RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.68 14.9671 0.402147
2 to 25 15.74 19.0594 0.674868
3 to 26 16.03 9.9674 0.095027
4 to 27 15.79 17.1148 0.553386
5 to 28 16.08 14.5047 0.368887
6 to 29 15.91 21.9635 0.813874
7 to 30 15.94 17.2018 0.559220
8 to 31 16.03 6.9373 0.015653
9 to 32 15.71 19.9458 0.722988
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.766670
Tough bday spacings test for dh-ranFile-2018-07-06_17:31: 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 5 32 66 113 101 83 40 33 18 6 3
(O-E)^2/E 1.9 0.6 0.7 2.4 0.1 0.3 2.8 0.4 0.7 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.157, p= 0.573
RESULTS OF GCD FOR dh-ranFile-2018-07-06_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.566134
p-value, dist. of gcd's: 0.789076
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.324 0.669 0.898 0.758 0.875 0.546 0.149 0.889
Bits 8 to 15---> 0.890 0.467 0.467 0.667 0.708 0.529 0.655 0.611
Bits 16 to 23---> 0.563 0.943 0.119 0.417 0.517 0.225 0.625 0.568
Bits 24 to 31---> 0.399 0.281 0.435 0.840 0.519 0.364 0.974 0.006
KS test for the above 32 p values: 0.749
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_17:31,
p-values for 5 runs: 0.7333, 0.5716, 0.5830, 0.4437, 0.6419
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 186 211.4 3.056 3.056
r= 29 5123 5134.0 0.024 3.080
r= 30 23307 23103.0 1.800 4.880
r= 31 11384 11551.5 2.429 7.309
chi-square = 7.309 with df = 3; p-value = 0.937
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5128 5134.0 0.007 0.017
r= 31 22967 23103.0 0.801 0.818
r= 32 11695 11551.5 1.782 2.600
chi-square = 2.600 with df = 3; p-value = 0.542
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_17:31
b-rank test for bits 1 to 8, p=0.06348
b-rank test for bits 2 to 9, p=0.74844
b-rank test for bits 3 to 10, p=0.11112
b-rank test for bits 4 to 11, p=0.72585
b-rank test for bits 5 to 12, p=0.97323
b-rank test for bits 6 to 13, p=0.87354
b-rank test for bits 7 to 14, p=0.16393
b-rank test for bits 8 to 15, p=0.95265
b-rank test for bits 9 to 16, p=0.84096
b-rank test for bits 10 to 17, p=0.25242
b-rank test for bits 11 to 18, p=0.63074
b-rank test for bits 12 to 19, p=0.00542
b-rank test for bits 13 to 20, p=0.37761
b-rank test for bits 14 to 21, p=0.42637
b-rank test for bits 15 to 22, p=0.94055
b-rank test for bits 16 to 23, p=0.98351
b-rank test for bits 17 to 24, p=0.97173
b-rank test for bits 18 to 25, p=0.57914
b-rank test for bits 19 to 26, p=0.34720
b-rank test for bits 20 to 27, p=0.02339
b-rank test for bits 21 to 28, p=0.13041
b-rank test for bits 22 to 29, p=0.37560
b-rank test for bits 23 to 30, p=0.13363
b-rank test for bits 24 to 31, p=0.32604
b-rank test for bits 25 to 32, p=0.20122
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 = 0.287356
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_17:31
(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 141944 0.08 0.532281
2 142692 1.83 0.966275
3 141488 -0.98 0.162456
4 141429 -1.12 0.130875
5 141787 -0.29 0.387509
6 141598 -0.73 0.233489
7 142026 0.27 0.607417
8 142354 1.04 0.850586
9 142399 1.14 0.873707
10 141957 0.11 0.544342
11 142550 1.50 0.932789
12 141840 -0.16 0.435658
13 141735 -0.41 0.341889
14 142937 2.40 0.991827
15 142155 0.57 0.717015
16 141832 -0.18 0.428310
17 142538 1.47 0.929064
