RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2019-08-29_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.82 14.7667 0.387721
2 to 25 15.78 18.2473 0.626597
3 to 26 15.64 29.5279 0.970042
4 to 27 15.73 17.2671 0.563586
5 to 28 15.62 18.4317 0.637893
6 to 29 15.81 16.4111 0.505099
7 to 30 15.74 11.6533 0.179336
8 to 31 15.89 12.3733 0.222977
9 to 32 15.74 11.7892 0.187268
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.754251
Tough bday spacings test for dh-ranFile-2019-08-29_07:31: 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 20 32 72 101 96 61 57 33 15 7 6
(O-E)^2/E 12.8 0.6 0.0 0.1 0.0 3.8 0.5 0.4 0.0 0.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 19.102, p= 0.961
RESULTS OF GCD FOR dh-ranFile-2019-08-29_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.170717
p-value, dist. of gcd's: 0.140189
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2019-08-29_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.370 0.458 0.841 0.959 0.507 0.681 0.236 0.260
Bits 8 to 15---> 0.898 0.790 0.960 0.895 0.804 0.107 0.241 0.143
Bits 16 to 23---> 0.536 0.939 0.510 0.892 0.063 0.509 0.743 0.224
Bits 24 to 31---> 0.740 0.260 0.152 0.710 0.827 0.670 0.265 0.052
KS test for the above 32 p values: 0.372
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2019-08-29_07:31,
p-values for 5 runs: 0.4190, 0.4291, 0.5981, 0.5255, 0.4153
Rank test for binary matrices (31x31) for dh-ranFile-2019-08-29_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 223 211.4 0.634 0.634
r= 29 5153 5134.0 0.070 0.705
r= 30 23119 23103.0 0.011 0.716
r= 31 11505 11551.5 0.187 0.903
chi-square = 0.903 with df = 3; p-value = 0.175
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2019-08-29_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 190 211.4 2.170 2.170
r= 30 5123 5134.0 0.024 2.193
r= 31 22953 23103.0 0.975 3.168
r= 32 11734 11551.5 2.883 6.050
chi-square = 6.050 with df = 3; p-value = 0.891
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2019-08-29_07:31
b-rank test for bits 1 to 8, p=0.84236
b-rank test for bits 2 to 9, p=0.94089
b-rank test for bits 3 to 10, p=0.47685
b-rank test for bits 4 to 11, p=0.21105
b-rank test for bits 5 to 12, p=0.14652
b-rank test for bits 6 to 13, p=0.50435
b-rank test for bits 7 to 14, p=0.10334
b-rank test for bits 8 to 15, p=0.20974
b-rank test for bits 9 to 16, p=0.55096
b-rank test for bits 10 to 17, p=0.50568
b-rank test for bits 11 to 18, p=0.10385
b-rank test for bits 12 to 19, p=0.34694
b-rank test for bits 13 to 20, p=0.95265
b-rank test for bits 14 to 21, p=0.85294
b-rank test for bits 15 to 22, p=0.42157
b-rank test for bits 16 to 23, p=0.13813
b-rank test for bits 17 to 24, p=0.94316
b-rank test for bits 18 to 25, p=0.12822
b-rank test for bits 19 to 26, p=0.55353
b-rank test for bits 20 to 27, p=0.66262
b-rank test for bits 21 to 28, p=0.63726
b-rank test for bits 22 to 29, p=0.82163
b-rank test for bits 23 to 30, p=0.97520
b-rank test for bits 24 to 31, p=0.22261
b-rank test for bits 25 to 32, p=0.63771
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 = 0.778444
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2019-08-29_07:31
(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 142335 0.99 0.840024
2 142349 1.03 0.847852
3 142334 0.99 0.839455
4 141706 -0.48 0.317369
5 141425 -1.13 0.128899
6 141971 0.14 0.557285
7 141926 0.04 0.515534
8 142686 1.81 0.965211
9 141737 -0.40 0.343607
10 141741 -0.39 0.347051
