RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_08:31
(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 11.9650 0.197747
2 to 25 15.95 17.8715 0.603009
3 to 26 16.01 16.7299 0.527191
4 to 27 15.87 27.7935 0.952590
5 to 28 15.74 17.2432 0.561987
6 to 29 15.84 22.0290 0.816394
7 to 30 15.84 18.1493 0.620519
8 to 31 15.75 12.2449 0.214917
9 to 32 15.70 28.3549 0.959042
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.390650
Tough bday spacings test for dh-ranFile-2018-06-29_08:31: 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 11 43 89 99 95 69 43 25 14 6 6
(O-E)^2/E 0.4 1.1 3.4 0.0 0.1 1.1 1.6 0.8 0.1 0.1 0.9
Birthday Spacings: Sum(O-E)^2/E= 9.403, p= 0.506
RESULTS OF GCD FOR dh-ranFile-2018-06-29_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.756887
p-value, dist. of gcd's: 0.303780
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.708 0.026 0.269 0.022 0.156 0.704 0.278 0.457
Bits 8 to 15---> 0.904 0.744 0.150 0.532 0.512 0.280 0.238 0.607
Bits 16 to 23---> 0.629 0.685 0.211 0.387 0.780 0.627 0.711 0.251
Bits 24 to 31---> 0.315 0.915 0.140 0.627 0.653 0.736 0.666 0.087
KS test for the above 32 p values: 0.530
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_08:31,
p-values for 5 runs: 0.4998, 0.1311, 0.9092, 0.1610, 0.6932
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 205 211.4 0.195 0.195
r= 29 5150 5134.0 0.050 0.245
r= 30 22976 23103.0 0.699 0.943
r= 31 11669 11551.5 1.195 2.138
chi-square = 2.138 with df = 3; p-value = 0.456
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 190 211.4 2.170 2.170
r= 30 5151 5134.0 0.056 2.226
r= 31 23175 23103.0 0.224 2.450
r= 32 11484 11551.5 0.395 2.845
chi-square = 2.845 with df = 3; p-value = 0.584
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_08:31
b-rank test for bits 1 to 8, p=0.59586
b-rank test for bits 2 to 9, p=0.84129
b-rank test for bits 3 to 10, p=0.28134
b-rank test for bits 4 to 11, p=0.62544
b-rank test for bits 5 to 12, p=0.02770
b-rank test for bits 6 to 13, p=0.36624
b-rank test for bits 7 to 14, p=0.31562
b-rank test for bits 8 to 15, p=0.22227
b-rank test for bits 9 to 16, p=0.12188
b-rank test for bits 10 to 17, p=0.73026
b-rank test for bits 11 to 18, p=0.11458
b-rank test for bits 12 to 19, p=0.58791
b-rank test for bits 13 to 20, p=0.50527
b-rank test for bits 14 to 21, p=0.37863
b-rank test for bits 15 to 22, p=0.66769
b-rank test for bits 16 to 23, p=0.34487
b-rank test for bits 17 to 24, p=0.34573
b-rank test for bits 18 to 25, p=0.30329
b-rank test for bits 19 to 26, p=0.17567
b-rank test for bits 20 to 27, p=0.84765
b-rank test for bits 21 to 28, p=0.42719
b-rank test for bits 22 to 29, p=0.41613
b-rank test for bits 23 to 30, p=0.00104
b-rank test for bits 24 to 31, p=0.80324
b-rank test for bits 25 to 32, p=0.73985
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 = 0.276851
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_08:31
(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 142031 0.28 0.611900
2 141161 -1.75 0.040194
3 141541 -0.86 0.194734
4 141802 -0.25 0.400996
5 141156 -1.76 0.039194
6 141804 -0.25 0.402803
7 141422 -1.14 0.127431
8 142130 0.52 0.696928
9 141841 -0.16 0.436579
10 142406 1.16 0.877066
11 141533 -0.88 0.189626
12 141238 -1.57 0.058379
13 142223 0.73 0.768182
14 142386 1.11 0.867299