18 141943 0.08 0.531352
19 142456 1.28 0.899246
20 141860 -0.12 0.454121
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_17:31
Bits used No. missing words z-score p-value
23 to 32 142316 1.4023 0.919589
22 to 31 142332 1.4575 0.927508
21 to 30 141909 -0.0011 0.499546
20 to 29 141571 -1.1667 0.121675
19 to 28 142197 0.9920 0.839393
18 to 27 142073 0.5644 0.713752
17 to 26 141652 -0.8873 0.187447
16 to 25 142236 1.1264 0.870012
15 to 24 142090 0.6230 0.733358
14 to 23 141793 -0.4011 0.344159
13 to 22 141806 -0.3563 0.360804
12 to 21 141968 0.2023 0.580163
11 to 20 142096 0.6437 0.740112
10 to 19 141776 -0.4598 0.322845
9 to 18 141652 -0.8873 0.187447
8 to 17 141667 -0.8356 0.201684
7 to 16 142347 1.5092 0.934377
6 to 15 141618 -1.0046 0.157548
5 to 14 141867 -0.1460 0.441974
4 to 13 141847 -0.2149 0.414911
3 to 12 142137 0.7851 0.783793
2 to 11 141798 -0.3839 0.350528
1 to 10 142197 0.9920 0.839393
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_17:31
Bits used No. missing words z-score p-value
28 to 32 142258 1.1819 0.881384
27 to 31 142188 0.9446 0.827580
26 to 30 142100 0.6463 0.740970
25 to 29 141754 -0.5265 0.299256
24 to 28 141663 -0.8350 0.201854
23 to 27 141899 -0.0350 0.486033
22 to 26 142183 0.9277 0.823217
21 to 25 141968 0.1989 0.578822
20 to 24 142276 1.2429 0.893057
19 to 23 141382 -1.7876 0.036924
18 to 22 141603 -1.0384 0.149540
17 to 21 142417 1.7209 0.957367
16 to 20 141434 -1.6113 0.053558
15 to 19 141754 -0.5265 0.299256
14 to 18 141744 -0.5604 0.287589
13 to 17 141871 -0.1299 0.448310
12 to 16 141448 -1.5638 0.058929
11 to 15 142446 1.8192 0.965561
10 to 14 141914 0.0158 0.506315
9 to 13 141441 -1.5876 0.056193
8 to 12 141610 -1.0147 0.155130
7 to 11 141867 -0.1435 0.442951
6 to 10 142036 0.4294 0.666180
5 to 9 142023 0.3853 0.650001
4 to 8 141428 -1.6316 0.051379
3 to 7 142098 0.6396 0.738770
2 to 6 142204 0.9989 0.841074
1 to 5 141872 -0.1265 0.449651
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_17:31
Bits used No. missing words z-score p-value
31 to 32 141429 -1.4169 0.078256
30 to 31 141900 -0.0275 0.489022
29 to 30 142059 0.4415 0.670576
28 to 29 141617 -0.8623 0.194253
27 to 28 141966 0.1672 0.566381
26 to 27 141889 -0.0600 0.476090
25 to 26 141224 -2.0216 0.021608
24 to 25 141621 -0.8505 0.197515
23 to 24 141725 -0.5437 0.293308
22 to 23 141986 0.2262 0.589464
21 to 22 141704 -0.6057 0.272359
20 to 21 141832 -0.2281 0.409780
19 to 20 142081 0.5064 0.693713
18 to 19 141946 0.1082 0.543070
17 to 18 142244 0.9872 0.838234
16 to 17 141990 0.2380 0.594046
15 to 16 141803 -0.3137 0.376891
14 to 15 141713 -0.5791 0.281246
13 to 14 142315 1.1967 0.884282
12 to 13 141466 -1.3078 0.095478
11 to 12 142103 0.5713 0.716101
10 to 11 141554 -1.0482 0.147280
9 to 10 141963 0.1583 0.562897
8 to 9 142105 0.5772 0.718097
7 to 8 141909 -0.0010 0.499612
6 to 7 141575 -0.9862 0.162012
5 to 6 141870 -0.1160 0.453819
4 to 5 141497 -1.2163 0.111933
3 to 4 142194 0.8397 0.799471
2 to 3 142689 2.2999 0.989273
1 to 2 141670 -0.7060 0.240098
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2447.98 -0.736 0.230963
Test results for specific bytes for dh-ranFile-2018-07-06_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2568.45 0.968 0.833492
2 to 9 2488.81 -0.158 0.437156
3 to 10 2529.14 0.412 0.659863
