RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.07 13.5453 0.301017
2 to 25 15.86 25.2723 0.911222
3 to 26 15.46 17.9445 0.607649
4 to 27 16.00 13.3609 0.288290
5 to 28 15.78 20.2845 0.740064
6 to 29 15.76 19.0321 0.673306
7 to 30 15.57 19.1563 0.680367
8 to 31 15.69 9.5994 0.080436
9 to 32 15.74 21.5974 0.799298
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.702490
Tough bday spacings test for dh-ranFile-2018-07-08_21:31: 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 43 74 100 101 74 49 22 17 10 3
(O-E)^2/E 0.5 1.1 0.0 0.1 0.1 0.2 0.2 2.0 0.3 1.7 0.3
Birthday Spacings: Sum(O-E)^2/E= 6.534, p= 0.231
RESULTS OF GCD FOR dh-ranFile-2018-07-08_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.873025
p-value, dist. of gcd's: 0.373874
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.428 0.873 0.678 0.617 0.572 0.434 0.600 0.359
Bits 8 to 15---> 0.397 0.717 0.566 0.895 0.464 0.063 0.801 0.152
Bits 16 to 23---> 0.791 0.388 0.736 0.739 0.299 0.036 0.509 0.111
Bits 24 to 31---> 0.471 0.378 0.119 0.098 0.747 0.047 0.022 0.529
KS test for the above 32 p values: 0.609
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_21:31,
p-values for 5 runs: 0.5492, 0.1927, 0.4214, 0.1756, 0.6446
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5091 5134.0 0.360 0.874
r= 30 23160 23103.0 0.140 1.014
r= 31 11548 11551.5 0.001 1.015
chi-square = 1.015 with df = 3; p-value = 0.202
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 204 211.4 0.260 0.260
r= 30 5118 5134.0 0.050 0.310
r= 31 23068 23103.0 0.053 0.363
r= 32 11610 11551.5 0.296 0.659
chi-square = 0.659 with df = 3; p-value = 0.117
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_21:31
b-rank test for bits 1 to 8, p=0.04542
b-rank test for bits 2 to 9, p=0.49166
b-rank test for bits 3 to 10, p=0.25669
b-rank test for bits 4 to 11, p=0.43876
b-rank test for bits 5 to 12, p=0.01264
b-rank test for bits 6 to 13, p=0.11766
b-rank test for bits 7 to 14, p=0.06259
b-rank test for bits 8 to 15, p=0.32634
b-rank test for bits 9 to 16, p=0.32352
b-rank test for bits 10 to 17, p=0.66004
b-rank test for bits 11 to 18, p=0.91146
b-rank test for bits 12 to 19, p=0.44234
b-rank test for bits 13 to 20, p=0.13539
b-rank test for bits 14 to 21, p=0.55385
b-rank test for bits 15 to 22, p=0.18050
b-rank test for bits 16 to 23, p=0.62438
b-rank test for bits 17 to 24, p=0.73566
b-rank test for bits 18 to 25, p=0.09419
b-rank test for bits 19 to 26, p=0.13740
b-rank test for bits 20 to 27, p=0.76949
b-rank test for bits 21 to 28, p=0.13024
b-rank test for bits 22 to 29, p=0.17537
b-rank test for bits 23 to 30, p=0.88326
b-rank test for bits 24 to 31, p=0.40839
b-rank test for bits 25 to 32, p=0.84001
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 = 0.088483
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_21:31
(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 141808 -0.24 0.406425
2 142140 0.54 0.705039
3 142065 0.36 0.641965
4 141512 -0.93 0.176615
5 141816 -0.22 0.413691
6 141221 -1.61 0.053890
7 142474 1.32 0.906469
8 142143 0.55 0.707453
9 141672 -0.55 0.289615
10 142022 0.26 0.603820
11 142328 0.98 0.836013
12 141368 -1.26 0.102973
13 141548 -0.84 0.199271
14 141684 -0.53 0.299280
15 141046 -2.02 0.021841
16 141709 -0.47 0.319871
