RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-01_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.63 20.6746 0.758814
2 to 25 15.64 21.6413 0.801089
3 to 26 15.59 17.0248 0.547315
4 to 27 15.74 17.9855 0.610244
5 to 28 15.69 25.7507 0.920875
6 to 29 15.67 22.1081 0.819403
7 to 30 15.80 14.1115 0.340807
8 to 31 15.71 15.3123 0.427000
9 to 32 15.73 12.6625 0.241527
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.423404
Tough bday spacings test for dh-ranFile-2018-07-01_05:31: 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 15 28 75 100 94 78 51 27 21 5 6
(O-E)^2/E 3.7 2.0 0.0 0.1 0.1 0.0 0.0 0.3 2.5 0.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 10.103, p= 0.569
RESULTS OF GCD FOR dh-ranFile-2018-07-01_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.696695
p-value, dist. of gcd's: 0.735849
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-01_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.824 0.084 0.128 0.809 0.536 0.176 0.910 0.522
Bits 8 to 15---> 0.262 0.919 0.656 0.012 0.316 0.923 0.747 0.158
Bits 16 to 23---> 0.986 0.135 0.598 0.654 0.343 0.260 0.842 0.936
Bits 24 to 31---> 0.106 0.961 0.804 0.713 0.981 0.376 0.634 0.653
KS test for the above 32 p values: 0.745
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-01_05:31,
p-values for 5 runs: 0.5425, 0.4315, 0.1346, 0.9650, 0.4438
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-01_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5175 5134.0 0.327 0.359
r= 30 23099 23103.0 0.001 0.359
r= 31 11512 11551.5 0.135 0.495
chi-square = 0.495 with df = 3; p-value = 0.080
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-01_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 228 211.4 1.301 1.301
r= 30 5173 5134.0 0.296 1.597
r= 31 23205 23103.0 0.450 2.047
r= 32 11394 11551.5 2.148 4.195
chi-square = 4.195 with df = 3; p-value = 0.759
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-01_05:31
b-rank test for bits 1 to 8, p=0.47658
b-rank test for bits 2 to 9, p=0.16047
b-rank test for bits 3 to 10, p=0.11073
b-rank test for bits 4 to 11, p=0.21649
b-rank test for bits 5 to 12, p=0.50764
b-rank test for bits 6 to 13, p=0.16193
b-rank test for bits 7 to 14, p=0.43638
b-rank test for bits 8 to 15, p=0.59273
b-rank test for bits 9 to 16, p=0.40466
b-rank test for bits 10 to 17, p=0.90577
b-rank test for bits 11 to 18, p=0.76453
b-rank test for bits 12 to 19, p=0.94757
b-rank test for bits 13 to 20, p=0.03694
b-rank test for bits 14 to 21, p=0.04527
b-rank test for bits 15 to 22, p=0.78263
b-rank test for bits 16 to 23, p=0.41393
b-rank test for bits 17 to 24, p=0.07855
b-rank test for bits 18 to 25, p=0.11384
b-rank test for bits 19 to 26, p=0.40918
b-rank test for bits 20 to 27, p=0.78900
b-rank test for bits 21 to 28, p=0.56101
b-rank test for bits 22 to 29, p=0.85946
b-rank test for bits 23 to 30, p=0.58754
b-rank test for bits 24 to 31, p=0.19218
b-rank test for bits 25 to 32, p=0.44173
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 = 0.489790
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-01_05:31
(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 141975 0.15 0.560972
2 141968 0.14 0.554516
3 141513 -0.93 0.177222
4 142276 0.86 0.804196
5 141165 -1.74 0.041010
6 142293 0.90 0.814987
7 141769 -0.33 0.371504
8 142442 1.24 0.893353
9 141010 -2.10 0.017810
10 141850 -0.14 0.444875
11 141698 -0.49 0.310737
