RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_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 15.93 16.2487 0.493724
2 to 25 15.98 29.0026 0.965498
3 to 26 15.93 16.7293 0.527153
4 to 27 15.67 19.8327 0.717127
5 to 28 15.79 21.0988 0.778098
6 to 29 15.75 10.7389 0.130187
7 to 30 15.69 13.7578 0.315833
8 to 31 16.05 15.4084 0.433913
9 to 32 16.11 5.7700 0.005398
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.914351
Tough bday spacings test for dh-ranFile-2018-06-20_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 7 55 76 84 103 84 48 24 9 7 3
(O-E)^2/E 0.5 9.2 0.1 1.9 0.3 0.4 0.3 1.1 2.3 0.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 16.536, p= 0.915
RESULTS OF GCD FOR dh-ranFile-2018-06-20_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.354185
p-value, dist. of gcd's: 0.043627
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.748 0.767 0.739 0.661 0.769 0.914 0.524 0.584
Bits 8 to 15---> 0.085 0.220 0.178 0.551 0.630 0.957 0.451 0.987
Bits 16 to 23---> 0.910 0.319 0.613 0.050 0.897 0.960 0.390 0.208
Bits 24 to 31---> 0.815 0.321 0.047 0.819 0.957 0.391 0.916 0.981
KS test for the above 32 p values: 0.957
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_05:31,
p-values for 5 runs: 0.4920, 0.5175, 0.6363, 0.3386, 0.6995
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 192 211.4 1.783 1.783
r= 29 5172 5134.0 0.281 2.065
r= 30 22974 23103.0 0.721 2.785
r= 31 11662 11551.5 1.057 3.842
chi-square = 3.842 with df = 3; p-value = 0.721
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5239 5134.0 2.147 2.157
r= 31 23113 23103.0 0.004 2.161
r= 32 11438 11551.5 1.116 3.276
chi-square = 3.276 with df = 3; p-value = 0.649
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_05:31
b-rank test for bits 1 to 8, p=0.54161
b-rank test for bits 2 to 9, p=0.48464
b-rank test for bits 3 to 10, p=0.99366
b-rank test for bits 4 to 11, p=0.99240
b-rank test for bits 5 to 12, p=0.82683
b-rank test for bits 6 to 13, p=0.12990
b-rank test for bits 7 to 14, p=0.57462
b-rank test for bits 8 to 15, p=0.17766
b-rank test for bits 9 to 16, p=0.31331
b-rank test for bits 10 to 17, p=0.90778
b-rank test for bits 11 to 18, p=0.74575
b-rank test for bits 12 to 19, p=0.73777
b-rank test for bits 13 to 20, p=0.72517
b-rank test for bits 14 to 21, p=0.46872
b-rank test for bits 15 to 22, p=0.16433
b-rank test for bits 16 to 23, p=0.75596
b-rank test for bits 17 to 24, p=0.46312
b-rank test for bits 18 to 25, p=0.48093
b-rank test for bits 19 to 26, p=0.68440
b-rank test for bits 20 to 27, p=0.88374
b-rank test for bits 21 to 28, p=0.26020
b-rank test for bits 22 to 29, p=0.63786
b-rank test for bits 23 to 30, p=0.20841
b-rank test for bits 24 to 31, p=0.68462
b-rank test for bits 25 to 32, p=0.58772
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 = 0.224422
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_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 142474 1.32 0.906469
2 142103 0.45 0.674546
3 141554 -0.83 0.203210
4 141642 -0.62 0.266116
5 142060 0.35 0.637593
6 141768 -0.33 0.370621
7 142063 0.36 0.640218
8 141835 -0.17 0.431063
9 141883 -0.06 0.475473
10 142291 0.89 0.813737
11 142169 0.61 0.727977
12 142365 1.06 0.856483
13 142014 0.24 0.596600
14 141875 -0.08 0.468035
15 141685 -0.52 0.300092
