RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 11.4305 0.166672
2 to 25 15.64 13.6837 0.310651
3 to 26 15.84 12.9504 0.260501
4 to 27 15.67 15.4102 0.434039
5 to 28 15.76 19.5985 0.704722
6 to 29 15.79 12.2475 0.215076
7 to 30 15.66 18.4880 0.641301
8 to 31 15.57 17.2938 0.565364
9 to 32 15.55 19.9439 0.722893
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.548678
Tough bday spacings test for dh-ranFile-2018-06-24_16:31: 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 16 40 77 97 92 76 45 30 17 8 2
(O-E)^2/E 5.1 0.3 0.2 0.0 0.3 0.1 1.0 0.0 0.3 0.3 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.616, p= 0.431
RESULTS OF GCD FOR dh-ranFile-2018-06-24_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.762832
p-value, dist. of gcd's: 0.754738
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.662 0.872 0.647 0.539 0.898 0.831 0.007 0.988
Bits 8 to 15---> 0.590 0.520 0.907 0.187 0.572 0.651 0.775 0.154
Bits 16 to 23---> 0.170 0.495 0.745 0.173 0.489 0.609 0.320 0.958
Bits 24 to 31---> 0.873 0.030 0.787 0.367 0.574 0.336 0.122 0.019
KS test for the above 32 p values: 0.223
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_16:31,
p-values for 5 runs: 0.3060, 0.5381, 0.6859, 0.3085, 0.5427
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5268 5134.0 3.497 3.499
r= 30 22845 23103.0 2.882 6.381
r= 31 11675 11551.5 1.320 7.701
chi-square = 7.701 with df = 3; p-value = 0.947
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 223 211.4 0.634 0.634
r= 30 5133 5134.0 0.000 0.635
r= 31 23056 23103.0 0.096 0.730
r= 32 11588 11551.5 0.115 0.846
chi-square = 0.846 with df = 3; p-value = 0.161
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_16:31
b-rank test for bits 1 to 8, p=0.64212
b-rank test for bits 2 to 9, p=0.91568
b-rank test for bits 3 to 10, p=0.43497
b-rank test for bits 4 to 11, p=0.68013
b-rank test for bits 5 to 12, p=0.88171
b-rank test for bits 6 to 13, p=0.06092
b-rank test for bits 7 to 14, p=0.34538
b-rank test for bits 8 to 15, p=0.21992
b-rank test for bits 9 to 16, p=0.44999
b-rank test for bits 10 to 17, p=0.57490
b-rank test for bits 11 to 18, p=0.91843
b-rank test for bits 12 to 19, p=0.95191
b-rank test for bits 13 to 20, p=0.82779
b-rank test for bits 14 to 21, p=0.90079
b-rank test for bits 15 to 22, p=0.31884
b-rank test for bits 16 to 23, p=0.46401
b-rank test for bits 17 to 24, p=0.33938
b-rank test for bits 18 to 25, p=0.43537
b-rank test for bits 19 to 26, p=0.93427
b-rank test for bits 20 to 27, p=0.69055
b-rank test for bits 21 to 28, p=0.87518
b-rank test for bits 22 to 29, p=0.45538
b-rank test for bits 23 to 30, p=0.90399
b-rank test for bits 24 to 31, p=0.04352
b-rank test for bits 25 to 32, p=0.31838
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 = 0.159059
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_16:31
(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 141794 -0.27 0.393787
2 141841 -0.16 0.436579
3 142346 1.02 0.846197
4 142227 0.74 0.771023
5 141284 -1.46 0.072001
6 142459 1.28 0.900477
7 141745 -0.38 0.350508
8 142352 1.03 0.849496
9 141740 -0.40 0.346189
10 141553 -0.83 0.202550
11 141831 -0.18 0.427394
12 142113 0.48 0.682915
13 141992 0.19 0.576581
14 142302 0.92 0.820547
15 141610 -0.70 0.242161
16 141153 -1.77 0.038604
17 142490 1.36 0.912563
