RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.61 15.1169 0.412940
2 to 25 15.91 12.6641 0.241633
3 to 26 15.60 14.5955 0.375408
4 to 27 15.68 22.6745 0.839850
5 to 28 15.88 19.8818 0.719678
6 to 29 15.66 14.1138 0.340973
7 to 30 15.47 23.9257 0.878533
8 to 31 15.87 17.4089 0.572988
9 to 32 16.07 10.1323 0.102028
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.970273
Tough bday spacings test for dh-ranFile-2018-06-25_18:31: 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 37 77 97 112 69 55 30 12 4 2
(O-E)^2/E 1.9 0.0 0.2 0.0 2.1 1.1 0.2 0.0 0.6 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.062, p= 0.377
RESULTS OF GCD FOR dh-ranFile-2018-06-25_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.647033
p-value, dist. of gcd's: 0.895505
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.722 0.649 0.869 0.638 0.185 0.991 0.803 0.985
Bits 8 to 15---> 0.080 0.918 0.326 0.011 0.651 0.366 0.504 0.886
Bits 16 to 23---> 0.850 0.435 0.451 0.194 0.271 0.987 0.766 0.765
Bits 24 to 31---> 0.986 0.804 0.508 0.328 0.047 0.015 0.298 0.523
KS test for the above 32 p values: 0.768
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_18:31,
p-values for 5 runs: 0.3796, 0.3532, 0.4694, 0.8176, 0.6609
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 206 211.4 0.139 0.139
r= 29 5185 5134.0 0.506 0.645
r= 30 23078 23103.0 0.027 0.672
r= 31 11531 11551.5 0.036 0.709
chi-square = 0.709 with df = 3; p-value = 0.129
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 199 211.4 0.729 0.729
r= 30 5188 5134.0 0.568 1.297
r= 31 23110 23103.0 0.002 1.299
r= 32 11503 11551.5 0.204 1.503
chi-square = 1.503 with df = 3; p-value = 0.318
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_18:31
b-rank test for bits 1 to 8, p=0.60585
b-rank test for bits 2 to 9, p=0.63520
b-rank test for bits 3 to 10, p=0.13850
b-rank test for bits 4 to 11, p=0.43099
b-rank test for bits 5 to 12, p=0.39534
b-rank test for bits 6 to 13, p=0.38158
b-rank test for bits 7 to 14, p=0.81811
b-rank test for bits 8 to 15, p=0.92158
b-rank test for bits 9 to 16, p=0.75025
b-rank test for bits 10 to 17, p=0.16238
b-rank test for bits 11 to 18, p=0.01910
b-rank test for bits 12 to 19, p=0.93612
b-rank test for bits 13 to 20, p=0.94106
b-rank test for bits 14 to 21, p=0.77081
b-rank test for bits 15 to 22, p=0.50673
b-rank test for bits 16 to 23, p=0.09741
b-rank test for bits 17 to 24, p=0.81643
b-rank test for bits 18 to 25, p=0.40498
b-rank test for bits 19 to 26, p=0.57930
b-rank test for bits 20 to 27, p=0.82858
b-rank test for bits 21 to 28, p=0.40654
b-rank test for bits 22 to 29, p=0.73563
b-rank test for bits 23 to 30, p=0.88406
b-rank test for bits 24 to 31, p=0.49030
b-rank test for bits 25 to 32, p=0.26917
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 = 0.556297
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_18:31
(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 141881 -0.07 0.473613
2 142107 0.46 0.677904
3 141417 -1.15 0.125009
4 142048 0.32 0.627029
5 141318 -1.38 0.083545
6 141285 -1.46 0.072322
7 141996 0.20 0.580237
8 141960 0.12 0.547120
9 141504 -0.95 0.171811
10 141680 -0.54 0.296042
11 141804 -0.25 0.402803
12 142347 1.02 0.846750
13 141546 -0.85 0.197968
14 141945 0.08 0.533210
15 141574 -0.78 0.216672
16 141562 -0.81 0.208534
