with df = 3; p-value = 0.483
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 226 211.4 1.006 1.006
r= 30 5049 5134.0 1.408 2.413
r= 31 23119 23103.0 0.011 2.424
r= 32 11606 11551.5 0.257 2.681
chi-square = 2.681 with df = 3; p-value = 0.557
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_09:31
b-rank test for bits 1 to 8, p=0.07898
b-rank test for bits 2 to 9, p=0.19353
b-rank test for bits 3 to 10, p=0.40757
b-rank test for bits 4 to 11, p=0.90246
b-rank test for bits 5 to 12, p=0.38354
b-rank test for bits 6 to 13, p=0.56521
b-rank test for bits 7 to 14, p=0.51895
b-rank test for bits 8 to 15, p=0.66346
b-rank test for bits 9 to 16, p=0.36277
b-rank test for bits 10 to 17, p=0.79593
b-rank test for bits 11 to 18, p=0.59120
b-rank test for bits 12 to 19, p=0.81184
b-rank test for bits 13 to 20, p=0.68779
b-rank test for bits 14 to 21, p=0.45762
b-rank test for bits 15 to 22, p=0.40742
b-rank test for bits 16 to 23, p=0.35056
b-rank test for bits 17 to 24, p=0.04372
b-rank test for bits 18 to 25, p=0.62438
b-rank test for bits 19 to 26, p=0.83921
b-rank test for bits 20 to 27, p=0.81925
b-rank test for bits 21 to 28, p=0.71960
b-rank test for bits 22 to 29, p=0.13935
b-rank test for bits 23 to 30, p=0.27474
b-rank test for bits 24 to 31, p=0.08213
b-rank test for bits 25 to 32, p=0.16949
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.832898
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_09:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 141613 -0.69 0.244356
2 141819 -0.21 0.416424
3 142078 0.39 0.653242
4 142084 0.41 0.658403
5 141876 -0.08 0.468964
6 141400 -1.19 0.117019
7 141735 -0.41 0.341889
8 141887 -0.05 0.479196
9 142056 0.34 0.634083
10 141243 -1.56 0.059754
11 141830 -0.19 0.426477
12 142266 0.83 0.797674
13 141638 -0.63 0.263057
14 141824 -0.20 0.420987
15 142645 1.72 0.957180
16 141688 -0.52 0.302534
17 141518 -0.91 0.180274
18 141217 -1.62 0.052875
19 142239 0.77 0.779426
20 140721 -2.78 0.002748
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_09:31
Bits used No. missing words z-score p-value
23 to 32 141821 -0.3046 0.380341
22 to 31 142358 1.5471 0.939085
21 to 30 142138 0.7885 0.784803
20 to 29 142827 3.1644 0.999223
19 to 28 141758 -0.5218 0.300895
18 to 27 142258 1.2023 0.885378
17 to 26 141929 0.0678 0.527039
16 to 25 142195 0.9851 0.837705
15 to 24 141528 -1.3149 0.094267
14 to 23 141528 -1.3149 0.094267
13 to 22 141904 -0.0184 0.492668
12 to 21 142029 0.4127 0.660070
11 to 20 141702 -0.7149 0.237326
10 to 19 142131 0.7644 0.777679
9 to 18 142121 0.7299 0.767273
8 to 17 142305 1.3644 0.913776
7 to 16 141814 -0.3287 0.371182
6 to 15 141903 -0.0218 0.491293
5 to 14 142547 2.1989 0.986056
4 to 13 142180 0.9333 0.824679
3 to 12 141966 0.1954 0.577466
2 to 11 141786 -0.4253 0.335318
1 to 10 141780 -0.4460 0.327811
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_09:31
Bits used No. missing words z-score p-value
28 to 32 142239 1.1175 0.868115
27 to 31 141997 0.2972 0.616838
26 to 30 141963 0.1819 0.572182
25 to 29 142081 0.5819 0.719694
24 to 28 141663 -0.8350 0.201854
23 to 27 141492 -1.4147 0.078581
22 to 26 141507 -1.3638 0.086310
21 to 25 141905 -0.0147 0.494145
20 to 24 141674 -0.7977 0.212514
19 to 23 142287 1.2802 0.899769
18 to 22 141653 -0.8689 0.192447