16 141810 -0.23 0.408238
17 142283 0.87 0.808685
18 141338 -1.33 0.090957
19 141568 -0.80 0.212580
20 142418 1.19 0.882678
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_05:31
Bits used No. missing words z-score p-value
23 to 32 142186 0.9540 0.829967
22 to 31 142187 0.9575 0.830838
21 to 30 141723 -0.6425 0.260269
20 to 29 141745 -0.5667 0.285474
19 to 28 141660 -0.8598 0.194961
18 to 27 142148 0.8230 0.794746
17 to 26 141834 -0.2598 0.397525
16 to 25 142330 1.4506 0.926552
15 to 24 142383 1.6333 0.948802
14 to 23 142458 1.8920 0.970752
13 to 22 142264 1.2230 0.889335
12 to 21 141940 0.1058 0.542113
11 to 20 141917 0.0264 0.510550
10 to 19 142061 0.5230 0.699513
9 to 18 141864 -0.1563 0.437894
8 to 17 141581 -1.1322 0.128781
7 to 16 141485 -1.4632 0.071705
6 to 15 141521 -1.3391 0.090274
5 to 14 141839 -0.2425 0.404190
4 to 13 142049 0.4816 0.684962
3 to 12 142476 1.9540 0.974651
2 to 11 142078 0.5816 0.719589
1 to 10 141515 -1.3598 0.086953
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_05:31
Bits used No. missing words z-score p-value
28 to 32 141714 -0.6621 0.253942
27 to 31 142041 0.4463 0.672324
26 to 30 141892 -0.0587 0.476577
25 to 29 141517 -1.3299 0.091770
24 to 28 142206 1.0057 0.842711
23 to 27 142036 0.4294 0.666180
22 to 26 141695 -0.7265 0.233753
21 to 25 142311 1.3616 0.913337
20 to 24 141617 -0.9909 0.160855
19 to 23 141927 0.0599 0.523882
18 to 22 142379 1.5921 0.944319
17 to 21 141252 -2.2282 0.012932
16 to 20 141680 -0.7774 0.218464
15 to 19 141523 -1.3096 0.095167
14 to 18 141897 -0.0418 0.483330
13 to 17 142037 0.4328 0.667413
12 to 16 141646 -0.8926 0.186024
11 to 15 141810 -0.3367 0.368167
10 to 14 141773 -0.4621 0.321992
9 to 13 141423 -1.6486 0.049617
8 to 12 141874 -0.1198 0.452336
7 to 11 142253 1.1650 0.877987
6 to 10 142017 0.3650 0.642438
5 to 9 142154 0.8294 0.796558
4 to 8 141443 -1.5808 0.056964
3 to 7 141492 -1.4147 0.078581
2 to 6 141772 -0.4655 0.320778
1 to 5 141756 -0.5198 0.301615
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_05:31
Bits used No. missing words z-score p-value
31 to 32 141408 -1.4788 0.069590
30 to 31 141920 0.0315 0.512555
29 to 30 142029 0.3530 0.637959
28 to 29 141160 -2.2104 0.013538
27 to 28 142112 0.5978 0.725029
26 to 27 142403 1.4563 0.927339
25 to 26 141633 -0.8151 0.207498
24 to 25 141532 -1.1131 0.132840
23 to 24 141948 0.1141 0.545409
22 to 23 141911 0.0049 0.501965
21 to 22 141562 -1.0246 0.152783
20 to 21 142106 0.5801 0.719092
19 to 20 141612 -0.8771 0.190222
18 to 19 142068 0.4681 0.680127
17 to 18 141764 -0.4287 0.334070
16 to 17 142340 1.2704 0.898031
15 to 16 141953 0.1288 0.551250
14 to 15 141524 -1.1367 0.127839
13 to 14 141962 0.1554 0.561735
12 to 13 142347 1.2911 0.901659
11 to 12 142360 1.3294 0.908144
10 to 11 141853 -0.1662 0.434014
9 to 10 141595 -0.9272 0.176904
8 to 9 142338 1.2645 0.896977
7 to 8 141447 -1.3638 0.086314
6 to 7 141874 -0.1042 0.458498
5 to 6 142104 0.5742 0.717100
4 to 5 141665 -0.7207 0.235536
3 to 4 141440 -1.3845 0.083110
2 to 3 142250 1.0049 0.842534
1 to 2 141729 -0.5319 0.297381
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2567.99 0.962 0.831859
Test results for specific bytes for dh-ranFile-2018-06-20_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2430.41 -0.984 0.162532
2 to 9 2529.90 0.423 0.663780
