RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_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 15.95 22.6886 0.840333
2 to 25 15.82 22.8468 0.845694
3 to 26 15.91 14.8250 0.391912
4 to 27 15.98 11.2029 0.154179
5 to 28 15.67 19.5265 0.700838
6 to 29 15.92 29.8359 0.972447
7 to 30 15.60 23.2520 0.858773
8 to 31 15.81 12.4654 0.228825
9 to 32 15.73 18.8683 0.663855
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.275603
Tough bday spacings test for dh-ranFile-2018-07-08_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 9 36 63 120 95 82 53 19 15 4 4
(O-E)^2/E 0.0 0.0 1.4 5.1 0.1 0.2 0.0 3.9 0.0 1.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 11.761, p= 0.699
RESULTS OF GCD FOR dh-ranFile-2018-07-08_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.628388
p-value, dist. of gcd's: 0.028123
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.564 0.650 0.386 0.687 0.342 0.104 0.909 0.703
Bits 8 to 15---> 0.022 0.618 0.502 0.924 0.657 0.144 0.372 0.191
Bits 16 to 23---> 0.734 0.226 0.534 0.589 0.812 0.279 0.764 0.381
Bits 24 to 31---> 0.657 0.574 0.196 0.316 0.481 0.025 0.953 0.278
KS test for the above 32 p values: 0.188
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_08:31,
p-values for 5 runs: 0.1113, 0.1121, 0.8189, 0.0298, 0.5008
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5128 5134.0 0.007 0.068
r= 30 23071 23103.0 0.044 0.112
r= 31 11586 11551.5 0.103 0.215
chi-square = 0.215 with df = 3; p-value = 0.025
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 226 211.4 1.006 1.006
r= 30 5143 5134.0 0.016 1.021
r= 31 23096 23103.0 0.002 1.024
r= 32 11535 11551.5 0.024 1.047
chi-square = 1.047 with df = 3; p-value = 0.210
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_08:31
b-rank test for bits 1 to 8, p=0.87123
b-rank test for bits 2 to 9, p=0.41009
b-rank test for bits 3 to 10, p=0.56721
b-rank test for bits 4 to 11, p=0.40665
b-rank test for bits 5 to 12, p=0.08309
b-rank test for bits 6 to 13, p=0.93637
b-rank test for bits 7 to 14, p=0.96693
b-rank test for bits 8 to 15, p=0.95306
b-rank test for bits 9 to 16, p=0.93044
b-rank test for bits 10 to 17, p=0.39102
b-rank test for bits 11 to 18, p=0.55427
b-rank test for bits 12 to 19, p=0.64150
b-rank test for bits 13 to 20, p=0.88369
b-rank test for bits 14 to 21, p=0.67180
b-rank test for bits 15 to 22, p=0.21140
b-rank test for bits 16 to 23, p=0.20390
b-rank test for bits 17 to 24, p=0.10715
b-rank test for bits 18 to 25, p=0.35911
b-rank test for bits 19 to 26, p=0.48031
b-rank test for bits 20 to 27, p=0.47271
b-rank test for bits 21 to 28, p=0.22060
b-rank test for bits 22 to 29, p=0.88767
b-rank test for bits 23 to 30, p=0.81282
b-rank test for bits 24 to 31, p=0.28398
b-rank test for bits 25 to 32, p=0.12249
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 = 0.622230
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_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 141633 -0.65 0.259259
2 142238 0.77 0.778733
3 141957 0.11 0.544342
4 141792 -0.27 0.391990
5 142339 1.00 0.842287
6 142834 2.16 0.984631
7 141124 -1.83 0.033262
8 141883 -0.06 0.475473
9 142492 1.36 0.913303
10 142606 1.63 0.948209
11 142014 0.24 0.596600
12 142189 0.65 0.743262
13 140948 -2.25 0.012349
14 141346 -1.32 0.094055
15 141865 -0.10 0.458753
16 141210 -1.63 0.051135
17 141825 -0.20 0.421901
