RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.84 14.5960 0.375442
2 to 25 15.59 10.8141 0.133936
3 to 26 15.77 22.3349 0.827819
4 to 27 15.79 12.1447 0.208701
5 to 28 15.72 12.1554 0.209364
6 to 29 15.71 14.2832 0.353034
7 to 30 15.60 13.7609 0.316051
8 to 31 15.53 25.9624 0.924851
9 to 32 15.64 16.4837 0.510156
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.541572
Tough bday spacings test for dh-ranFile-2018-06-22_09:31: 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 12 30 73 98 94 93 56 25 13 4 2
(O-E)^2/E 0.9 1.2 0.0 0.0 0.1 2.8 0.3 0.8 0.2 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.426, p= 0.413
RESULTS OF GCD FOR dh-ranFile-2018-06-22_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.520420
p-value, dist. of gcd's: 0.836619
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.729 0.002 0.443 0.723 0.549 0.599 0.958 0.074
Bits 8 to 15---> 0.977 0.388 0.502 0.026 0.814 0.928 0.894 0.153
Bits 16 to 23---> 0.747 0.533 0.851 0.356 0.013 0.824 0.336 0.316
Bits 24 to 31---> 0.985 0.866 0.355 0.557 0.827 0.186 0.736 0.744
KS test for the above 32 p values: 0.755
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_09:31,
p-values for 5 runs: 0.4095, 0.9669, 0.4393, 0.2404, 0.4237
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 234 211.4 2.412 2.412
r= 29 5189 5134.0 0.589 3.001
r= 30 23153 23103.0 0.108 3.109
r= 31 11424 11551.5 1.408 4.517
chi-square = 4.517 with df = 3; p-value = 0.789
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 249 211.4 6.681 6.681
r= 30 5087 5134.0 0.430 7.111
r= 31 23309 23103.0 1.836 8.947
r= 32 11355 11551.5 3.343 12.290
chi-square = 12.290 with df = 3; p-value = 0.994
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_09:31
b-rank test for bits 1 to 8, p=0.97608
b-rank test for bits 2 to 9, p=0.65253
b-rank test for bits 3 to 10, p=0.70670
b-rank test for bits 4 to 11, p=0.72486
b-rank test for bits 5 to 12, p=0.89848
b-rank test for bits 6 to 13, p=0.90198
b-rank test for bits 7 to 14, p=0.90423
b-rank test for bits 8 to 15, p=0.81111
b-rank test for bits 9 to 16, p=0.94070
b-rank test for bits 10 to 17, p=0.63964
b-rank test for bits 11 to 18, p=0.33089
b-rank test for bits 12 to 19, p=0.67646
b-rank test for bits 13 to 20, p=0.88861
b-rank test for bits 14 to 21, p=0.67489
b-rank test for bits 15 to 22, p=0.18933
b-rank test for bits 16 to 23, p=0.00542
b-rank test for bits 17 to 24, p=0.34123
b-rank test for bits 18 to 25, p=0.04844
b-rank test for bits 19 to 26, p=0.82137
b-rank test for bits 20 to 27, p=0.80868
b-rank test for bits 21 to 28, p=0.77979
b-rank test for bits 22 to 29, p=0.27611
b-rank test for bits 23 to 30, p=0.92004
b-rank test for bits 24 to 31, p=0.53807
b-rank test for bits 25 to 32, p=0.92996
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 = 0.005845
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_09:31
(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 142035 0.29 0.615476
2 141725 -0.43 0.333351
3 142154 0.57 0.716223
4 141646 -0.62 0.269193
5 141952 0.10 0.539707
6 141774 -0.32 0.375929
7 141648 -0.61 0.270738
8 141848 -0.14 0.443029
9 142855 2.21 0.986430
10 142125 0.50 0.692835
11 141564 -0.81 0.209878
12 141334 -1.34 0.089437
13 142174 0.62 0.731840
14 142393 1.13 0.870777
15 142451 1.27 0.897169
16 141727 -0.43 0.335052