15 142223 0.73 0.768182
16 142547 1.49 0.931873
17 141608 -0.70 0.240703
18 142639 1.70 0.955888
19 142172 0.61 0.730298
20 142289 0.89 0.812482
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_08:31
Bits used No. missing words z-score p-value
23 to 32 141613 -1.0218 0.153431
22 to 31 141892 -0.0598 0.476174
21 to 30 141367 -1.8701 0.030735
20 to 29 141754 -0.5356 0.296110
19 to 28 141811 -0.3391 0.367279
18 to 27 141783 -0.4356 0.331556
17 to 26 142109 0.6885 0.754436
16 to 25 141711 -0.6839 0.247020
15 to 24 142100 0.6575 0.744565
14 to 23 141945 0.1230 0.548947
13 to 22 141894 -0.0529 0.478921
12 to 21 141893 -0.0563 0.477547
11 to 20 141594 -1.0873 0.138442
10 to 19 142233 1.1161 0.867811
9 to 18 142132 0.7678 0.778705
8 to 17 141976 0.2299 0.590914
7 to 16 142373 1.5989 0.945074
6 to 15 141820 -0.3080 0.379028
5 to 14 142121 0.7299 0.767273
4 to 13 142349 1.5161 0.935253
3 to 12 141980 0.2437 0.596264
2 to 11 142393 1.6678 0.952325
1 to 10 141994 0.2920 0.614844
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_08:31
Bits used No. missing words z-score p-value
28 to 32 142053 0.4870 0.686877
27 to 31 141767 -0.4825 0.314734
26 to 30 141602 -1.0418 0.148753
25 to 29 142066 0.5311 0.702320
24 to 28 141434 -1.6113 0.053558
23 to 27 141730 -0.6079 0.271628
22 to 26 141969 0.2023 0.580148
21 to 25 142237 1.1107 0.866661
20 to 24 141816 -0.3164 0.375860
19 to 23 141864 -0.1537 0.438939
18 to 22 142161 0.8531 0.803203
17 to 21 141900 -0.0316 0.487385
16 to 20 142286 1.2768 0.899172
15 to 19 142041 0.4463 0.672324
14 to 18 142406 1.6836 0.953873
13 to 17 142166 0.8701 0.807868
12 to 16 141783 -0.4282 0.334239
11 to 15 142143 0.7921 0.785849
10 to 14 141769 -0.4757 0.317146
9 to 13 141472 -1.4825 0.069107
8 to 12 141888 -0.0723 0.471180
7 to 11 141541 -1.2486 0.105910
6 to 10 142125 0.7311 0.767636
5 to 9 141972 0.2124 0.584118
4 to 8 141415 -1.6757 0.046899
3 to 7 141652 -0.8723 0.191521
2 to 6 142534 2.1175 0.982892
1 to 5 142112 0.6870 0.753964
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_08:31
Bits used No. missing words z-score p-value
31 to 32 141833 -0.2252 0.410927
30 to 31 141479 -1.2694 0.102147
29 to 30 142019 0.3235 0.626846
28 to 29 141931 0.0639 0.525484
27 to 28 141423 -1.4346 0.075700
26 to 27 142295 1.1377 0.872371
25 to 26 141936 0.0787 0.531354
24 to 25 141830 -0.2340 0.407488
23 to 24 142087 0.5241 0.699896
22 to 23 141764 -0.4287 0.334070
21 to 22 142050 0.4150 0.660913
20 to 21 142573 1.9577 0.974869
19 to 20 141665 -0.7207 0.235536
18 to 19 141856 -0.1573 0.437498
17 to 18 141695 -0.6322 0.263614
16 to 17 141643 -0.7856 0.216041
15 to 16 141952 0.1259 0.550083
14 to 15 141800 -0.3225 0.373534
13 to 14 142013 0.3058 0.620126
12 to 13 141912 0.0079 0.503142
11 to 12 141986 0.2262 0.589464
10 to 11 141977 0.1996 0.579110
9 to 10 141769 -0.4140 0.339454
8 to 9 141989 0.2350 0.592901
7 to 8 142039 0.3825 0.648958
6 to 7 141542 -1.0836 0.139278
5 to 6 141575 -0.9862 0.162012
4 to 5 141670 -0.7060 0.240098
3 to 4 141744 -0.4877 0.312882
2 to 3 141940 0.0905 0.536044
1 to 2 142436 1.5536 0.939860
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2434.03 -0.933 0.175419
Test results for specific bytes for dh-ranFile-2018-06-29_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2599.33 1.405 0.919956
2 to 9 2551.59 0.730 0.767195