4 to 11 2551.80 0.733 0.768099
5 to 12 2600.41 1.420 0.922190
6 to 13 2532.90 0.465 0.679118
7 to 14 2407.65 -1.306 0.095764
8 to 15 2616.49 1.647 0.950271
9 to 16 2601.97 1.442 0.925369
10 to 17 2375.48 -1.761 0.039115
11 to 18 2575.20 1.063 0.856221
12 to 19 2475.93 -0.340 0.366773
13 to 20 2495.32 -0.066 0.473628
14 to 21 2459.17 -0.577 0.281821
15 to 22 2670.11 2.406 0.991929
16 to 23 2515.40 0.218 0.586208
17 to 24 2532.60 0.461 0.677628
18 to 25 2489.91 -0.143 0.443287
19 to 26 2509.10 0.129 0.551227
20 to 27 2396.42 -1.465 0.071473
21 to 28 2482.84 -0.243 0.404125
22 to 29 2556.85 0.804 0.789277
23 to 30 2499.10 -0.013 0.494928
24 to 31 2494.85 -0.073 0.470942
25 to 32 2420.14 -1.129 0.129364
CDPARK for dh-ranFile-2018-07-06_17:31: 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
3526 0.1370 0.554479
3491 -1.4612 0.071982
3550 1.2329 0.891189
3499 -1.0959 0.136563
3557 1.5525 0.939730
3505 -0.8219 0.205562
3540 0.7763 0.781201
3501 -1.0046 0.157553
3541 0.8219 0.794438
3503 -0.9132 0.180558
Square side=100, avg. no. parked=3521.30 sample std.=22.99
p-value of the KSTEST for those 10 p-values: 0.538477
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_17:31
0.2351,0.9917,0.9709,0.0158,0.0278,0.5614,0.0863,0.4237,0.5570,0.1737,
The KS test for those 10 p-values: 0.143111
The 3DSPHERES test for dh-ranFile-2018-07-06_17:31
sample no r^3 equiv. uni.
1 9.828 0.279340
2 52.251 0.824776
3 18.007 0.451315
4 94.647 0.957357
5 12.437 0.339371
6 81.707 0.934359
7 20.322 0.492063
8 0.208 0.006907
9 6.183 0.186246
10 18.981 0.468843
11 333.960 0.999985
12 7.213 0.213715
13 30.095 0.633286
14 0.146 0.004854
15 4.266 0.132563
16 3.194 0.100999
17 22.969 0.534964
18 69.211 0.900442
19 84.982 0.941148
20 39.726 0.733981
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.288140
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 1.1 -0.3 -0.2 -0.1
0.4 -0.0 0.5 -1.4 1.2 -0.2
-2.3 -0.5 -0.1 -1.6 1.4 2.0
0.3 1.5 1.1 -1.1 -2.3 -0.2
-0.5 0.0 0.3 0.7 -0.1 0.3
1.3 0.1 0.3 -0.8 0.2 0.4
-0.7 2.1 0.9 -0.1 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:39.547509
z-score=-0.267589, p-value=0.420817
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_17:31
Test no p-value
1 0.200035
2 0.296737
3 0.204922
4 0.408944
5 0.560638
6 0.401890
7 0.235489
8 0.103353
9 0.566721
10 0.518945
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.090266
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_17:31:
(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 66724 0.05 66528 0.29
3 25000.00 24999 0.00 25094 0.35
4 6666.67 6639 0.11 6654 0.02
5 1388.89 1372 0.21 1450 2.69
6 238.10 224 0.83 225 0.72
7 34.72 36 0.05 46 3.66
8 4.96 5 0.00 2 1.77
p=0.02574 p=0.85295
Number of rngs required: 687831, p-value: 0.255
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_17:31
No. of wins: Observed Expected
98784 98585.9
z-score= 0.886, pvalue=0.81225
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66762 66666.7 0.136 0.136
2 37768 37654.3 0.343 0.480
3 27079 26954.7 0.573 1.052
4 19205 19313.5 0.609 1.662
5 13873 13851.4 0.034 1.695
6 9806 9943.5 1.903 3.598
7 7217 7145.0 0.725 4.323
8 5021 5139.1 2.713 7.035
9 3696 3699.9 0.004 7.040
10 2657 2666.3 0.032 7.072
11 1952 1923.3 0.427 7.499
12 1389 1388.7 0.000 7.499
13 981 1003.7 0.514 8.013
14 750 726.1 0.784 8.797