3 to 10 2502.03 0.029 0.511467
4 to 11 2592.58 1.309 0.904775
5 to 12 2514.62 0.207 0.581886
6 to 13 2447.47 -0.743 0.228768
7 to 14 2407.61 -1.307 0.095679
8 to 15 2468.25 -0.449 0.326700
9 to 16 2582.65 1.169 0.878757
10 to 17 2587.95 1.244 0.893203
11 to 18 2521.35 0.302 0.618639
12 to 19 2590.01 1.273 0.898487
13 to 20 2386.07 -1.611 0.053574
14 to 21 2621.50 1.718 0.957121
15 to 22 2585.51 1.209 0.886722
16 to 23 2542.21 0.597 0.724711
17 to 24 2575.86 1.073 0.858338
18 to 25 2452.48 -0.672 0.250803
19 to 26 2452.65 -0.670 0.251549
20 to 27 2545.54 0.644 0.740224
21 to 28 2554.92 0.777 0.781341
22 to 29 2499.60 -0.006 0.497717
23 to 30 2546.17 0.653 0.743115
24 to 31 2505.68 0.080 0.532002
25 to 32 2461.14 -0.550 0.291292
CDPARK for dh-ranFile-2018-06-20_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
3545 1.0046 0.842447
3534 0.5023 0.692266
3553 1.3699 0.914635
3527 0.1826 0.572463
3494 -1.3242 0.092718
3479 -2.0091 0.022262
3554 1.4155 0.921543
3498 -1.1416 0.126820
3534 0.5023 0.692266
3520 -0.1370 0.445521
Square side=100, avg. no. parked=3523.80 sample std.=24.51
p-value of the KSTEST for those 10 p-values: 0.689937
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_05:31
0.0813,0.7479,0.6716,0.5930,0.5342,0.5228,0.1370,0.1912,0.4471,0.9832,
The KS test for those 10 p-values: 0.919299
The 3DSPHERES test for dh-ranFile-2018-06-20_05:31
sample no r^3 equiv. uni.
1 7.912 0.231826
2 10.062 0.284944
3 91.936 0.953324
4 26.843 0.591292
5 16.575 0.424483
6 142.453 0.991335
7 52.967 0.828911
8 4.986 0.153112
9 138.053 0.989966
10 13.990 0.372712
11 12.803 0.347376
12 59.853 0.863998
13 18.857 0.466650
14 150.762 0.993431
15 29.371 0.624326
16 34.019 0.678240
17 36.673 0.705486
18 23.729 0.546598
19 18.377 0.458050
20 17.063 0.433781
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.088086
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 -0.6 0.6 0.1 -1.2
0.6 -0.9 1.0 0.3 0.4 0.9
-0.3 -2.1 0.4 -0.4 1.0 0.3
0.1 -0.8 0.7 -1.0 0.5 -0.4
-0.0 1.3 -0.5 1.9 -2.0 0.3
0.7 0.9 -0.6 -1.0 -0.4 -0.1
-1.4 -1.3 0.1 -0.1 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:30.283013
z-score=-1.278428, p-value=0.089027
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_05:31
Test no p-value
1 0.819183
2 0.033794
3 0.138459
4 0.007261
5 0.168943
6 0.076403
7 0.012758
8 0.003622
9 0.128999
10 0.537149
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000053
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_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 66722 0.05 66516 0.34
3 25000.00 25199 1.58 25060 0.14
4 6666.67 6511 3.63 6740 0.81
5 1388.89 1323 3.13 1394 0.02
6 238.10 206 4.33 250 0.60
7 34.72 30 0.64 35 0.00
8 4.96 8 1.86 4 0.19
p=0.98140 p=0.08907
Number of rngs required: 688901, p-value: 0.717
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_05:31
No. of wins: Observed Expected
98550 98585.9
z-score=-0.160, pvalue=0.43629
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66405 66666.7 1.027 1.027
2 37641 37654.3 0.005 1.032
3 27124 26954.7 1.063 2.095
4 19274 19313.5 0.081 2.175
5 13820 13851.4 0.071 2.247
6 9883 9943.5 0.369 2.615
7 7280 7145.0 2.550 5.165
8 5211 5139.1 1.007 6.172
9 3615 3699.9 1.947 8.118
10 2704 2666.3 0.533 8.651
11 1945 1923.3 0.244 8.896
12 1454 1388.7 3.067 11.962
13 990 1003.7 0.187 12.150