12 142041 0.31 0.620822
13 141386 -1.22 0.110715
14 141388 -1.22 0.111600
15 142260 0.82 0.793699
16 141722 -0.44 0.330807
17 141780 -0.30 0.381260
18 141708 -0.47 0.319036
19 141165 -1.74 0.041010
20 141934 0.06 0.522982
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-01_05:31
Bits used No. missing words z-score p-value
23 to 32 142261 1.2127 0.887369
22 to 31 142103 0.6678 0.747878
21 to 30 141443 -1.6080 0.053914
20 to 29 142406 1.7127 0.956612
19 to 28 141961 0.1782 0.570706
18 to 27 141619 -1.0011 0.158380
17 to 26 141986 0.2644 0.604256
16 to 25 142127 0.7506 0.773549
15 to 24 141810 -0.3425 0.365981
14 to 23 141485 -1.4632 0.071705
13 to 22 141249 -2.2770 0.011393
12 to 21 141639 -0.9322 0.175624
11 to 20 141817 -0.3184 0.375099
10 to 19 141969 0.2058 0.581510
9 to 18 142041 0.4540 0.675098
8 to 17 141506 -1.3908 0.082144
7 to 16 142024 0.3954 0.653731
6 to 15 141658 -0.8667 0.193066
5 to 14 141619 -1.0011 0.158380
4 to 13 141811 -0.3391 0.367279
3 to 12 142181 0.9368 0.825568
2 to 11 141509 -1.3804 0.083724
1 to 10 142107 0.6816 0.752261
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-01_05:31
Bits used No. missing words z-score p-value
28 to 32 141581 -1.1130 0.132858
27 to 31 142040 0.4429 0.671099
26 to 30 142039 0.4396 0.669872
25 to 29 142268 1.2158 0.887975
24 to 28 141472 -1.4825 0.069107
23 to 27 141807 -0.3469 0.364340
22 to 26 141618 -0.9876 0.161684
21 to 25 141896 -0.0452 0.481979
20 to 24 141391 -1.7571 0.039455
19 to 23 142188 0.9446 0.827580
18 to 22 141581 -1.1130 0.132858
17 to 21 141269 -2.1706 0.014980
16 to 20 141720 -0.6418 0.260503
15 to 19 141831 -0.2655 0.395302
14 to 18 142125 0.7311 0.767636
13 to 17 141972 0.2124 0.584118
12 to 16 142230 1.0870 0.861485
11 to 15 141793 -0.3943 0.346665
10 to 14 142384 1.6091 0.946197
9 to 13 141909 -0.0011 0.499554
8 to 12 142358 1.5209 0.935859
7 to 11 142014 0.3548 0.638635
6 to 10 141342 -1.9232 0.027230
5 to 9 140949 -3.2554 0.000566
4 to 8 141897 -0.0418 0.483330
3 to 7 141883 -0.0893 0.464440
2 to 6 141889 -0.0689 0.472529
1 to 5 142371 1.5650 0.941207
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-01_05:31
Bits used No. missing words z-score p-value
31 to 32 141796 -0.3343 0.369074
30 to 31 141649 -0.7679 0.221263
29 to 30 141919 0.0285 0.511378
28 to 29 141380 -1.5614 0.059209
27 to 28 142057 0.4356 0.668438
26 to 27 141929 0.0580 0.523135
25 to 26 142013 0.3058 0.620126
24 to 25 142245 0.9902 0.838956
23 to 24 141173 -2.1721 0.014925
22 to 23 142132 0.6568 0.744359
21 to 22 141752 -0.4641 0.321288
20 to 21 141626 -0.8358 0.201639
19 to 20 142303 1.1613 0.877234
18 to 19 142087 0.5241 0.699896
17 to 18 141614 -0.8712 0.191828
16 to 17 141028 -2.5998 0.004664
15 to 16 141700 -0.6175 0.268455
14 to 15 142060 0.4445 0.671643
13 to 14 142263 1.0433 0.851589
12 to 13 141408 -1.4788 0.069590
11 to 12 142132 0.6568 0.744359
10 to 11 142387 1.4091 0.920591
9 to 10 141864 -0.1337 0.446813
8 to 9 141879 -0.0895 0.464355
7 to 8 141591 -0.9390 0.173859
6 to 7 142606 2.0551 0.980064
5 to 6 141919 0.0285 0.511378
4 to 5 142009 0.2940 0.615626
3 to 4 141635 -0.8092 0.209191
2 to 3 142041 0.3884 0.651143
1 to 2 142017 0.3176 0.624610
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-01_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2566.81 0.945 0.827644
Test results for specific bytes for dh-ranFile-2018-07-01_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2563.23 0.894 0.814388