18 142301 0.92 0.819935
19 141779 -0.30 0.380370
20 142226 0.74 0.770315
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_16:31
Bits used No. missing words z-score p-value
23 to 32 141677 -0.8011 0.211526
22 to 31 141640 -0.9287 0.176516
21 to 30 141824 -0.2942 0.384287
20 to 29 142210 1.0368 0.850084
19 to 28 141880 -0.1011 0.459721
18 to 27 142242 1.1471 0.874338
17 to 26 141769 -0.4839 0.314230
16 to 25 142193 0.9782 0.836006
15 to 24 141982 0.2506 0.598933
14 to 23 142093 0.6333 0.736746
13 to 22 142447 1.8540 0.968133
12 to 21 141547 -1.2494 0.105757
11 to 20 141763 -0.5046 0.306925
10 to 19 141543 -1.2632 0.103257
9 to 18 141351 -1.9253 0.027097
8 to 17 142067 0.5437 0.706673
7 to 16 142375 1.6058 0.945837
6 to 15 142004 0.3264 0.627957
5 to 14 141253 -2.2632 0.011811
4 to 13 141603 -1.0563 0.145413
3 to 12 142142 0.8023 0.788813
2 to 11 141816 -0.3218 0.373792
1 to 10 141968 0.2023 0.580163
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_16:31
Bits used No. missing words z-score p-value
28 to 32 141576 -1.1299 0.129252
27 to 31 141812 -0.3299 0.370726
26 to 30 141958 0.1650 0.565521
25 to 29 141731 -0.6045 0.272753
24 to 28 142076 0.5650 0.713957
23 to 27 141584 -1.1028 0.135054
22 to 26 141387 -1.7706 0.038313
21 to 25 141832 -0.2621 0.396609
20 to 24 141626 -0.9604 0.168417
19 to 23 142244 1.1345 0.871702
18 to 22 141859 -0.1706 0.432265
17 to 21 142258 1.1819 0.881384
16 to 20 141844 -0.2215 0.412368
15 to 19 142061 0.5141 0.696421
14 to 18 141591 -1.0791 0.140275
13 to 17 141947 0.1277 0.550805
12 to 16 141648 -0.8859 0.187845
11 to 15 141863 -0.1571 0.437602
10 to 14 141626 -0.9604 0.168417
9 to 13 141803 -0.3604 0.359259
8 to 12 142155 0.8328 0.797516
7 to 11 142925 3.4429 0.999712
6 to 10 142147 0.8057 0.789781
5 to 9 142092 0.6192 0.732114
4 to 8 142522 2.0768 0.981092
3 to 7 141749 -0.5435 0.293396
2 to 6 141665 -0.8282 0.203768
1 to 5 141748 -0.5469 0.292230
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_16:31
Bits used No. missing words z-score p-value
31 to 32 142358 1.3235 0.907167
30 to 31 141332 -1.7030 0.044280
29 to 30 142040 0.3855 0.650051
28 to 29 142539 1.8574 0.968375
27 to 28 141942 0.0964 0.538387
26 to 27 142271 1.0669 0.856985
25 to 26 142420 1.5064 0.934018
24 to 25 142219 0.9135 0.819505
23 to 24 141572 -0.9951 0.159850
22 to 23 141289 -1.8299 0.033634
21 to 22 141502 -1.2016 0.114766
20 to 21 142040 0.3855 0.650051
19 to 20 141956 0.1377 0.554749
18 to 19 141255 -1.9302 0.026792
17 to 18 141577 -0.9803 0.163463
16 to 17 142120 0.6214 0.732847
15 to 16 141467 -1.3048 0.095979
14 to 15 142662 2.2203 0.986800
13 to 14 141596 -0.9243 0.177671
12 to 13 142119 0.6185 0.731876
11 to 12 142159 0.7365 0.769284
10 to 11 141629 -0.8269 0.204138
9 to 10 141381 -1.5585 0.059558
8 to 9 142187 0.8191 0.793631
7 to 8 142450 1.5949 0.944632
6 to 7 141128 -2.3048 0.010589
5 to 6 141996 0.2557 0.600895
4 to 5 141800 -0.3225 0.373534
3 to 4 141263 -1.9066 0.028288
2 to 3 141828 -0.2399 0.405199
1 to 2 141655 -0.7502 0.226556
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2427.80 -1.021 0.153613
Test results for specific bytes for dh-ranFile-2018-06-24_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2559.45 0.841 0.799768
2 to 9 2521.98 0.311 0.622024
3 to 10 2426.96 -1.033 0.150808