17 to 21 141746 -0.5537 0.289905
16 to 20 142203 0.9955 0.840251
15 to 19 142083 0.5887 0.721973
14 to 18 142145 0.7989 0.787820
13 to 17 141747 -0.5503 0.291067
12 to 16 141921 0.0396 0.515778
11 to 15 141735 -0.5909 0.277277
10 to 14 141712 -0.6689 0.251775
9 to 13 142359 1.5243 0.936284
8 to 12 141977 0.2294 0.590717
7 to 11 142205 1.0023 0.841894
6 to 10 142158 0.8429 0.800372
5 to 9 141791 -0.4011 0.344166
4 to 8 142226 1.0735 0.858467
3 to 7 141723 -0.6316 0.263815
2 to 6 142359 1.5243 0.936284
1 to 5 141981 0.2429 0.595978
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_09:31
Bits used No. missing words z-score p-value
31 to 32 141609 -0.8859 0.187828
30 to 31 141532 -1.1131 0.132840
29 to 30 141874 -0.1042 0.458498
28 to 29 141696 -0.6293 0.264579
27 to 28 142193 0.8368 0.798643
26 to 27 142787 2.5890 0.995187
25 to 26 142241 0.9784 0.836056
24 to 25 141797 -0.3314 0.370187
23 to 24 141673 -0.6971 0.242858
22 to 23 141517 -1.1573 0.123572
21 to 22 141878 -0.0924 0.463183
20 to 21 141415 -1.4582 0.072393
19 to 20 141823 -0.2547 0.399493
18 to 19 141999 0.2645 0.604308
17 to 18 142423 1.5153 0.935146
16 to 17 141625 -0.8387 0.200810
15 to 16 141944 0.1023 0.540729
14 to 15 142238 0.9695 0.833859
13 to 14 141239 -1.9774 0.024000
12 to 13 141853 -0.1662 0.434014
11 to 12 142113 0.6008 0.726012
10 to 11 142105 0.5772 0.718097
9 to 10 141979 0.2055 0.581416
8 to 9 141994 0.2498 0.598615
7 to 8 141364 -1.6086 0.053847
6 to 7 142376 1.3766 0.915683
5 to 6 142462 1.6303 0.948480
4 to 5 141514 -1.1662 0.121774
3 to 4 142057 0.4356 0.668438
2 to 3 141599 -0.9154 0.179984
1 to 2 141865 -0.1308 0.447980
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2468.95 -0.439 0.330268
Test results for specific bytes for dh-ranFile-2018-07-08_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2493.78 -0.088 0.464972
2 to 9 2487.09 -0.183 0.427552
3 to 10 2456.96 -0.609 0.271382
4 to 11 2508.82 0.125 0.549647
5 to 12 2581.88 1.158 0.876563
6 to 13 2561.17 0.865 0.806508
7 to 14 2474.57 -0.360 0.359534
8 to 15 2606.23 1.502 0.933486
9 to 16 2504.37 0.062 0.524644
10 to 17 2530.41 0.430 0.666427
11 to 18 2577.35 1.094 0.862993
12 to 19 2513.13 0.186 0.573630
13 to 20 2712.67 3.008 0.998684
14 to 21 2645.52 2.058 0.980203
15 to 22 2443.59 -0.798 0.212492
16 to 23 2497.22 -0.039 0.484340
17 to 24 2470.88 -0.412 0.340241
18 to 25 2465.63 -0.486 0.313444
19 to 26 2515.26 0.216 0.585456
20 to 27 2524.55 0.347 0.635770
21 to 28 2431.24 -0.972 0.165438
22 to 29 2636.23 1.927 0.972981
23 to 30 2475.36 -0.349 0.363726
24 to 31 2426.72 -1.036 0.150020
25 to 32 2446.50 -0.757 0.224644
CDPARK for dh-ranFile-2018-07-08_09:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3478 -2.0548 0.019949
3541 0.8219 0.794438
3516 -0.3196 0.374623
3564 1.8721 0.969407
3498 -1.1416 0.126820
3520 -0.1370 0.445521
3534 0.5023 0.692266
3509 -0.6393 0.261324
3500 -1.0502 0.146807
3505 -0.8219 0.205562
Square side=100, avg. no. parked=3516.50 sample std.=23.37
p-value of the KSTEST for those 10 p-values: 0.476913
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_09:31
0.7352,0.9672,0.9958,0.8691,0.4082,0.9745,0.7824,0.5131,0.8650,0.6435,
The KS test for those 10 p-values: 0.002454
The 3DSPHERES test for dh-ranFile-2018-07-08_09:31
sample no r^3 equiv. uni.