2 to 9 2584.65 1.197 0.884363
3 to 10 2555.43 0.784 0.783430
4 to 11 2613.19 1.601 0.945276
5 to 12 2544.30 0.626 0.734494
6 to 13 2405.94 -1.330 0.091728
7 to 14 2545.96 0.650 0.742141
8 to 15 2423.79 -1.078 0.140570
9 to 16 2486.53 -0.191 0.424452
10 to 17 2404.80 -1.346 0.089094
11 to 18 2520.36 0.288 0.613283
12 to 19 2551.55 0.729 0.767025
13 to 20 2510.45 0.148 0.558741
14 to 21 2503.67 0.052 0.520722
15 to 22 2506.01 0.085 0.533870
16 to 23 2530.59 0.433 0.667358
17 to 24 2546.78 0.662 0.745891
18 to 25 2418.33 -1.155 0.124051
19 to 26 2477.45 -0.319 0.374903
20 to 27 2595.67 1.353 0.911964
21 to 28 2516.35 0.231 0.591443
22 to 29 2484.33 -0.222 0.412329
23 to 30 2477.37 -0.320 0.374462
24 to 31 2483.35 -0.236 0.406909
25 to 32 2486.17 -0.196 0.422457
CDPARK for dh-ranFile-2018-07-01_05:31: 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
3540 0.7763 0.781201
3527 0.1826 0.572463
3548 1.1416 0.873180
3520 -0.1370 0.445521
3543 0.9132 0.819442
3503 -0.9132 0.180558
3539 0.7306 0.767486
3544 0.9589 0.831196
3529 0.2740 0.607947
3551 1.2785 0.899470
Square side=100, avg. no. parked=3534.40 sample std.=13.99
p-value of the KSTEST for those 10 p-values: 0.063153
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-01_05:31
0.0155,0.4717,0.2974,0.2383,0.8909,0.4516,0.5365,0.2998,0.2906,0.0280,
The KS test for those 10 p-values: 0.124791
The 3DSPHERES test for dh-ranFile-2018-07-01_05:31
sample no r^3 equiv. uni.
1 16.316 0.419510
2 45.147 0.777957
3 19.164 0.472074
4 33.882 0.676769
5 88.603 0.947840
6 44.933 0.776371
7 17.776 0.447067
8 5.839 0.176868
9 8.501 0.246745
10 55.441 0.842456
11 4.265 0.132529
12 152.754 0.993853
13 23.750 0.546908
14 8.835 0.255085
15 15.267 0.398847
16 17.406 0.440213
17 2.128 0.068483
18 18.550 0.461159
19 13.869 0.370163
20 11.691 0.322738
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.734679
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-01_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 0.1 -0.8 -0.5 -0.1
-0.0 1.8 1.3 -1.5 0.2 0.7
-0.6 0.7 -1.0 -0.7 -1.1 1.8
-1.0 0.7 -0.4 -1.2 0.9 -1.2
0.6 1.4 0.0 -0.5 1.7 1.1
2.0 -0.3 -1.7 1.4 -0.4 0.1
-0.9 -0.7 -0.4 -0.7 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:40.714295
z-score=-0.140282, p-value=0.472601
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-01_05:31
Test no p-value
1 0.007208
2 0.351796
3 0.227542
4 0.146944
5 0.713138
6 0.225507
7 0.002738
8 0.575488
9 0.714040
10 0.107220
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.026157
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-01_05:31:
(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 66853 0.52 66875 0.65
3 25000.00 24879 0.59 24880 0.58
4 6666.67 6633 0.17 6574 1.29
5 1388.89 1373 0.18 1415 0.49
6 238.10 229 0.35 223 0.96
7 34.72 25 2.72 28 1.30
8 4.96 7 0.84 4 0.19
p=0.50219 p=0.51242
Number of rngs required: 686718, p-value: 0.023
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-01_05:31
No. of wins: Observed Expected
98500 98585.9
z-score=-0.384, pvalue=0.35049
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66437 66666.7 0.791 0.791
2 37685 37654.3 0.025 0.816
3 26864 26954.7 0.305 1.122
4 19505 19313.5 1.900 3.021
5 13746 13851.4 0.802 3.823
6 10090 9943.5 2.157 5.981
7 7083 7145.0 0.538 6.519
8 5180 5139.1 0.326 6.845
9 3748 3699.9 0.626 7.471
10 2654 2666.3 0.057 7.528