14 741 726.1 0.304 12.454
15 507 525.8 0.675 13.128
16 378 381.2 0.026 13.155
17 278 276.5 0.008 13.162
18 191 200.8 0.481 13.643
19 153 146.0 0.337 13.981
20 100 106.2 0.364 14.344
21 306 287.1 1.242 15.586
Chisq= 15.59 for 20 degrees of freedom, p= 0.25808
SUMMARY of craptest
p-value for no. of wins: 0.436291
p-value for throws/game: 0.258077
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_05:31
No. of wins: Observed Expected
98857 98585.9
z-score= 1.213, pvalue=0.88738
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66943 66666.7 1.145 1.145
2 37830 37654.3 0.820 1.965
3 26794 26954.7 0.958 2.924
4 19323 19313.5 0.005 2.928
5 13797 13851.4 0.214 3.142
6 9873 9943.5 0.500 3.642
7 7052 7145.0 1.211 4.854
8 5133 5139.1 0.007 4.861
9 3643 3699.9 0.874 5.735
10 2679 2666.3 0.061 5.795
11 1921 1923.3 0.003 5.798
12 1349 1388.7 1.137 6.935
13 1004 1003.7 0.000 6.935
14 705 726.1 0.615 7.551
15 532 525.8 0.072 7.623
16 402 381.2 1.140 8.764
17 266 276.5 0.402 9.165
18 210 200.8 0.419 9.584
19 141 146.0 0.170 9.754
20 102 106.2 0.167 9.922
21 301 287.1 0.672 10.593
Chisq= 10.59 for 20 degrees of freedom, p= 0.04390
SUMMARY of craptest
p-value for no. of wins: 0.887378
p-value for throws/game: 0.043900
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0036,0.0054,0.0073,0.0128,0.0129,0.0135,0.0223,0.0338,0.0436,
0.0439,0.0466,0.0496,0.0502,0.0536,0.0570,0.0696,0.0717,0.0764,0.0786,
0.0813,0.0831,0.0848,0.0863,0.0870,0.0881,0.0890,0.0891,0.0903,0.0910,
0.0918,0.0927,0.0952,0.0957,0.1268,0.1278,0.1288,0.1290,0.1299,0.1302,
0.1328,0.1370,0.1385,0.1528,0.1531,0.1609,0.1625,0.1643,0.1689,0.1769,
0.1777,0.1785,0.1860,0.1902,0.1912,0.1950,0.2032,0.2075,0.2076,0.2084,
0.2126,0.2185,0.2196,0.2244,0.2288,0.2318,0.2338,0.2355,0.2508,0.2515,
0.2539,0.2581,0.2602,0.2603,0.2661,0.2849,0.2855,0.2913,0.2974,0.3001,
0.3016,0.3133,0.3158,0.3194,0.3206,0.3208,0.3220,0.3267,0.3341,0.3386,
0.3474,0.3542,0.3682,0.3706,0.3727,0.3903,0.3906,0.3975,0.4042,0.4082,
0.4245,0.4311,0.4338,0.4339,0.4340,0.4363,0.4379,0.4455,0.4471,0.4507,
0.4523,0.4581,0.4585,0.4631,0.4666,0.4680,0.4687,0.4755,0.4766,0.4809,
0.4833,0.4846,0.4920,0.4937,0.4977,0.5020,0.5106,0.5115,0.5126,0.5175,
0.5228,0.5239,0.5244,0.5272,0.5320,0.5342,0.5371,0.5416,0.5421,0.5454,
0.5466,0.5509,0.5513,0.5617,0.5725,0.5746,0.5819,0.5839,0.5877,0.5913,
0.5930,0.5966,0.6134,0.6186,0.6243,0.6300,0.6363,0.6376,0.6379,0.6380,
0.6402,0.6424,0.6491,0.6607,0.6638,0.6662,0.6674,0.6716,0.6723,0.6745,
0.6782,0.6801,0.6844,0.6846,0.6850,0.6899,0.6923,0.6923,0.6995,0.6995,
0.7055,0.7171,0.7171,0.7171,0.7191,0.7196,0.7210,0.7247,0.7250,0.7252,
0.7280,0.7378,0.7388,0.7402,0.7431,0.7458,0.7479,0.7485,0.7560,0.7673,
0.7690,0.7781,0.7813,0.7947,0.7966,0.8087,0.8137,0.8149,0.8187,0.8192,
0.8268,0.8289,0.8300,0.8308,0.8319,0.8424,0.8425,0.8427,0.8565,0.8583,
0.8640,0.8780,0.8788,0.8827,0.8837,0.8867,0.8874,0.8893,0.8932,0.8970,
0.8975,0.8980,0.8985,0.9017,0.9048,0.9065,0.9078,0.9081,0.9098,0.9133,
0.9138,0.9144,0.9146,0.9147,0.9157,0.9193,0.9215,0.9266,0.9273,0.9443,
0.9488,0.9533,0.9565,0.9569,0.9571,0.9574,0.9603,0.9655,0.9708,0.9747,
0.9807,0.9814,0.9832,0.9872,0.9900,0.9913,0.9924,0.9934,0.9937,
Overall p-value after applying KStest on 269 p-values = 0.213957
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.