17 141523 -0.90 0.183358
18 141794 -0.27 0.393787
19 142286 0.88 0.810589
20 142295 0.90 0.816232
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_21:31
Bits used No. missing words z-score p-value
23 to 32 141688 -0.7632 0.222670
22 to 31 142192 0.9747 0.835151
21 to 30 142190 0.9678 0.833435
20 to 29 142061 0.5230 0.699513
19 to 28 141985 0.2609 0.602927
18 to 27 141828 -0.2804 0.389567
17 to 26 142096 0.6437 0.740112
16 to 25 141392 -1.7839 0.037220
15 to 24 141337 -1.9736 0.024216
14 to 23 141624 -0.9839 0.162583
13 to 22 141894 -0.0529 0.478921
12 to 21 141544 -1.2598 0.103878
11 to 20 142234 1.1196 0.868548
10 to 19 141914 0.0161 0.506424
9 to 18 141985 0.2609 0.602927
8 to 17 142449 1.8609 0.968623
7 to 16 141952 0.1471 0.558488
6 to 15 141513 -1.3667 0.085867
5 to 14 141195 -2.4632 0.006885
4 to 13 141837 -0.2494 0.401520
3 to 12 141761 -0.5115 0.304507
2 to 11 141676 -0.8046 0.210529
1 to 10 141581 -1.1322 0.128781
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_21:31
Bits used No. missing words z-score p-value
28 to 32 142267 1.2124 0.887328
27 to 31 141867 -0.1435 0.442951
26 to 30 141905 -0.0147 0.494145
25 to 29 141864 -0.1537 0.438939
24 to 28 141542 -1.2452 0.106532
23 to 27 142242 1.1277 0.870276
22 to 26 142253 1.1650 0.877987
21 to 25 141921 0.0396 0.515778
20 to 24 141630 -0.9469 0.171850
19 to 23 141783 -0.4282 0.334239
18 to 22 142193 0.9616 0.831873
17 to 21 141847 -0.2113 0.416331
16 to 20 141867 -0.1435 0.442951
15 to 19 141768 -0.4791 0.315939
14 to 18 141925 0.0531 0.521181
13 to 17 142017 0.3650 0.642438
12 to 16 141357 -1.8723 0.030582
11 to 15 141844 -0.2215 0.412368
10 to 14 141683 -0.7672 0.221475
9 to 13 142218 1.0463 0.852298
8 to 12 141610 -1.0147 0.155130
7 to 11 141915 0.0192 0.507667
6 to 10 142111 0.6836 0.752895
5 to 9 141731 -0.6045 0.272753
4 to 8 141553 -1.2079 0.113543
3 to 7 141989 0.2701 0.606446
2 to 6 141554 -1.2045 0.114197
1 to 5 142101 0.6497 0.742066
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_21:31
Bits used No. missing words z-score p-value
31 to 32 141100 -2.3874 0.008484
30 to 31 142445 1.5801 0.942963
29 to 30 142377 1.3796 0.916139
28 to 29 142036 0.3737 0.645671
27 to 28 142102 0.5683 0.715101
26 to 27 142242 0.9813 0.836784
25 to 26 142590 2.0079 0.977672
24 to 25 141344 -1.6676 0.047694
23 to 24 142604 2.0492 0.979777
22 to 23 141689 -0.6499 0.257865
21 to 22 141483 -1.2576 0.104266
20 to 21 142730 2.4209 0.992258
19 to 20 141453 -1.3461 0.089134
18 to 19 141896 -0.0393 0.484317
17 to 18 142007 0.2881 0.613370
16 to 17 141679 -0.6794 0.248430
15 to 16 141728 -0.5349 0.296361
14 to 15 142167 0.7601 0.776399
13 to 14 142388 1.4120 0.921026
12 to 13 141497 -1.2163 0.111933
11 to 12 141569 -1.0039 0.157708
10 to 11 142694 2.3147 0.989684
9 to 10 141993 0.2468 0.597474
8 to 9 141692 -0.6411 0.260732
7 to 8 141943 0.0993 0.539559
6 to 7 141700 -0.6175 0.268455
5 to 6 141957 0.1406 0.555915
4 to 5 141628 -0.8299 0.203303
3 to 4 142460 1.6244 0.947854
2 to 3 142071 0.4769 0.683284
1 to 2 142520 1.8014 0.964179
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2577.60 1.097 0.863777
Test results for specific bytes for dh-ranFile-2018-07-08_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2575.76 1.071 0.857992
2 to 9 2563.75 0.902 0.816367