17 141972 0.15 0.558207
18 141995 0.20 0.579324
19 141960 0.12 0.547120
20 142352 1.03 0.849496
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_18:31
Bits used No. missing words z-score p-value
23 to 32 141767 -0.4908 0.311786
22 to 31 141537 -1.2839 0.099589
21 to 30 141729 -0.6218 0.267028
20 to 29 141844 -0.2253 0.410882
19 to 28 142304 1.3609 0.913232
18 to 27 142110 0.6920 0.755521
17 to 26 141833 -0.2632 0.396196
16 to 25 142105 0.6747 0.750075
15 to 24 141452 -1.5770 0.057398
14 to 23 141772 -0.4736 0.317910
13 to 22 141758 -0.5218 0.300895
12 to 21 141441 -1.6149 0.053163
11 to 20 141798 -0.3839 0.350528
10 to 19 142065 0.5368 0.704295
9 to 18 141808 -0.3494 0.363389
8 to 17 141776 -0.4598 0.322845
7 to 16 141690 -0.7563 0.224732
6 to 15 141603 -1.0563 0.145413
5 to 14 141273 -2.1942 0.014109
4 to 13 142269 1.2402 0.892557
3 to 12 141593 -1.0908 0.137682
2 to 11 142137 0.7851 0.783793
1 to 10 142219 1.0678 0.857201
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_18:31
Bits used No. missing words z-score p-value
28 to 32 142135 0.7650 0.777859
27 to 31 142085 0.5955 0.724243
26 to 30 141801 -0.3672 0.356727
25 to 29 141360 -1.8621 0.031292
24 to 28 142156 0.8362 0.798470
23 to 27 141846 -0.2147 0.415009
22 to 26 141652 -0.8723 0.191521
21 to 25 142205 1.0023 0.841894
20 to 24 141987 0.2633 0.603836
19 to 23 142535 2.1209 0.983036
18 to 22 142526 2.0904 0.981709
17 to 21 141918 0.0294 0.511723
16 to 20 141682 -0.7706 0.220469
15 to 19 142299 1.3209 0.906735
14 to 18 141615 -0.9977 0.159205
13 to 17 141725 -0.6248 0.266036
12 to 16 141089 -2.7808 0.002711
11 to 15 142021 0.3785 0.647486
10 to 14 142639 2.4735 0.993309
9 to 13 142042 0.4497 0.673547
8 to 12 142678 2.6057 0.995415
7 to 11 141927 0.0599 0.523882
6 to 10 141782 -0.4316 0.333006
5 to 9 141586 -1.0960 0.136532
4 to 8 142141 0.7853 0.783868
3 to 7 141927 0.0599 0.523882
2 to 6 142217 1.0429 0.851514
1 to 5 141548 -1.2248 0.110316
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_18:31
Bits used No. missing words z-score p-value
31 to 32 142150 0.7099 0.761130
30 to 31 142506 1.7601 0.960804
29 to 30 141512 -1.1721 0.120586
28 to 29 142030 0.3560 0.639064
27 to 28 141942 0.0964 0.538387
26 to 27 142424 1.5182 0.935518
25 to 26 142249 1.0020 0.841823
24 to 25 141808 -0.2989 0.382505
23 to 24 141923 0.0403 0.516083
22 to 23 141854 -0.1632 0.435174
21 to 22 142179 0.7955 0.786835
20 to 21 141999 0.2645 0.604308
19 to 20 141899 -0.0305 0.487845
18 to 19 142391 1.4209 0.922321
17 to 18 142152 0.7158 0.762955
16 to 17 141437 -1.3933 0.081764
15 to 16 141728 -0.5349 0.296361
14 to 15 141712 -0.5821 0.280252
13 to 14 142043 0.3943 0.653323
12 to 13 142029 0.3530 0.637959
11 to 12 142174 0.7807 0.782522
10 to 11 141543 -1.0806 0.139933
9 to 10 141427 -1.4228 0.077397
8 to 9 142078 0.4976 0.690600
7 to 8 142003 0.2763 0.608846
6 to 7 141872 -0.1101 0.456158
5 to 6 142483 1.6922 0.954700
4 to 5 141887 -0.0659 0.473741
3 to 4 141941 0.0934 0.537216
2 to 3 141619 -0.8564 0.195880
1 to 2 141953 0.1288 0.551250
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2562.81 0.888 0.812810
Test results for specific bytes for dh-ranFile-2018-06-25_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2555.80 0.789 0.784976
2 to 9 2445.07 -0.777 0.218651
3 to 10 2383.45 -1.648 0.049645