1 24.499 0.558081
2 19.383 0.475915
3 68.801 0.899075
4 31.808 0.653636
5 14.218 0.377453
6 4.643 0.143383
7 5.806 0.175958
8 71.848 0.908823
9 40.191 0.738074
10 12.330 0.337007
11 55.276 0.841584
12 22.124 0.521678
13 6.510 0.195061
14 23.128 0.537420
15 3.919 0.122471
16 14.515 0.383592
17 67.690 0.895265
18 80.473 0.931604
19 17.107 0.434600
20 13.701 0.366634
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.749432
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.9 0.3 -1.0 0.6 0.5
0.2 0.2 0.9 -2.0 1.1 1.8
-0.3 1.5 1.3 -1.3 -1.5 0.2
-0.8 -1.1 -1.6 0.6 -0.2 1.1
-0.2 0.1 0.1 0.4 -1.1 2.3
0.9 0.6 1.2 1.3 0.3 -0.5
-0.7 -1.0 -0.8 0.4 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:42.364170
z-score=0.039734, p-value=0.544742
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_09:31
Test no p-value
1 0.863726
2 0.082023
3 0.441060
4 0.673145
5 0.706660
6 0.692021
7 0.299090
8 0.018930
9 0.333785
10 0.195314
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.735952
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_09:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66502 0.41 66557 0.18
3 25000.00 25197 1.55 25082 0.27
4 6666.67 6603 0.61 6676 0.01
5 1388.89 1416 0.53 1410 0.32
6 238.10 244 0.15 235 0.04
7 34.72 32 0.21 31 0.40
8 4.96 5 0.00 8 1.86
p=0.25021 p=0.20194
Number of rngs required: 688961, p-value: 0.740
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_09:31
No. of wins: Observed Expected
98486 98585.9
z-score=-0.447, pvalue=0.32757
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66514 66666.7 0.350 0.350
2 37598 37654.3 0.084 0.434
3 26905 26954.7 0.092 0.526
4 19253 19313.5 0.189 0.715
5 13971 13851.4 1.032 1.747
6 10089 9943.5 2.128 3.875
7 7101 7145.0 0.271 4.146
8 5116 5139.1 0.104 4.250
9 3726 3699.9 0.185 4.434
10 2702 2666.3 0.478 4.913
11 1853 1923.3 2.572 7.484
12 1483 1388.7 6.398 13.882
13 1009 1003.7 0.028 13.910
14 719 726.1 0.070 13.980
15 520 525.8 0.065 14.045
16 381 381.2 0.000 14.045
17 248 276.5 2.945 16.990
18 223 200.8 2.447 19.438
19 146 146.0 0.000 19.438
20 120 106.2 1.789 21.227
21 323 287.1 4.485 25.712
Chisq= 25.71 for 20 degrees of freedom, p= 0.82446
SUMMARY of craptest
p-value for no. of wins: 0.327573
p-value for throws/game: 0.824465
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_09:31
No. of wins: Observed Expected
98146 98585.9
z-score=-1.967, pvalue=0.02457
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66588 66666.7 0.093 0.093
2 37663 37654.3 0.002 0.095
3 26724 26954.7 1.975 2.070
4 19385 19313.5 0.265 2.335
5 13867 13851.4 0.018 2.352
6 10076 9943.5 1.764 4.117