17 142101 0.45 0.672861
18 142702 1.85 0.967989
19 142378 1.10 0.863247
20 141266 -1.50 0.066406
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-22_09:31
Bits used No. missing words z-score p-value
23 to 32 142254 1.1885 0.882685
22 to 31 141859 -0.1736 0.431109
21 to 30 141775 -0.4632 0.321608
20 to 29 142114 0.7058 0.759831
19 to 28 142184 0.9471 0.828216
18 to 27 142084 0.6023 0.726516
17 to 26 141380 -1.8253 0.033980
16 to 25 141735 -0.6011 0.273874
15 to 24 141624 -0.9839 0.162583
14 to 23 141926 0.0575 0.522920
13 to 22 141551 -1.2356 0.108300
12 to 21 141663 -0.8494 0.197826
11 to 20 141663 -0.8494 0.197826
10 to 19 142242 1.1471 0.874338
9 to 18 141484 -1.4667 0.071235
8 to 17 141743 -0.5736 0.283136
7 to 16 142015 0.3644 0.642213
6 to 15 142212 1.0437 0.851686
5 to 14 142418 1.7540 0.960288
4 to 13 141826 -0.2873 0.386924
3 to 12 142046 0.4713 0.681278
2 to 11 141782 -0.4391 0.330306
1 to 10 141706 -0.7011 0.241609
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-22_09:31
Bits used No. missing words z-score p-value
28 to 32 141606 -1.0282 0.151919
27 to 31 141590 -1.0825 0.139521
26 to 30 141884 -0.0859 0.465787
25 to 29 141742 -0.5672 0.285282
24 to 28 142135 0.7650 0.777859
23 to 27 141329 -1.9672 0.024579
22 to 26 142097 0.6362 0.737667
21 to 25 142127 0.7379 0.769702
20 to 24 141288 -2.1062 0.017593
19 to 23 142049 0.4735 0.682057
18 to 22 141886 -0.0791 0.468483
17 to 21 141781 -0.4350 0.331775
16 to 20 142028 0.4023 0.656258
15 to 19 141896 -0.0452 0.481979
14 to 18 142365 1.5446 0.938784
13 to 17 141654 -0.8655 0.193375
12 to 16 141981 0.2429 0.595978
11 to 15 141771 -0.4689 0.319565
10 to 14 141688 -0.7503 0.226546
9 to 13 142190 0.9514 0.829305
8 to 12 142243 1.1311 0.870990
7 to 11 141801 -0.3672 0.356727
6 to 10 141718 -0.6486 0.258306
5 to 9 142093 0.6226 0.733230
4 to 8 141800 -0.3706 0.355464
3 to 7 141678 -0.7842 0.216470
2 to 6 141650 -0.8791 0.189678
1 to 5 142247 1.1446 0.873822
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-22_09:31
Bits used No. missing words z-score p-value
31 to 32 141348 -1.6558 0.048877
30 to 31 141818 -0.2694 0.393807
29 to 30 141893 -0.0482 0.480790
28 to 29 141995 0.2527 0.599755
27 to 28 141579 -0.9744 0.164923
26 to 27 142630 2.1259 0.983243
25 to 26 141543 -1.0806 0.139933
24 to 25 142124 0.6332 0.736713
23 to 24 141984 0.2203 0.587168
22 to 23 141491 -1.2340 0.108599
21 to 22 141240 -1.9744 0.024167
20 to 21 142988 3.1819 0.999268
19 to 20 141648 -0.7709 0.220388
18 to 19 141947 0.1111 0.544240
17 to 18 141523 -1.1396 0.127223
16 to 17 141727 -0.5378 0.295342
15 to 16 141699 -0.6204 0.267483
14 to 15 142730 2.4209 0.992258
13 to 14 142381 1.3914 0.917941
12 to 13 142344 1.2822 0.900116
11 to 12 141296 -1.8092 0.035207
10 to 11 141632 -0.8181 0.206655
9 to 10 141875 -0.1013 0.459669
8 to 9 141892 -0.0511 0.479615
7 to 8 141412 -1.4671 0.071181
6 to 7 142785 2.5831 0.995104
5 to 6 142189 0.8250 0.795310
4 to 5 141971 0.1819 0.572176
3 to 4 141653 -0.7561 0.224784
2 to 3 141441 -1.3815 0.083562
1 to 2 142214 0.8987 0.815602
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2490.03 -0.141 0.443922
Test results for specific bytes for dh-ranFile-2018-06-22_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2506.69 0.095 0.537686
2 to 9 2603.27 1.461 0.927925
3 to 10 2596.57 1.366 0.913988