15 528 525.8 0.009 8.806
16 358 381.2 1.406 10.212
17 264 276.5 0.569 10.781
18 180 200.8 2.160 12.942
19 134 146.0 0.984 13.925
20 107 106.2 0.006 13.931
21 273 287.1 0.694 14.625
Chisq= 14.62 for 20 degrees of freedom, p= 0.20255
SUMMARY of craptest
p-value for no. of wins: 0.812246
p-value for throws/game: 0.202550
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_17:31
No. of wins: Observed Expected
98441 98585.9
z-score=-0.648, pvalue=0.25853
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66779 66666.7 0.189 0.189
2 37723 37654.3 0.125 0.315
3 26663 26954.7 3.157 3.472
4 19200 19313.5 0.667 4.139
5 13730 13851.4 1.064 5.203
6 9962 9943.5 0.034 5.237
7 7110 7145.0 0.172 5.409
8 5241 5139.1 2.022 7.430
9 3763 3699.9 1.077 8.508
10 2764 2666.3 3.580 12.088
11 1950 1923.3 0.370 12.458
12 1415 1388.7 0.497 12.954
13 1024 1003.7 0.410 13.364
14 742 726.1 0.346 13.711
15 519 525.8 0.089 13.800
16 382 381.2 0.002 13.801
17 274 276.5 0.023 13.825
18 224 200.8 2.673 16.498
19 128 146.0 2.216 18.714
20 114 106.2 0.571 19.284
21 293 287.1 0.121 19.405
Chisq= 19.40 for 20 degrees of freedom, p= 0.50433
SUMMARY of craptest
p-value for no. of wins: 0.258527
p-value for throws/game: 0.504328
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0049,0.0054,0.0061,0.0069,0.0157,0.0158,0.0216,0.0234,0.0257,0.0278,
0.0369,0.0391,0.0514,0.0536,0.0562,0.0589,0.0635,0.0715,0.0720,0.0783,
0.0863,0.0903,0.0950,0.0955,0.0958,0.1010,0.1034,0.1111,0.1119,0.1191,
0.1217,0.1294,0.1304,0.1309,0.1326,0.1336,0.1366,0.1431,0.1473,0.1493,
0.1495,0.1551,0.1575,0.1576,0.1620,0.1625,0.1639,0.1737,0.1806,0.1862,
0.1874,0.1874,0.1943,0.1975,0.2000,0.2012,0.2017,0.2019,0.2026,0.2049,
0.2056,0.2137,0.2245,0.2310,0.2335,0.2351,0.2355,0.2401,0.2524,0.2546,
0.2585,0.2724,0.2793,0.2812,0.2814,0.2818,0.2874,0.2876,0.2881,0.2933,
0.2967,0.2993,0.2993,0.3228,0.3241,0.3260,0.3394,0.3419,0.3442,0.3472,
0.3505,0.3608,0.3640,0.3668,0.3689,0.3756,0.3769,0.3776,0.3875,0.3990,
0.4019,0.4021,0.4041,0.4089,0.4098,0.4149,0.4165,0.4208,0.4237,0.4264,
0.4283,0.4347,0.4357,0.4372,0.4420,0.4430,0.4433,0.4437,0.4483,0.4497,
0.4513,0.4538,0.4541,0.4674,0.4674,0.4688,0.4709,0.4736,0.4761,0.4860,
0.4890,0.4921,0.4949,0.4995,0.4996,0.5043,0.5063,0.5166,0.5189,0.5190,
0.5292,0.5314,0.5323,0.5350,0.5385,0.5425,0.5431,0.5443,0.5465,0.5512,
0.5534,0.5545,0.5570,0.5592,0.5606,0.5614,0.5625,0.5629,0.5661,0.5664,
0.5667,0.5681,0.5716,0.5732,0.5788,0.5791,0.5802,0.5830,0.5862,0.5895,
0.5940,0.6074,0.6106,0.6253,0.6307,0.6333,0.6419,0.6500,0.6550,0.6599,
0.6662,0.6673,0.6688,0.6706,0.6749,0.6776,0.6791,0.6937,0.7082,0.7138,
0.7161,0.7170,0.7181,0.7230,0.7258,0.7333,0.7334,0.7340,0.7388,0.7401,
0.7410,0.7484,0.7495,0.7583,0.7667,0.7681,0.7812,0.7838,0.7891,0.7893,
0.7944,0.7995,0.8122,0.8139,0.8232,0.8248,0.8276,0.8335,0.8382,0.8394,
0.8394,0.8404,0.8410,0.8411,0.8506,0.8529,0.8562,0.8700,0.8735,0.8737,
0.8747,0.8814,0.8843,0.8885,0.8904,0.8912,0.8931,0.8980,0.8992,0.9004,
0.9196,0.9222,0.9254,0.9275,0.9291,0.9328,0.9344,0.9344,0.9373,0.9397,
0.9405,0.9411,0.9427,0.9503,0.9527,0.9574,0.9574,0.9656,0.9663,0.9709,
0.9717,0.9732,0.9739,0.9835,0.9893,0.9917,0.9918,0.9919,1.0000,
Overall p-value after applying KStest on 269 p-values = 0.877739
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.