11 141960 0.12 0.547120
12 142388 1.12 0.868299
13 141930 0.05 0.519259
14 140940 -2.26 0.011763
15 142407 1.16 0.877541
16 141653 -0.60 0.274619
17 141815 -0.22 0.412781
18 141701 -0.49 0.313217
19 141485 -0.99 0.160739
20 141206 -1.64 0.050161
----------------------------------------------------------------
OPSO test for dh-ranFile-2019-08-29_07:31
Bits used No. missing words z-score p-value
23 to 32 142134 0.7747 0.780749
22 to 31 141941 0.1092 0.543481
21 to 30 141750 -0.5494 0.291361
20 to 29 142023 0.3920 0.652458
19 to 28 141338 -1.9701 0.024413
18 to 27 141344 -1.9494 0.025623
17 to 26 141844 -0.2253 0.410882
16 to 25 142556 2.2299 0.987123
15 to 24 142017 0.3713 0.644784
14 to 23 142122 0.7333 0.768326
13 to 22 142158 0.8575 0.804411
12 to 21 141467 -1.5253 0.063595
11 to 20 142040 0.4506 0.673856
10 to 19 141600 -1.0667 0.143064
9 to 18 141642 -0.9218 0.178309
8 to 17 142029 0.4127 0.660070
7 to 16 141361 -1.8908 0.029326
6 to 15 141940 0.1058 0.542113
5 to 14 142622 2.4575 0.993004
4 to 13 141791 -0.4080 0.341624
3 to 12 142147 0.8196 0.793764
2 to 11 141792 -0.4046 0.342891
1 to 10 142501 2.0402 0.979337
-----------------------------------------------------------------
OQSO test for dh-ranFile-2019-08-29_07:31
Bits used No. missing words z-score p-value
28 to 32 141377 -1.8045 0.035576
27 to 31 141585 -1.0994 0.135792
26 to 30 141657 -0.8554 0.196177
25 to 29 141859 -0.1706 0.432265
24 to 28 142179 0.9141 0.819677
23 to 27 142007 0.3311 0.629710
22 to 26 141037 -2.9571 0.001553
21 to 25 141861 -0.1638 0.434932
20 to 24 141558 -1.1909 0.116837
19 to 23 142453 1.8429 0.967332
18 to 22 141688 -0.7503 0.226546
17 to 21 142282 1.2633 0.896757
16 to 20 141632 -0.9401 0.173583
15 to 19 141840 -0.2350 0.407098
14 to 18 141220 -2.3367 0.009727
13 to 17 141682 -0.7706 0.220469
12 to 16 141906 -0.0113 0.495497
11 to 15 141612 -1.0079 0.156752
10 to 14 141809 -0.3401 0.366890
9 to 13 142175 0.9006 0.816093
8 to 12 141852 -0.1943 0.422955
7 to 11 142202 0.9921 0.839426
6 to 10 141921 0.0396 0.515778
5 to 9 141479 -1.4587 0.072318
4 to 8 142496 1.9887 0.976634
3 to 7 141656 -0.8587 0.195240
2 to 6 141930 0.0701 0.527930
1 to 5 142062 0.5175 0.697605
-----------------------------------------------------------------
DNA test for dh-ranFile-2019-08-29_07:31
Bits used No. missing words z-score p-value
31 to 32 141608 -0.8889 0.187034
30 to 31 141601 -0.9095 0.181536
29 to 30 142119 0.6185 0.731876
28 to 29 142106 0.5801 0.719092
27 to 28 141489 -1.2399 0.107504
26 to 27 142059 0.4415 0.670576
25 to 26 141633 -0.8151 0.207498
24 to 25 141349 -1.6529 0.049177
23 to 24 142010 0.2970 0.616752
22 to 23 141794 -0.3402 0.366851
21 to 22 141894 -0.0452 0.481966
20 to 21 142063 0.4533 0.674835
19 to 20 141772 -0.4051 0.342701
18 to 19 142034 0.3678 0.643473
17 to 18 141254 -1.9331 0.026610
16 to 17 141907 -0.0069 0.497258
15 to 16 141959 0.1465 0.558244
14 to 15 142702 2.3383 0.990313
13 to 14 141750 -0.4700 0.319178
12 to 13 141875 -0.1013 0.459669
11 to 12 141537 -1.0983 0.136033
10 to 11 141708 -0.5939 0.276292
9 to 10 142085 0.5182 0.697841
8 to 9 142162 0.7453 0.771967
7 to 8 142248 0.9990 0.841109
6 to 7 142146 0.6981 0.757456
5 to 6 142117 0.6126 0.729928
4 to 5 141437 -1.3933 0.081764
3 to 4 142028 0.3501 0.636853
2 to 3 142231 0.9489 0.828659
1 to 2 141787 -0.3609 0.359104
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2019-08-29_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2490.76 -0.131 0.448003