3 to 10 2488.81 -0.158 0.437121
4 to 11 2445.55 -0.770 0.220635
5 to 12 2495.99 -0.057 0.477363
6 to 13 2498.64 -0.019 0.492302
7 to 14 2446.24 -0.760 0.223522
8 to 15 2511.83 0.167 0.566431
9 to 16 2527.41 0.388 0.650861
10 to 17 2413.29 -1.226 0.110049
11 to 18 2522.74 0.322 0.626107
12 to 19 2517.42 0.246 0.597319
13 to 20 2509.67 0.137 0.554408
14 to 21 2530.29 0.428 0.665811
15 to 22 2488.54 -0.162 0.435628
16 to 23 2457.54 -0.600 0.274109
17 to 24 2623.98 1.753 0.960228
18 to 25 2398.26 -1.439 0.075094
19 to 26 2613.81 1.609 0.946244
20 to 27 2584.54 1.196 0.884071
21 to 28 2575.45 1.067 0.857004
22 to 29 2421.74 -1.107 0.134206
23 to 30 2472.75 -0.385 0.349980
24 to 31 2511.28 0.159 0.563351
25 to 32 2492.83 -0.101 0.459628
CDPARK for dh-ranFile-2018-06-29_08:31: 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
3501 -1.0046 0.157553
3571 2.1918 0.985802
3527 0.1826 0.572463
3539 0.7306 0.767486
3512 -0.5023 0.307734
3547 1.0959 0.863437
3519 -0.1826 0.427537
3543 0.9132 0.819442
3510 -0.5936 0.276387
3545 1.0046 0.842447
Square side=100, avg. no. parked=3531.40 sample std.=20.30
p-value of the KSTEST for those 10 p-values: 0.423089
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_08:31
0.1298,0.7702,0.2762,0.8461,0.3489,0.1047,0.2040,0.5531,0.5715,0.8837,
The KS test for those 10 p-values: 0.951264
The 3DSPHERES test for dh-ranFile-2018-06-29_08:31
sample no r^3 equiv. uni.
1 9.370 0.268251
2 17.026 0.433087
3 49.061 0.805120
4 112.095 0.976163
5 0.738 0.024297
6 1.616 0.052451
7 84.487 0.940170
8 1.191 0.038912
9 92.413 0.954061
10 58.180 0.856200
11 34.760 0.686094
12 83.363 0.937886
13 1.136 0.037160
14 11.607 0.320852
15 5.605 0.170405
16 51.053 0.817639
17 9.088 0.261345
18 24.277 0.554795
19 62.944 0.877315
20 22.604 0.529275
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.256876
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -2.0 1.3 0.6 -0.5 -1.6
-0.3 -1.2 0.4 0.4 0.4 0.4
-0.0 -0.2 -0.2 1.0 0.7 -1.7
-1.0 0.6 -0.8 0.6 0.6 0.5
-0.5 -0.7 1.8 0.3 -1.2 0.4
0.5 -0.1 -0.4 1.7 -0.4 -0.3
-0.5 -0.1 0.9 -1.3 -0.6 1.0
-1.1
Chi-square with 42 degrees of freedom:33.129183
z-score=-0.967885, p-value=0.165598
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_08:31
Test no p-value
1 0.001477
2 0.448108
3 0.392828
4 0.054287
5 0.368906
6 0.594062
7 0.120009
8 0.003773
9 0.583705
10 0.145869
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.006475
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_08:31:
(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 66468 0.59 66718 0.04
3 25000.00 25178 1.27 24941 0.14
4 6666.67 6688 0.07 6650 0.04
5 1388.89 1375 0.14 1423 0.84
6 238.10 249 0.50 237 0.01
7 34.72 35 0.00 26 2.19
8 4.96 6 0.22 4 0.19
p=0.16485 p=0.24794
Number of rngs required: 689019, p-value: 0.762
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_08:31
No. of wins: Observed Expected
98905 98585.9
z-score= 1.427, pvalue=0.92327
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66685 66666.7 0.005 0.005
2 38060 37654.3 4.371 4.376
3 26915 26954.7 0.059 4.434
4 19196 19313.5 0.714 5.149
5 13787 13851.4 0.300 5.448
6 9859 9943.5 0.719 6.167
7 7116 7145.0 0.118 6.285
8 5026 5139.1 2.488 8.773
9 3653 3699.9 0.594 9.367
10 2667 2666.3 0.000 9.367
11 1946 1923.3 0.267 9.634
12 1361 1388.7 0.554 10.188
13 997 1003.7 0.045 10.233