3 to 10 2593.40 1.321 0.906720
4 to 11 2465.82 -0.483 0.314428
5 to 12 2456.25 -0.619 0.268041
6 to 13 2620.05 1.698 0.955219
7 to 14 2377.27 -1.736 0.041308
8 to 15 2406.80 -1.318 0.093751
9 to 16 2612.46 1.590 0.944137
10 to 17 2640.65 1.989 0.976651
11 to 18 2482.47 -0.248 0.402122
12 to 19 2558.84 0.832 0.797334
13 to 20 2430.60 -0.982 0.163165
14 to 21 2524.02 0.340 0.632980
15 to 22 2482.02 -0.254 0.399649
16 to 23 2464.06 -0.508 0.305641
17 to 24 2513.34 0.189 0.574793
18 to 25 2509.83 0.139 0.555280
19 to 26 2446.31 -0.759 0.223857
20 to 27 2665.59 2.342 0.990403
21 to 28 2532.70 0.462 0.678126
22 to 29 2492.67 -0.104 0.458735
23 to 30 2594.41 1.335 0.909081
24 to 31 2368.42 -1.861 0.031380
25 to 32 2514.15 0.200 0.579316
CDPARK for dh-ranFile-2018-07-08_21:31: 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
3492 -1.4155 0.078457
3494 -1.3242 0.092718
3546 1.0502 0.853193
3503 -0.9132 0.180558
3490 -1.5068 0.065925
3500 -1.0502 0.146807
3525 0.0913 0.536383
3530 0.3196 0.625377
3511 -0.5479 0.291865
3516 -0.3196 0.374623
Square side=100, avg. no. parked=3510.70 sample std.=17.56
p-value of the KSTEST for those 10 p-values: 0.078703
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_21:31
0.9084,0.7876,0.7915,0.8900,0.1872,0.1337,0.8600,0.0982,0.3145,0.0198,
The KS test for those 10 p-values: 0.372398
The 3DSPHERES test for dh-ranFile-2018-07-08_21:31
sample no r^3 equiv. uni.
1 58.879 0.859510
2 14.077 0.374518
3 31.326 0.648026
4 22.785 0.532104
5 48.713 0.802847
6 1.466 0.047693
7 67.428 0.894346
8 1.300 0.042402
9 24.677 0.560691
10 4.352 0.135040
11 96.327 0.959679
12 9.983 0.283060
13 13.439 0.361084
14 10.921 0.305136
15 10.062 0.284946
16 63.777 0.880675
17 18.462 0.459584
18 47.619 0.795520
19 53.017 0.829196
20 20.941 0.502444
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.912198
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 1.8 1.6 0.6 -1.6
0.8 1.3 0.3 -0.2 1.0 -0.7
1.0 -0.9 0.3 -0.7 0.4 0.6
0.2 0.1 1.0 -0.2 -0.5 -1.8
1.3 -1.9 -0.3 -0.1 -0.5 0.1
0.4 -1.9 -0.2 -0.8 1.5 0.2
0.3 -0.7 0.1 -0.7 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:35.844429
z-score=-0.671628, p-value=0.263099
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_21:31
Test no p-value
1 0.007109
2 0.183014
3 0.737826
4 0.247822
5 0.772565
6 0.010937
7 0.063335
8 0.056874
9 0.015263
10 0.439426
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001232
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_21:31:
(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 66663 0.00 66496 0.44
3 25000.00 25048 0.09 25169 1.14
4 6666.67 6630 0.20 6613 0.43
5 1388.89 1372 0.21 1440 1.88
6 238.10 248 0.41 251 0.70
7 34.72 34 0.01 27 1.72
8 4.96 4 0.19 3 0.77
p=0.01900 p=0.68674
Number of rngs required: 689048, p-value: 0.772
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_21:31
No. of wins: Observed Expected
98822 98585.9
z-score= 1.056, pvalue=0.85455
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66857 66666.7 0.543 0.543
2 37598 37654.3 0.084 0.628
3 26725 26954.7 1.958 2.586
4 19356 19313.5 0.094 2.679
5 13785 13851.4 0.318 2.998
6 9884 9943.5 0.357 3.354
7 7244 7145.0 1.371 4.725
8 5052 5139.1 1.475 6.201
9 3765 3699.9 1.147 7.347
10 2726 2666.3 1.337 8.684
11 1906 1923.3 0.156 8.840