4 to 11 2544.39 0.628 0.734927
5 to 12 2557.08 0.807 0.790217
6 to 13 2620.14 1.699 0.955346
7 to 14 2431.40 -0.970 0.165996
8 to 15 2434.40 -0.928 0.176762
9 to 16 2568.17 0.964 0.832502
10 to 17 2392.10 -1.526 0.063506
11 to 18 2543.52 0.615 0.730855
12 to 19 2480.69 -0.273 0.392412
13 to 20 2473.51 -0.375 0.353981
14 to 21 2460.57 -0.558 0.288533
15 to 22 2536.77 0.520 0.698447
16 to 23 2488.56 -0.162 0.435714
17 to 24 2575.26 1.064 0.856401
18 to 25 2624.99 1.768 0.961443
19 to 26 2561.25 0.866 0.806827
20 to 27 2405.85 -1.331 0.091513
21 to 28 2503.53 0.050 0.519904
22 to 29 2611.21 1.573 0.942114
23 to 30 2389.34 -1.565 0.058796
24 to 31 2513.27 0.188 0.574428
25 to 32 2513.37 0.189 0.575004
CDPARK for dh-ranFile-2018-06-25_18:31: 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
3509 -0.6393 0.261324
3514 -0.4110 0.340551
3517 -0.2740 0.392053
3498 -1.1416 0.126820
3549 1.1872 0.882429
3538 0.6849 0.753306
3521 -0.0913 0.463617
3527 0.1826 0.572463
3560 1.6895 0.954438
3538 0.6849 0.753306
Square side=100, avg. no. parked=3527.10 sample std.=18.12
p-value of the KSTEST for those 10 p-values: 0.916049
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_18:31
0.2478,0.2929,0.1228,0.9558,0.3926,0.8724,0.7133,0.4860,0.7249,0.8750,
The KS test for those 10 p-values: 0.767453
The 3DSPHERES test for dh-ranFile-2018-06-25_18:31
sample no r^3 equiv. uni.
1 1.036 0.033933
2 56.608 0.848463
3 166.505 0.996113
4 22.743 0.531452
5 40.093 0.737222
6 43.635 0.766483
7 3.838 0.120093
8 2.108 0.067852
9 17.513 0.442203
10 4.892 0.150477
11 13.573 0.363927
12 15.535 0.404188
13 4.025 0.125567
14 21.892 0.517958
15 16.343 0.420029
16 73.453 0.913570
17 3.042 0.096421
18 2.521 0.080593
19 8.132 0.237438
20 13.552 0.363484
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.212993
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.6 -0.6 -1.1 -0.3 1.1
-1.6 -0.8 -0.7 1.3 1.6 1.0
-0.9 1.1 0.1 -0.8 0.4 -1.1
0.0 0.9 0.8 -0.2 -1.3 -0.2
-0.2 1.2 -2.0 -1.0 0.8 0.8
-0.4 -0.5 -1.4 0.3 1.9 -0.5
-0.7 0.8 -1.2 -0.7 0.1 -1.0
0.8
Chi-square with 42 degrees of freedom:42.712043
z-score=0.077690, p-value=0.559608
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_18:31
Test no p-value
1 0.009170
2 0.136354
3 0.901773
4 0.016387
5 0.062040
6 0.400585
7 0.231366
8 0.166396
9 0.349709
10 0.239629
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.005228
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_18:31:
(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 66610 0.05 66833 0.41
3 25000.00 25035 0.05 24799 1.62
4 6666.67 6661 0.00 6677 0.02
5 1388.89 1411 0.35 1402 0.12
6 238.10 243 0.10 248 0.41
7 34.72 34 0.01 34 0.01
8 4.96 5 0.00 6 0.22
p=0.00312 p=0.16842
Number of rngs required: 688130, p-value: 0.377
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_18:31
No. of wins: Observed Expected
98715 98585.9
z-score= 0.578, pvalue=0.71823
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66822 66666.7 0.362 0.362
2 37661 37654.3 0.001 0.363
3 27014 26954.7 0.130 0.493
4 19137 19313.5 1.612 2.106
5 13762 13851.4 0.577 2.683
6 9794 9943.5 2.249 4.932
7 7196 7145.0 0.364 5.296
8 5173 5139.1 0.224 5.520
9 3711 3699.9 0.034 5.553
10 2620 2666.3 0.804 6.357
11 1992 1923.3 2.452 8.809
12 1427 1388.7 1.054 9.863
13 1038 1003.7 1.171 11.034