Test results for specific bytes for dh-ranFile-2019-08-29_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2527.80 0.393 0.652878
2 to 9 2479.22 -0.294 0.384402
3 to 10 2364.15 -1.921 0.027348
4 to 11 2640.39 1.985 0.976452
5 to 12 2508.14 0.115 0.545835
6 to 13 2553.59 0.758 0.775750
7 to 14 2574.71 1.057 0.854641
8 to 15 2422.69 -1.093 0.137129
9 to 16 2484.98 -0.212 0.415866
10 to 17 2443.37 -0.801 0.211618
11 to 18 2421.22 -1.114 0.132609
12 to 19 2467.50 -0.460 0.322907
13 to 20 2411.80 -1.247 0.106147
14 to 21 2602.86 1.455 0.927122
15 to 22 2539.76 0.562 0.713037
16 to 23 2489.69 -0.146 0.442043
17 to 24 2457.98 -0.594 0.276189
18 to 25 2495.82 -0.059 0.476440
19 to 26 2402.54 -1.378 0.084046
20 to 27 2471.38 -0.405 0.342814
21 to 28 2675.10 2.476 0.993363
22 to 29 2485.45 -0.206 0.418476
23 to 30 2392.48 -1.521 0.064182
24 to 31 2563.73 0.901 0.816285
25 to 32 2453.35 -0.660 0.254699
CDPARK for dh-ranFile-2019-08-29_07:31: 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
3515 -0.3653 0.357445
3561 1.7352 0.958644
3526 0.1370 0.554479
3530 0.3196 0.625377
3516 -0.3196 0.374623
3495 -1.2785 0.100530
3526 0.1370 0.554479
3484 -1.7808 0.037471
3536 0.5936 0.723613
3524 0.0457 0.518210
Square side=100, avg. no. parked=3521.30 sample std.=20.17
p-value of the KSTEST for those 10 p-values: 0.869214
Results for the MINIMUM DISTANCE test for dh-ranFile-2019-08-29_07:31
0.6625,0.5931,0.9823,0.8071,0.2284,0.0004,0.1981,0.3008,0.2293,0.8452,
The KS test for those 10 p-values: 0.532952
The 3DSPHERES test for dh-ranFile-2019-08-29_07:31
sample no r^3 equiv. uni.
1 50.484 0.814146
2 105.030 0.969833
3 27.299 0.597465
4 11.901 0.327453
5 39.024 0.727682
6 3.625 0.113814
7 25.082 0.566584
8 16.913 0.430930
9 67.409 0.894281
10 48.509 0.801500
11 1.198 0.039162
12 4.746 0.146329
13 4.215 0.131079
14 2.055 0.066196
15 24.637 0.560113
16 20.031 0.487106
17 22.085 0.521052
18 2.077 0.066892
19 28.583 0.614328
20 6.902 0.205527
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.704973
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2019-08-29_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 -0.4 0.9 -1.6 1.7
0.7 -0.4 -0.6 -0.2 -1.5 0.4
0.4 1.0 -0.7 1.2 0.1 -1.1
-0.6 0.3 1.5 -1.3 0.3 1.3
-0.8 0.7 0.0 -1.4 0.7 0.8
-0.1 -2.9 0.6 -1.5 -1.0 0.2
-0.7 -0.1 -1.2 -1.3 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:40.878380
z-score=-0.122379, p-value=0.479861
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2019-08-29_07:31
Test no p-value
1 0.169108
2 0.033161
3 0.048157
4 0.050832
5 0.822162
6 0.029925
7 0.523132
8 0.172147
9 0.026014
10 0.232807
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000357
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2019-08-29_07:31:
(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 66634 0.02 66952 1.22
3 25000.00 25068 0.18 24958 0.07
4 6666.67 6697 0.14 6510 3.68
5 1388.89 1327 2.76 1335 2.09
6 238.10 238 0.00 215 2.24
7 34.72 30 0.64 27 1.72
8 4.96 5 0.00 2 1.77
p=0.28803 p=0.95347
Number of rngs required: 688026, p-value: 0.332
RESULTS OF CRAPS TEST for dh-ranFile-2019-08-29_07:31
No. of wins: Observed Expected
98681 98585.9
z-score= 0.426, pvalue=0.66477
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66772 66666.7 0.166 0.166
2 37582 37654.3 0.139 0.305
3 27053 26954.7 0.358 0.664
4 19488 19313.5 1.577 2.241
5 13688 13851.4 1.928 4.169
6 9910 9943.5 0.113 4.282
7 7255 7145.0 1.693 5.975
8 5090 5139.1 0.469 6.443