4 to 11 2455.05 -0.636 0.262498
5 to 12 2577.02 1.089 0.861979
6 to 13 2523.44 0.332 0.629867
7 to 14 2495.53 -0.063 0.474803
8 to 15 2390.50 -1.549 0.060750
9 to 16 2515.28 0.216 0.585531
10 to 17 2421.93 -1.104 0.134790
11 to 18 2378.91 -1.712 0.043407
12 to 19 2574.78 1.058 0.854877
13 to 20 2450.43 -0.701 0.241647
14 to 21 2388.98 -1.570 0.058196
15 to 22 2442.86 -0.808 0.209511
16 to 23 2565.71 0.929 0.823621
17 to 24 2486.27 -0.194 0.423035
18 to 25 2400.68 -1.405 0.080061
19 to 26 2590.63 1.282 0.900028
20 to 27 2609.56 1.549 0.939350
21 to 28 2441.56 -0.826 0.204282
22 to 29 2491.24 -0.124 0.450726
23 to 30 2624.49 1.761 0.960841
24 to 31 2468.00 -0.453 0.325448
25 to 32 2469.13 -0.437 0.331201
CDPARK for dh-ranFile-2018-06-22_09:31: 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
3521 -0.0913 0.463617
3525 0.0913 0.536383
3519 -0.1826 0.427537
3545 1.0046 0.842447
3550 1.2329 0.891189
3571 2.1918 0.985802
3527 0.1826 0.572463
3554 1.4155 0.921543
3526 0.1370 0.554479
3541 0.8219 0.794438
Square side=100, avg. no. parked=3537.90 sample std.=16.22
p-value of the KSTEST for those 10 p-values: 0.042388
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_09:31
0.7077,0.8385,0.4040,0.5378,0.7012,0.7488,0.8431,0.6711,0.8054,0.2225,
The KS test for those 10 p-values: 0.097572
The 3DSPHERES test for dh-ranFile-2018-06-22_09:31
sample no r^3 equiv. uni.
1 112.429 0.976427
2 36.090 0.699711
3 28.896 0.618334
4 7.132 0.211580
5 13.527 0.362948
6 1.570 0.050983
7 29.787 0.629504
8 110.974 0.975255
9 10.123 0.286398
10 39.866 0.735224
11 0.666 0.021953
12 32.277 0.659007
13 32.026 0.656145
14 10.280 0.290123
15 47.394 0.793985
16 30.384 0.636798
17 6.143 0.185170
18 58.230 0.856439
19 6.091 0.183739
20 8.621 0.249766
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.865990
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 -0.6 0.6 0.6 -0.8
0.5 -0.4 0.1 -1.6 1.2 -0.4
0.4 1.0 0.0 -1.0 -0.8 0.0
-1.1 -0.2 0.9 0.1 -0.0 0.9
1.0 -0.1 0.6 -0.9 0.0 0.5
0.4 0.8 -0.3 0.0 -0.4 0.8
-1.4 -2.0 0.1 0.4 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:24.683704
z-score=-1.889363, p-value=0.015305
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-22_09:31
Test no p-value
1 0.002575
2 0.102030
3 0.881916
4 0.860113
5 0.322946
6 0.490373
7 0.540873
8 0.376971
9 0.471123
10 0.025850
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.286956
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_09:31:
(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 66489 0.47 66885 0.72
3 25000.00 25128 0.66 24909 0.33
4 6666.67 6663 0.00 6584 1.03
5 1388.89 1437 1.67 1376 0.12
6 238.10 234 0.07 216 2.05
7 34.72 40 0.80 27 1.72
8 4.96 8 1.86 2 1.77
p=0.52264 p=0.74101
Number of rngs required: 687967, p-value: 0.308
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_09:31
No. of wins: Observed Expected
98467 98585.9
z-score=-0.532, pvalue=0.29750
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66322 66666.7 1.782 1.782
2 37750 37654.3 0.243 2.025
3 27173 26954.7 1.767 3.792
4 18990 19313.5 5.417 9.210
5 13993 13851.4 1.447 10.657
6 9978 9943.5 0.119 10.776
7 7081 7145.0 0.574 11.350
8 5177 5139.1 0.280 11.630
9 3858 3699.9 6.759 18.389
10 2613 2666.3 1.065 19.454
11 1962 1923.3 0.778 20.232
12 1378 1388.7 0.083 20.315
13 1013 1003.7 0.086 20.401