12 1450 1388.7 2.702 11.543
13 977 1003.7 0.711 12.254
14 729 726.1 0.011 12.265
15 514 525.8 0.266 12.531
16 392 381.2 0.309 12.840
17 266 276.5 0.402 13.242
18 207 200.8 0.190 13.431
19 133 146.0 1.155 14.586
20 126 106.2 3.685 18.272
21 308 287.1 1.519 19.791
Chisq= 19.79 for 20 degrees of freedom, p= 0.52892
SUMMARY of craptest
p-value for no. of wins: 0.854553
p-value for throws/game: 0.528925
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_21:31
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 66563 66666.7 0.161 0.161
2 37681 37654.3 0.019 0.180
3 26974 26954.7 0.014 0.194
4 19108 19313.5 2.186 2.380
5 13769 13851.4 0.490 2.870
6 9924 9943.5 0.038 2.908
7 7171 7145.0 0.094 3.003
8 5235 5139.1 1.791 4.794
9 3813 3699.9 3.459 8.253
10 2638 2666.3 0.300 8.553
11 1964 1923.3 0.860 9.413
12 1403 1388.7 0.146 9.560
13 1048 1003.7 1.954 11.514
14 754 726.1 1.069 12.583
15 528 525.8 0.009 12.591
16 378 381.2 0.026 12.617
17 283 276.5 0.151 12.768
18 198 200.8 0.040 12.808
19 138 146.0 0.437 13.245
20 130 106.2 5.326 18.571
21 300 287.1 0.578 19.149
Chisq= 19.15 for 20 degrees of freedom, p= 0.48787
SUMMARY of craptest
p-value for no. of wins: 0.436291
p-value for throws/game: 0.487867
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0069,0.0071,0.0085,0.0109,0.0126,0.0153,0.0190,0.0198,0.0217,
0.0218,0.0242,0.0306,0.0314,0.0364,0.0372,0.0413,0.0424,0.0454,0.0465,
0.0477,0.0477,0.0539,0.0569,0.0626,0.0633,0.0633,0.0659,0.0785,0.0787,
0.0804,0.0859,0.0885,0.0891,0.0927,0.0938,0.0942,0.0977,0.0982,0.1030,
0.1039,0.1043,0.1065,0.1105,0.1119,0.1135,0.1142,0.1173,0.1177,0.1193,
0.1288,0.1302,0.1337,0.1350,0.1354,0.1374,0.1468,0.1519,0.1551,0.1577,
0.1626,0.1632,0.1718,0.1754,0.1756,0.1766,0.1805,0.1806,0.1830,0.1834,
0.1872,0.1927,0.1993,0.2024,0.2033,0.2105,0.2215,0.2227,0.2239,0.2315,
0.2478,0.2484,0.2567,0.2579,0.2607,0.2631,0.2680,0.2685,0.2728,0.2831,
0.2849,0.2883,0.2896,0.2919,0.2964,0.2988,0.2993,0.3010,0.3045,0.3051,
0.3056,0.3144,0.3145,0.3159,0.3199,0.3235,0.3263,0.3342,0.3594,0.3611,
0.3724,0.3739,0.3745,0.3746,0.3781,0.3876,0.3896,0.3938,0.3967,0.3996,
0.4015,0.4021,0.4064,0.4084,0.4124,0.4137,0.4163,0.4214,0.4276,0.4339,
0.4363,0.4388,0.4389,0.4394,0.4423,0.4430,0.4430,0.4587,0.4596,0.4643,
0.4708,0.4789,0.4843,0.4879,0.4917,0.4941,0.5024,0.5064,0.5077,0.5090,
0.5158,0.5212,0.5289,0.5294,0.5321,0.5364,0.5396,0.5492,0.5539,0.5553,
0.5559,0.5585,0.5607,0.5659,0.5719,0.5748,0.5793,0.5975,0.6001,0.6029,
0.6029,0.6038,0.6064,0.6076,0.6093,0.6134,0.6168,0.6244,0.6254,0.6330,
0.6420,0.6424,0.6446,0.6457,0.6480,0.6600,0.6733,0.6776,0.6781,0.6804,
0.6833,0.6867,0.6995,0.7025,0.7050,0.7075,0.7151,0.7169,0.7357,0.7359,
0.7378,0.7388,0.7401,0.7401,0.7421,0.7472,0.7529,0.7695,0.7719,0.7726,
0.7764,0.7876,0.7909,0.7915,0.7955,0.7973,0.7993,0.8007,0.8028,0.8106,
0.8162,0.8164,0.8292,0.8319,0.8334,0.8352,0.8360,0.8368,0.8400,0.8523,
0.8532,0.8546,0.8580,0.8595,0.8600,0.8638,0.8685,0.8703,0.8726,0.8730,
0.8780,0.8807,0.8833,0.8873,0.8900,0.8943,0.8953,0.9065,0.9067,0.9084,
0.9091,0.9112,0.9115,0.9122,0.9161,0.9210,0.9430,0.9441,0.9479,0.9552,
0.9597,0.9642,0.9686,0.9767,0.9777,0.9798,0.9897,0.9904,0.9923,
Overall p-value after applying KStest on 269 p-values = 0.034066
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.