4 to 11 2470.46 -0.418 0.338074
5 to 12 2466.95 -0.467 0.320115
6 to 13 2500.14 0.002 0.500816
7 to 14 2492.69 -0.103 0.458832
8 to 15 2673.94 2.460 0.993052
9 to 16 2404.61 -1.349 0.088655
10 to 17 2462.92 -0.524 0.300015
11 to 18 2502.61 0.037 0.514744
12 to 19 2513.28 0.188 0.574498
13 to 20 2556.22 0.795 0.786721
14 to 21 2585.11 1.204 0.885625
15 to 22 2518.65 0.264 0.603996
16 to 23 2330.42 -2.398 0.008238
17 to 24 2602.58 1.451 0.926574
18 to 25 2502.50 0.035 0.514122
19 to 26 2390.66 -1.546 0.061017
20 to 27 2506.08 0.086 0.534263
21 to 28 2572.90 1.031 0.848709
22 to 29 2409.01 -1.287 0.099086
23 to 30 2507.73 0.109 0.543539
24 to 31 2518.16 0.257 0.601368
25 to 32 2494.91 -0.072 0.471296
CDPARK for dh-ranFile-2018-06-24_16:31: 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
3500 -1.0502 0.146807
3530 0.3196 0.625377
3547 1.0959 0.863437
3484 -1.7808 0.037471
3541 0.8219 0.794438
3522 -0.0457 0.481790
3509 -0.6393 0.261324
3544 0.9589 0.831196
3544 0.9589 0.831196
3525 0.0913 0.536383
Square side=100, avg. no. parked=3524.60 sample std.=20.14
p-value of the KSTEST for those 10 p-values: 0.804968
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_16:31
0.1859,0.4638,0.7087,0.1987,0.6380,0.8234,0.2755,0.0235,0.6913,0.2380,
The KS test for those 10 p-values: 0.620986
The 3DSPHERES test for dh-ranFile-2018-06-24_16:31
sample no r^3 equiv. uni.
1 29.797 0.629628
2 28.386 0.611786
3 38.411 0.722064
4 21.862 0.517486
5 37.865 0.716958
6 55.178 0.841065
7 33.101 0.668248
8 57.302 0.851928
9 11.165 0.310763
10 108.951 0.973529
11 2.294 0.073607
12 20.640 0.497415
13 2.794 0.088929
14 21.472 0.511163
15 49.692 0.809175
16 2.820 0.089728
17 46.701 0.789172
18 13.593 0.364339
19 23.445 0.542281
20 27.926 0.605788
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.374348
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 1.3 0.6 0.9 0.3
0.4 0.1 1.2 0.1 -0.3 0.3
-0.4 -1.3 0.7 0.8 -1.0 -0.8
0.2 1.2 -0.5 -1.5 1.0 0.6
-0.6 -1.8 -1.2 -0.1 2.2 1.3
1.6 1.4 0.1 1.7 -0.1 0.2
0.5 -0.1 -0.4 -0.7 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:37.072739
z-score=-0.537608, p-value=0.313255
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_16:31
Test no p-value
1 0.000644
2 0.024932
3 0.943900
4 0.211258
5 0.279122
6 0.806013
7 0.076032
8 0.576873
9 0.753388
10 0.352467
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.192661
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_16:31:
(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 66585 0.10 66681 0.00
3 25000.00 25069 0.19 25106 0.45
4 6666.67 6738 0.76 6587 0.95
5 1388.89 1344 1.45 1334 2.17
6 238.10 224 0.83 243 0.10
7 34.72 35 0.00 42 1.53
8 4.96 4 0.19 6 0.22
p=0.25963 p=0.50876
Number of rngs required: 687246, p-value: 0.089
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_16:31
No. of wins: Observed Expected
98557 98585.9
z-score=-0.129, pvalue=0.44865
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66519 66666.7 0.327 0.327
2 38004 37654.3 3.247 3.574
3 27008 26954.7 0.105 3.680
4 19370 19313.5 0.166 3.845
5 13632 13851.4 3.476 7.321
6 9980 9943.5 0.134 7.455
7 7028 7145.0 1.917 9.371
8 5161 5139.1 0.094 9.465
9 3706 3699.9 0.010 9.475
10 2641 2666.3 0.240 9.715
11 1943 1923.3 0.201 9.916
12 1415 1388.7 0.497 10.413
13 997 1003.7 0.045 10.458