11 1966 1923.3 0.947 8.475
12 1381 1388.7 0.043 8.518
13 1024 1003.7 0.410 8.928
14 702 726.1 0.803 9.730
15 535 525.8 0.160 9.890
16 390 381.2 0.205 10.095
17 275 276.5 0.009 10.104
18 173 200.8 3.857 13.961
19 149 146.0 0.062 14.023
20 129 106.2 4.888 18.911
21 284 287.1 0.034 18.944
Chisq= 18.94 for 20 degrees of freedom, p= 0.47455
SUMMARY of craptest
p-value for no. of wins: 0.350486
p-value for throws/game: 0.474552
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-01_05:31
No. of wins: Observed Expected
98480 98585.9
z-score=-0.473, pvalue=0.31794
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66947 66666.7 1.179 1.179
2 37421 37654.3 1.446 2.625
3 27055 26954.7 0.373 2.998
4 19403 19313.5 0.415 3.413
5 13855 13851.4 0.001 3.414
6 9931 9943.5 0.016 3.429
7 7078 7145.0 0.629 4.058
8 5134 5139.1 0.005 4.063
9 3710 3699.9 0.028 4.091
10 2614 2666.3 1.026 5.117
11 1935 1923.3 0.071 5.187
12 1289 1388.7 7.163 12.351
13 1028 1003.7 0.588 12.938
14 729 726.1 0.011 12.950
15 482 525.8 3.654 16.604
16 415 381.2 3.006 19.610
17 272 276.5 0.075 19.685
18 180 200.8 2.160 21.845
19 148 146.0 0.028 21.873
20 108 106.2 0.030 21.903
21 266 287.1 1.553 23.456
Chisq= 23.46 for 20 degrees of freedom, p= 0.73302
SUMMARY of craptest
p-value for no. of wins: 0.317942
p-value for throws/game: 0.733023
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0027,0.0047,0.0072,0.0114,0.0117,0.0149,0.0150,0.0155,0.0178,
0.0234,0.0262,0.0272,0.0280,0.0369,0.0395,0.0410,0.0410,0.0453,0.0539,
0.0592,0.0632,0.0685,0.0691,0.0696,0.0717,0.0786,0.0800,0.0821,0.0837,
0.0844,0.0891,0.0917,0.1058,0.1072,0.1107,0.1107,0.1116,0.1138,0.1241,
0.1248,0.1276,0.1325,0.1329,0.1329,0.1346,0.1347,0.1406,0.1469,0.1582,
0.1584,0.1584,0.1605,0.1617,0.1619,0.1739,0.1756,0.1757,0.1769,0.1772,
0.1806,0.1918,0.1922,0.1931,0.2016,0.2092,0.2165,0.2213,0.2255,0.2275,
0.2383,0.2415,0.2467,0.2551,0.2598,0.2605,0.2616,0.2685,0.2906,0.2974,
0.2998,0.3107,0.3164,0.3179,0.3190,0.3213,0.3227,0.3308,0.3408,0.3426,
0.3467,0.3505,0.3518,0.3643,0.3660,0.3673,0.3691,0.3702,0.3715,0.3745,
0.3749,0.3751,0.3763,0.3813,0.3953,0.3988,0.4047,0.4069,0.4092,0.4123,
0.4139,0.4195,0.4225,0.4234,0.4245,0.4270,0.4315,0.4364,0.4402,0.4417,
0.4438,0.4449,0.4455,0.4468,0.4471,0.4516,0.4612,0.4644,0.4644,0.4717,
0.4721,0.4725,0.4726,0.4746,0.4766,0.4820,0.4833,0.4898,0.4996,0.5022,
0.5076,0.5114,0.5114,0.5124,0.5207,0.5215,0.5230,0.5231,0.5339,0.5356,
0.5365,0.5425,0.5469,0.5473,0.5545,0.5587,0.5610,0.5610,0.5685,0.5707,
0.5725,0.5755,0.5815,0.5841,0.5875,0.5914,0.5927,0.5975,0.6043,0.6079,
0.6102,0.6133,0.6156,0.6201,0.6208,0.6246,0.6336,0.6386,0.6511,0.6528,
0.6537,0.6540,0.6565,0.6674,0.6684,0.6699,0.6711,0.6716,0.6751,0.6768,
0.6967,0.6999,0.7130,0.7131,0.7140,0.7330,0.7345,0.7347,0.7358,0.7421,
0.7444,0.7444,0.7446,0.7459,0.7467,0.7479,0.7523,0.7588,0.7588,0.7645,
0.7670,0.7675,0.7676,0.7735,0.7764,0.7780,0.7812,0.7826,0.7834,0.7890,
0.7937,0.8011,0.8041,0.8042,0.8086,0.8144,0.8150,0.8194,0.8194,0.8242,
0.8256,0.8276,0.8276,0.8312,0.8390,0.8423,0.8425,0.8516,0.8595,0.8615,
0.8732,0.8772,0.8844,0.8874,0.8880,0.8909,0.8934,0.8995,0.9058,0.9101,
0.9120,0.9189,0.9206,0.9209,0.9227,0.9356,0.9359,0.9412,0.9453,0.9462,
0.9476,0.9478,0.9566,0.9611,0.9650,0.9801,0.9808,0.9861,0.9939,
Overall p-value after applying KStest on 269 p-values = 0.339864
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.