7 7273 7145.0 2.292 6.409
8 5025 5139.1 2.532 8.941
9 3699 3699.9 0.000 8.941
10 2701 2666.3 0.452 9.393
11 1929 1923.3 0.017 9.410
12 1392 1388.7 0.008 9.417
13 1018 1003.7 0.203 9.621
14 702 726.1 0.803 10.423
15 537 525.8 0.237 10.660
16 399 381.2 0.836 11.496
17 274 276.5 0.023 11.519
18 202 200.8 0.007 11.526
19 137 146.0 0.553 12.079
20 119 106.2 1.539 13.618
21 290 287.1 0.029 13.647
Chisq= 13.65 for 20 degrees of freedom, p= 0.15207
SUMMARY of craptest
p-value for no. of wins: 0.024574
p-value for throws/game: 0.152067
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0025,0.0027,0.0030,0.0110,0.0120,0.0189,0.0199,0.0240,0.0246,0.0286,
0.0437,0.0529,0.0538,0.0598,0.0724,0.0786,0.0790,0.0820,0.0821,0.0863,
0.0943,0.0943,0.1034,0.1170,0.1218,0.1225,0.1236,0.1261,0.1268,0.1299,
0.1328,0.1393,0.1434,0.1468,0.1500,0.1521,0.1654,0.1695,0.1741,0.1760,
0.1800,0.1803,0.1878,0.1924,0.1935,0.1951,0.1953,0.2008,0.2019,0.2019,
0.2056,0.2069,0.2125,0.2125,0.2246,0.2312,0.2373,0.2429,0.2444,0.2449,
0.2502,0.2518,0.2613,0.2631,0.2638,0.2646,0.2714,0.2747,0.2773,0.2841,
0.2860,0.2899,0.2903,0.2911,0.2920,0.2991,0.3009,0.3025,0.3134,0.3276,
0.3278,0.3278,0.3303,0.3338,0.3353,0.3370,0.3402,0.3419,0.3442,0.3506,
0.3595,0.3628,0.3637,0.3666,0.3702,0.3712,0.3746,0.3775,0.3777,0.3803,
0.3835,0.3836,0.3880,0.3995,0.4074,0.4076,0.4082,0.4164,0.4208,0.4210,
0.4265,0.4276,0.4340,0.4346,0.4411,0.4455,0.4480,0.4576,0.4585,0.4632,
0.4650,0.4669,0.4690,0.4758,0.4759,0.4769,0.4792,0.4796,0.4799,0.4825,
0.4843,0.4913,0.4927,0.4941,0.5090,0.5131,0.5158,0.5190,0.5217,0.5229,
0.5246,0.5270,0.5288,0.5374,0.5407,0.5447,0.5496,0.5566,0.5581,0.5634,
0.5652,0.5696,0.5722,0.5736,0.5775,0.5814,0.5855,0.5907,0.5912,0.5917,
0.5960,0.5986,0.6043,0.6147,0.6168,0.6244,0.6341,0.6358,0.6434,0.6435,
0.6532,0.6536,0.6584,0.6601,0.6635,0.6664,0.6684,0.6731,0.6830,0.6878,
0.6909,0.6920,0.6923,0.7067,0.7181,0.7183,0.7196,0.7197,0.7220,0.7260,
0.7352,0.7360,0.7381,0.7402,0.7494,0.7537,0.7589,0.7637,0.7673,0.7777,
0.7794,0.7824,0.7848,0.7878,0.7944,0.7959,0.7977,0.7986,0.8004,0.8065,
0.8118,0.8193,0.8245,0.8247,0.8283,0.8329,0.8339,0.8361,0.8377,0.8392,
0.8403,0.8416,0.8419,0.8424,0.8448,0.8585,0.8630,0.8637,0.8650,0.8681,
0.8691,0.8766,0.8854,0.8934,0.8953,0.8991,0.8998,0.9025,0.9088,0.9138,
0.9157,0.9207,0.9211,0.9243,0.9316,0.9335,0.9351,0.9363,0.9363,0.9391,
0.9402,0.9418,0.9485,0.9572,0.9604,0.9621,0.9637,0.9672,0.9694,0.9696,
0.9730,0.9745,0.9802,0.9817,0.9861,0.9952,0.9958,0.9987,0.9992,
Overall p-value after applying KStest on 269 p-values = 0.543750
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.