14 699 726.1 1.014 11.472
15 532 525.8 0.072 11.544
16 375 381.2 0.099 11.644
17 290 276.5 0.655 12.299
18 178 200.8 2.595 14.894
19 127 146.0 2.469 17.363
20 105 106.2 0.014 17.377
21 290 287.1 0.029 17.406
Chisq= 17.41 for 20 degrees of freedom, p= 0.37352
SUMMARY of craptest
p-value for no. of wins: 0.448650
p-value for throws/game: 0.373517
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_16:31
No. of wins: Observed Expected
98359 98585.9
z-score=-1.015, pvalue=0.15514
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66707 66666.7 0.024 0.024
2 37769 37654.3 0.349 0.374
3 26951 26954.7 0.001 0.374
4 19339 19313.5 0.034 0.408
5 13659 13851.4 2.673 3.081
6 9816 9943.5 1.636 4.717
7 7252 7145.0 1.602 6.319
8 5082 5139.1 0.634 6.952
9 3776 3699.9 1.567 8.519
10 2673 2666.3 0.017 8.536
11 1924 1923.3 0.000 8.536
12 1364 1388.7 0.441 8.977
13 1009 1003.7 0.028 9.005
14 739 726.1 0.228 9.232
15 543 525.8 0.560 9.793
16 380 381.2 0.003 9.796
17 259 276.5 1.112 10.909
18 227 200.8 3.410 14.319
19 148 146.0 0.028 14.347
20 104 106.2 0.046 14.393
21 279 287.1 0.229 14.622
Chisq= 14.62 for 20 degrees of freedom, p= 0.20240
SUMMARY of craptest
p-value for no. of wins: 0.155138
p-value for throws/game: 0.202398
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0072,0.0082,0.0106,0.0118,0.0187,0.0235,0.0249,0.0268,0.0271,
0.0283,0.0301,0.0336,0.0375,0.0383,0.0386,0.0435,0.0443,0.0596,0.0609,
0.0610,0.0720,0.0736,0.0760,0.0887,0.0888,0.0889,0.0897,0.0960,0.0991,
0.1033,0.1058,0.1148,0.1215,0.1293,0.1351,0.1403,0.1454,0.1468,0.1508,
0.1536,0.1538,0.1551,0.1591,0.1599,0.1615,0.1635,0.1667,0.1684,0.1684,
0.1702,0.1729,0.1765,0.1777,0.1859,0.1872,0.1878,0.1927,0.1987,0.2024,
0.2026,0.2038,0.2041,0.2113,0.2115,0.2151,0.2199,0.2229,0.2266,0.2380,
0.2422,0.2596,0.2605,0.2613,0.2728,0.2755,0.2791,0.2922,0.2934,0.3000,
0.3060,0.3069,0.3085,0.3107,0.3108,0.3133,0.3142,0.3184,0.3188,0.3201,
0.3205,0.3358,0.3381,0.3394,0.3454,0.3462,0.3505,0.3525,0.3593,0.3643,
0.3672,0.3707,0.3735,0.3735,0.3738,0.3743,0.3804,0.3843,0.3938,0.3966,
0.4052,0.4124,0.4274,0.4311,0.4323,0.4340,0.4350,0.4354,0.4366,0.4376,
0.4487,0.4500,0.4554,0.4588,0.4597,0.4638,0.4640,0.4713,0.4818,0.4893,
0.4951,0.4974,0.5008,0.5088,0.5112,0.5141,0.5147,0.5175,0.5198,0.5343,
0.5364,0.5381,0.5384,0.5395,0.5423,0.5427,0.5435,0.5487,0.5508,0.5547,
0.5654,0.5655,0.5722,0.5743,0.5745,0.5749,0.5766,0.5769,0.5802,0.5900,
0.5989,0.6009,0.6014,0.6040,0.6058,0.6090,0.6118,0.6210,0.6220,0.6254,
0.6280,0.6296,0.6380,0.6413,0.6421,0.6468,0.6501,0.6501,0.6513,0.6617,
0.6682,0.6801,0.6829,0.6859,0.6905,0.6913,0.6964,0.7047,0.7067,0.7087,
0.7140,0.7170,0.7221,0.7229,0.7319,0.7321,0.7328,0.7367,0.7453,0.7534,
0.7547,0.7628,0.7693,0.7703,0.7710,0.7746,0.7866,0.7867,0.7888,0.7892,
0.7898,0.7936,0.7944,0.7975,0.7998,0.8050,0.8060,0.8092,0.8195,0.8199,
0.8205,0.8234,0.8278,0.8306,0.8312,0.8312,0.8360,0.8411,0.8462,0.8487,
0.8495,0.8501,0.8519,0.8570,0.8634,0.8717,0.8720,0.8734,0.8743,0.8752,
0.8814,0.8817,0.8856,0.8982,0.9005,0.9008,0.9040,0.9072,0.9074,0.9126,
0.9157,0.9184,0.9266,0.9340,0.9343,0.9439,0.9446,0.9458,0.9474,0.9519,
0.9582,0.9681,0.9684,0.9735,0.9811,0.9868,0.9882,0.9931,0.9997,
Overall p-value after applying KStest on 269 p-values = 0.964193
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.