14 782 726.1 4.297 14.530
15 542 525.8 0.497 15.027
16 370 381.2 0.326 15.353
17 298 276.5 1.665 17.019
18 196 200.8 0.116 17.135
19 166 146.0 2.744 19.879
20 118 106.2 1.308 21.187
21 260 287.1 2.561 23.747
Chisq= 23.75 for 20 degrees of freedom, p= 0.74639
SUMMARY of craptest
p-value for no. of wins: 0.923266
p-value for throws/game: 0.746386
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_08:31
No. of wins: Observed Expected
98339 98585.9
z-score=-1.104, pvalue=0.13478
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66792 66666.7 0.236 0.236
2 37596 37654.3 0.090 0.326
3 26740 26954.7 1.711 2.037
4 19456 19313.5 1.052 3.089
5 14039 13851.4 2.540 5.629
6 9944 9943.5 0.000 5.629
7 7073 7145.0 0.726 6.355
8 5216 5139.1 1.152 7.506
9 3565 3699.9 4.916 12.422
10 2648 2666.3 0.126 12.548
11 1960 1923.3 0.699 13.247
12 1438 1388.7 1.747 14.994
13 1006 1003.7 0.005 15.000
14 687 726.1 2.110 17.109
15 495 525.8 1.808 18.918
16 352 381.2 2.229 21.147
17 259 276.5 1.112 22.260
18 205 200.8 0.087 22.346
19 152 146.0 0.248 22.594
20 85 106.2 4.237 26.832
21 292 287.1 0.083 26.915
Chisq= 26.91 for 20 degrees of freedom, p= 0.86232
SUMMARY of craptest
p-value for no. of wins: 0.134776
p-value for throws/game: 0.862320
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0015,0.0038,0.0065,0.0221,0.0243,0.0256,0.0277,0.0307,0.0372,
0.0389,0.0392,0.0402,0.0469,0.0525,0.0536,0.0543,0.0584,0.0691,0.0751,
0.0757,0.0868,0.1021,0.1047,0.1059,0.1100,0.1146,0.1200,0.1219,0.1274,
0.1298,0.1311,0.1342,0.1348,0.1384,0.1393,0.1398,0.1459,0.1488,0.1500,
0.1534,0.1562,0.1576,0.1610,0.1620,0.1649,0.1656,0.1704,0.1754,0.1757,
0.1896,0.1915,0.1947,0.1977,0.2040,0.2112,0.2149,0.2160,0.2206,0.2223,
0.2235,0.2355,0.2376,0.2401,0.2407,0.2470,0.2479,0.2513,0.2569,0.2613,
0.2636,0.2683,0.2687,0.2716,0.2741,0.2762,0.2764,0.2769,0.2777,0.2802,
0.2813,0.2961,0.3033,0.3038,0.3077,0.3129,0.3146,0.3147,0.3156,0.3171,
0.3209,0.3316,0.3341,0.3342,0.3395,0.3449,0.3457,0.3489,0.3500,0.3662,
0.3673,0.3689,0.3735,0.3759,0.3786,0.3790,0.3866,0.3906,0.3928,0.4010,
0.4028,0.4075,0.4109,0.4161,0.4231,0.4272,0.4275,0.4331,0.4356,0.4366,
0.4371,0.4375,0.4389,0.4481,0.4557,0.4574,0.4596,0.4712,0.4762,0.4774,
0.4775,0.4789,0.4874,0.4923,0.4998,0.5031,0.5053,0.5057,0.5117,0.5255,
0.5272,0.5293,0.5299,0.5314,0.5316,0.5360,0.5489,0.5501,0.5531,0.5544,
0.5548,0.5620,0.5634,0.5664,0.5715,0.5725,0.5791,0.5801,0.5837,0.5838,
0.5841,0.5879,0.5895,0.5909,0.5929,0.5941,0.5959,0.5963,0.5973,0.6030,
0.6065,0.6119,0.6148,0.6201,0.6205,0.6254,0.6261,0.6268,0.6269,0.6271,
0.6290,0.6490,0.6509,0.6532,0.6609,0.6658,0.6659,0.6677,0.6723,0.6851,
0.6861,0.6869,0.6932,0.6969,0.6999,0.7023,0.7041,0.7076,0.7109,0.7303,
0.7303,0.7364,0.7399,0.7441,0.7446,0.7464,0.7540,0.7544,0.7569,0.7615,
0.7672,0.7673,0.7675,0.7676,0.7682,0.7682,0.7702,0.7787,0.7805,0.7858,
0.8032,0.8032,0.8051,0.8079,0.8125,0.8164,0.8176,0.8194,0.8413,0.8424,
0.8461,0.8476,0.8562,0.8570,0.8623,0.8634,0.8667,0.8673,0.8678,0.8724,
0.8771,0.8773,0.8837,0.8841,0.8992,0.9042,0.9092,0.9153,0.9200,0.9233,
0.9319,0.9353,0.9379,0.9399,0.9402,0.9451,0.9462,0.9513,0.9523,0.9526,
0.9539,0.9541,0.9559,0.9590,0.9602,0.9749,0.9762,0.9829,0.9858,
Overall p-value after applying KStest on 269 p-values = 0.805058
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.