14 732 726.1 0.047 20.448
15 535 525.8 0.160 20.608
16 369 381.2 0.387 20.995
17 280 276.5 0.043 21.038
18 227 200.8 3.410 24.449
19 137 146.0 0.553 25.001
20 110 106.2 0.135 25.136
21 322 287.1 4.239 29.375
Chisq= 29.38 for 20 degrees of freedom, p= 0.91937
SUMMARY of craptest
p-value for no. of wins: 0.297500
p-value for throws/game: 0.919370
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_09:31
No. of wins: Observed Expected
98668 98585.9
z-score= 0.367, pvalue=0.64333
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66631 66666.7 0.019 0.019
2 37382 37654.3 1.969 1.989
3 26925 26954.7 0.033 2.021
4 19419 19313.5 0.577 2.598
5 13920 13851.4 0.340 2.938
6 9811 9943.5 1.767 4.704
7 7203 7145.0 0.470 5.175
8 5245 5139.1 2.183 7.358
9 3671 3699.9 0.225 7.583
10 2654 2666.3 0.057 7.640
11 2041 1923.3 7.199 14.839
12 1428 1388.7 1.110 15.949
13 990 1003.7 0.187 16.137
14 727 726.1 0.001 16.138
15 547 525.8 0.852 16.989
16 412 381.2 2.497 19.486
17 265 276.5 0.482 19.968
18 204 200.8 0.050 20.018
19 120 146.0 4.625 24.643
20 91 106.2 2.180 26.822
21 314 287.1 2.518 29.340
Chisq= 29.34 for 20 degrees of freedom, p= 0.91872
SUMMARY of craptest
p-value for no. of wins: 0.643334
p-value for throws/game: 0.918725
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0024,0.0026,0.0054,0.0058,0.0126,0.0153,0.0176,0.0220,0.0242,0.0246,
0.0258,0.0258,0.0340,0.0352,0.0424,0.0434,0.0484,0.0489,0.0510,0.0582,
0.0608,0.0664,0.0712,0.0712,0.0744,0.0801,0.0836,0.0894,0.0976,0.1020,
0.1083,0.1086,0.1272,0.1339,0.1348,0.1395,0.1399,0.1519,0.1527,0.1626,
0.1649,0.1837,0.1852,0.1865,0.1893,0.1897,0.1934,0.1978,0.1978,0.2043,
0.2067,0.2087,0.2094,0.2095,0.2099,0.2116,0.2165,0.2204,0.2225,0.2248,
0.2265,0.2404,0.2416,0.2416,0.2498,0.2583,0.2625,0.2675,0.2692,0.2707,
0.2739,0.2761,0.2831,0.2853,0.2864,0.2870,0.2901,0.2953,0.2975,0.3077,
0.3156,0.3161,0.3196,0.3216,0.3229,0.3254,0.3303,0.3309,0.3312,0.3318,
0.3334,0.3351,0.3356,0.3412,0.3530,0.3546,0.3555,0.3563,0.3567,0.3629,
0.3754,0.3759,0.3770,0.3869,0.3882,0.3938,0.4040,0.4095,0.4127,0.4230,
0.4237,0.4275,0.4311,0.4393,0.4430,0.4432,0.4439,0.4507,0.4597,0.4636,
0.4658,0.4685,0.4711,0.4748,0.4796,0.4808,0.4820,0.4904,0.5016,0.5102,
0.5204,0.5226,0.5229,0.5331,0.5364,0.5377,0.5378,0.5381,0.5397,0.5409,
0.5416,0.5442,0.5489,0.5545,0.5574,0.5722,0.5725,0.5855,0.5872,0.5960,
0.5988,0.5998,0.6155,0.6183,0.6295,0.6299,0.6368,0.6396,0.6422,0.6433,
0.6525,0.6561,0.6563,0.6590,0.6711,0.6729,0.6749,0.6765,0.6813,0.6821,
0.6928,0.6997,0.7012,0.7067,0.7077,0.7162,0.7228,0.7249,0.7265,0.7292,
0.7318,0.7332,0.7352,0.7356,0.7367,0.7377,0.7410,0.7436,0.7470,0.7488,
0.7553,0.7598,0.7697,0.7779,0.7798,0.7892,0.7940,0.7944,0.7953,0.8054,
0.8087,0.8111,0.8137,0.8156,0.8214,0.8236,0.8239,0.8267,0.8278,0.8282,
0.8293,0.8366,0.8385,0.8424,0.8431,0.8510,0.8517,0.8549,0.8564,0.8601,
0.8620,0.8632,0.8657,0.8660,0.8708,0.8710,0.8738,0.8743,0.8819,0.8827,
0.8886,0.8912,0.8943,0.8972,0.8985,0.9000,0.9001,0.9020,0.9042,0.9140,
0.9179,0.9187,0.9194,0.9200,0.9215,0.9249,0.9279,0.9284,0.9300,0.9388,
0.9394,0.9407,0.9585,0.9603,0.9608,0.9669,0.9680,0.9753,0.9761,0.9764,
0.9768,0.9832,0.9849,0.9858,0.9864,0.9923,0.9935,0.9951,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.142667
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.