14 708 726.1 0.453 11.487
15 538 525.8 0.281 11.769
16 387 381.2 0.090 11.858
17 269 276.5 0.206 12.064
18 215 200.8 1.000 13.064
19 149 146.0 0.062 13.126
20 113 106.2 0.433 13.559
21 274 287.1 0.599 14.158
Chisq= 14.16 for 20 degrees of freedom, p= 0.17763
SUMMARY of craptest
p-value for no. of wins: 0.718231
p-value for throws/game: 0.177628
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_18:31
No. of wins: Observed Expected
98834 98585.9
z-score= 1.110, pvalue=0.86646
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67088 66666.7 2.663 2.663
2 37563 37654.3 0.221 2.884
3 26643 26954.7 3.605 6.490
4 19410 19313.5 0.483 6.972
5 13723 13851.4 1.191 8.163
6 9898 9943.5 0.209 8.371
7 7127 7145.0 0.045 8.417
8 5141 5139.1 0.001 8.417
9 3702 3699.9 0.001 8.419
10 2710 2666.3 0.716 9.135
11 1904 1923.3 0.194 9.329
12 1394 1388.7 0.020 9.349
13 1013 1003.7 0.086 9.435
14 758 726.1 1.398 10.833
15 543 525.8 0.560 11.393
16 397 381.2 0.659 12.052
17 254 276.5 1.837 13.889
18 218 200.8 1.468 15.357
19 129 146.0 1.976 17.333
20 98 106.2 0.635 17.969
21 287 287.1 0.000 17.969
Chisq= 17.97 for 20 degrees of freedom, p= 0.41053
SUMMARY of craptest
p-value for no. of wins: 0.866465
p-value for throws/game: 0.410534
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0027,0.0031,0.0052,0.0092,0.0113,0.0141,0.0149,0.0164,0.0191,0.0313,
0.0339,0.0466,0.0496,0.0532,0.0574,0.0588,0.0620,0.0635,0.0679,0.0723,
0.0774,0.0803,0.0806,0.0818,0.0835,0.0915,0.0964,0.0974,0.0996,0.1020,
0.1103,0.1201,0.1206,0.1228,0.1250,0.1256,0.1268,0.1289,0.1364,0.1365,
0.1377,0.1385,0.1399,0.1454,0.1505,0.1592,0.1624,0.1660,0.1664,0.1684,
0.1718,0.1768,0.1776,0.1846,0.1915,0.1937,0.1959,0.1980,0.2085,0.2130,
0.2167,0.2187,0.2205,0.2247,0.2314,0.2374,0.2396,0.2416,0.2478,0.2613,
0.2660,0.2670,0.2692,0.2712,0.2803,0.2885,0.2929,0.2960,0.2964,0.2985,
0.3009,0.3118,0.3179,0.3184,0.3228,0.3264,0.3277,0.3330,0.3406,0.3410,
0.3497,0.3505,0.3532,0.3540,0.3567,0.3634,0.3635,0.3639,0.3657,0.3754,
0.3767,0.3773,0.3796,0.3816,0.3825,0.3921,0.3924,0.3926,0.3953,0.3962,
0.4006,0.4028,0.4042,0.4050,0.4065,0.4105,0.4109,0.4129,0.4150,0.4200,
0.4310,0.4350,0.4352,0.4357,0.4422,0.4510,0.4562,0.4636,0.4694,0.4736,
0.4737,0.4860,0.4878,0.4903,0.5044,0.5067,0.5082,0.5117,0.5161,0.5180,
0.5199,0.5233,0.5239,0.5239,0.5315,0.5332,0.5372,0.5384,0.5471,0.5471,
0.5513,0.5563,0.5582,0.5596,0.5725,0.5730,0.5744,0.5750,0.5793,0.5793,
0.5802,0.6038,0.6043,0.6058,0.6088,0.6270,0.6352,0.6380,0.6385,0.6391,
0.6470,0.6475,0.6490,0.6514,0.6533,0.6609,0.6735,0.6779,0.6906,0.6984,
0.7043,0.7133,0.7182,0.7197,0.7219,0.7242,0.7249,0.7309,0.7349,0.7356,
0.7372,0.7501,0.7503,0.7533,0.7533,0.7555,0.7611,0.7630,0.7646,0.7661,
0.7665,0.7675,0.7679,0.7708,0.7779,0.7825,0.7838,0.7839,0.7850,0.7868,
0.7902,0.7985,0.8030,0.8036,0.8068,0.8128,0.8164,0.8176,0.8181,0.8286,
0.8325,0.8399,0.8418,0.8419,0.8467,0.8485,0.8495,0.8499,0.8515,0.8564,
0.8572,0.8665,0.8689,0.8724,0.8750,0.8785,0.8824,0.8841,0.8858,0.8926,
0.8955,0.9018,0.9067,0.9132,0.9136,0.9160,0.9176,0.9216,0.9223,0.9355,
0.9361,0.9411,0.9421,0.9544,0.9547,0.9553,0.9558,0.9608,0.9614,0.9703,
0.9817,0.9830,0.9852,0.9864,0.9870,0.9906,0.9933,0.9954,0.9961,
Overall p-value after applying KStest on 269 p-values = 0.930012
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.