9 3589 3699.9 3.322 9.765
10 2702 2666.3 0.478 10.243
11 1945 1923.3 0.244 10.488
12 1391 1388.7 0.004 10.491
13 973 1003.7 0.940 11.431
14 701 726.1 0.870 12.302
15 548 525.8 0.934 13.236
16 385 381.2 0.039 13.275
17 253 276.5 2.004 15.278
18 185 200.8 1.248 16.526
19 132 146.0 1.340 17.866
20 108 106.2 0.030 17.896
21 250 287.1 4.798 22.693
Chisq= 22.69 for 20 degrees of freedom, p= 0.69590
SUMMARY of craptest
p-value for no. of wins: 0.664774
p-value for throws/game: 0.695901
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2019-08-29_07:31
No. of wins: Observed Expected
98487 98585.9
z-score=-0.442, pvalue=0.32919
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66387 66666.7 1.173 1.173
2 37536 37654.3 0.372 1.545
3 26768 26954.7 1.294 2.839
4 19404 19313.5 0.424 3.263
5 13978 13851.4 1.157 4.420
6 9928 9943.5 0.024 4.444
7 7262 7145.0 1.915 6.359
8 5321 5139.1 6.440 12.800
9 3718 3699.9 0.089 12.888
10 2638 2666.3 0.300 13.189
11 1925 1923.3 0.001 13.190
12 1352 1388.7 0.972 14.162
13 1030 1003.7 0.688 14.851
14 741 726.1 0.304 15.155
15 557 525.8 1.847 17.002
16 399 381.2 0.836 17.837
17 275 276.5 0.009 17.846
18 203 200.8 0.023 17.869
19 150 146.0 0.110 17.980
20 114 106.2 0.571 18.551
21 314 287.1 2.518 21.068
Chisq= 21.07 for 20 degrees of freedom, p= 0.60687
SUMMARY of craptest
p-value for no. of wins: 0.329189
p-value for throws/game: 0.606870
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0004,0.0016,0.0097,0.0118,0.0244,0.0256,0.0260,0.0266,0.0273,
0.0293,0.0299,0.0332,0.0356,0.0375,0.0392,0.0482,0.0492,0.0502,0.0508,
0.0517,0.0627,0.0636,0.0642,0.0662,0.0669,0.0723,0.0818,0.0840,0.1005,
0.1033,0.1038,0.1061,0.1071,0.1075,0.1138,0.1168,0.1282,0.1289,0.1311,
0.1326,0.1358,0.1360,0.1371,0.1381,0.1402,0.1431,0.1433,0.1463,0.1465,
0.1521,0.1568,0.1607,0.1691,0.1707,0.1721,0.1736,0.1753,0.1783,0.1793,
0.1815,0.1870,0.1873,0.1952,0.1962,0.1981,0.2055,0.2075,0.2097,0.2111,
0.2116,0.2205,0.2226,0.2230,0.2235,0.2265,0.2284,0.2293,0.2328,0.2364,
0.2408,0.2547,0.2599,0.2600,0.2652,0.2746,0.2762,0.2763,0.2880,0.2914,
0.3008,0.3132,0.3174,0.3192,0.3229,0.3275,0.3292,0.3320,0.3416,0.3427,
0.3428,0.3429,0.3436,0.3469,0.3471,0.3574,0.3591,0.3669,0.3669,0.3697,
0.3723,0.3746,0.3844,0.3877,0.4071,0.4109,0.4128,0.4153,0.4159,0.4185,
0.4190,0.4216,0.4230,0.4291,0.4309,0.4323,0.4349,0.4420,0.4480,0.4583,
0.4597,0.4764,0.4768,0.4799,0.4820,0.4871,0.4955,0.4973,0.5043,0.5051,
0.5057,0.5071,0.5092,0.5102,0.5155,0.5158,0.5182,0.5193,0.5211,0.5231,
0.5255,0.5279,0.5330,0.5356,0.5421,0.5435,0.5458,0.5471,0.5510,0.5535,
0.5545,0.5545,0.5573,0.5582,0.5601,0.5636,0.5666,0.5931,0.5975,0.5981,
0.6069,0.6143,0.6168,0.6254,0.6266,0.6297,0.6369,0.6373,0.6377,0.6379,
0.6435,0.6448,0.6525,0.6529,0.6601,0.6625,0.6626,0.6648,0.6696,0.6706,
0.6739,0.6748,0.6812,0.6959,0.6976,0.6978,0.7050,0.7102,0.7130,0.7191,
0.7236,0.7277,0.7299,0.7319,0.7405,0.7428,0.7543,0.7575,0.7683,0.7720,
0.7757,0.7784,0.7807,0.7899,0.7938,0.8015,0.8038,0.8044,0.8071,0.8141,
0.8161,0.8163,0.8197,0.8216,0.8222,0.8271,0.8287,0.8394,0.8395,0.8400,
0.8409,0.8411,0.8424,0.8452,0.8479,0.8529,0.8546,0.8683,0.8692,0.8775,
0.8908,0.8918,0.8943,0.8945,0.8968,0.8977,0.9271,0.9394,0.9409,0.9432,
0.9527,0.9535,0.9586,0.9594,0.9598,0.9610,0.9652,0.9673,0.9698,0.9700,
0.9752,0.9765,0.9766,0.9793,0.9823,0.9871,0.9903,0.9930,0.9934,
Overall p-value after applying KStest on 269 p-values = 0.229247
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.