18 140822 -2.54 0.005535
19 142165 0.60 0.724866
20 142182 0.64 0.737963
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_08:31
Bits used No. missing words z-score p-value
23 to 32 141946 0.1264 0.550312
22 to 31 141708 -0.6942 0.243765
21 to 30 141656 -0.8736 0.191181
20 to 29 142110 0.6920 0.755521
19 to 28 142318 1.4092 0.920613
18 to 27 141705 -0.7046 0.240534
17 to 26 141625 -0.9804 0.163432
16 to 25 141926 0.0575 0.522920
15 to 24 142224 1.0851 0.861054
14 to 23 141865 -0.1529 0.439254
13 to 22 141795 -0.3942 0.346701
12 to 21 141974 0.2230 0.588232
11 to 20 141672 -0.8184 0.206570
10 to 19 141974 0.2230 0.588232
9 to 18 141554 -1.2253 0.110236
8 to 17 141993 0.2885 0.613525
7 to 16 141790 -0.4115 0.340359
6 to 15 142016 0.3678 0.643499
5 to 14 142477 1.9575 0.974855
4 to 13 142152 0.8368 0.798646
3 to 12 142000 0.3127 0.622729
2 to 11 141743 -0.5736 0.283136
1 to 10 141844 -0.2253 0.410882
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_08:31
Bits used No. missing words z-score p-value
28 to 32 141810 -0.3367 0.368167
27 to 31 142025 0.3921 0.652509
26 to 30 142227 1.0768 0.859226
25 to 29 142252 1.1616 0.877300
24 to 28 141583 -1.1062 0.134319
23 to 27 141999 0.3040 0.619423
22 to 26 141595 -1.0655 0.143319
21 to 25 141883 -0.0893 0.464440
20 to 24 141994 0.2870 0.612950
19 to 23 141528 -1.2926 0.098067
18 to 22 142152 0.8226 0.794635
17 to 21 142159 0.8463 0.801318
16 to 20 142531 2.1074 0.982457
15 to 19 142018 0.3684 0.643702
14 to 18 141410 -1.6926 0.045262
13 to 17 141620 -0.9808 0.163351
12 to 16 142316 1.3785 0.915982
11 to 15 141726 -0.6215 0.267149
10 to 14 141889 -0.0689 0.472529
9 to 13 142225 1.0701 0.857706
8 to 12 141951 0.1413 0.556166
7 to 11 141442 -1.5842 0.056578
6 to 10 142128 0.7413 0.770730
5 to 9 142176 0.9040 0.816993
4 to 8 142185 0.9345 0.824970
3 to 7 141626 -0.9604 0.168417
2 to 6 141493 -1.4113 0.079080
1 to 5 142722 2.7548 0.997064
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_08:31
Bits used No. missing words z-score p-value
31 to 32 141918 0.0256 0.510202
30 to 31 142452 1.6008 0.945289
29 to 30 141775 -0.3963 0.345959
28 to 29 142288 1.1170 0.868007
27 to 28 141299 -1.8004 0.035900
26 to 27 142069 0.4710 0.681181
25 to 26 141695 -0.6322 0.263614
24 to 25 142167 0.7601 0.776399
23 to 24 142147 0.7011 0.758377
22 to 23 141539 -1.0924 0.137325
21 to 22 141733 -0.5201 0.301480
20 to 21 142134 0.6627 0.746253
19 to 20 142463 1.6332 0.948791
18 to 19 142081 0.5064 0.693713
17 to 18 142043 0.3943 0.653323
16 to 17 141797 -0.3314 0.370187
15 to 16 142628 2.1200 0.982996
14 to 15 141448 -1.3609 0.086780
13 to 14 141935 0.0757 0.530180
12 to 13 142332 1.2468 0.893767
11 to 12 142184 0.8102 0.791098
10 to 11 141781 -0.3786 0.352509
9 to 10 141805 -0.3078 0.379133
8 to 9 141578 -0.9774 0.164192
7 to 8 142214 0.8987 0.815602
6 to 7 142140 0.6804 0.751888
5 to 6 141938 0.0846 0.533699
4 to 5 141466 -1.3078 0.095478
3 to 4 141842 -0.1986 0.421283
2 to 3 141292 -1.8210 0.034301
1 to 2 141227 -2.0128 0.022069
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2414.90 -1.203 0.114398
Test results for specific bytes for dh-ranFile-2018-07-08_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2406.53 -1.322 0.093118
2 to 9 2499.41 -0.008 0.496660
3 to 10 2470.61 -0.416 0.338821
4 to 11 2395.33 -1.480 0.069409
5 to 12 2421.70 -1.107 0.134090
6 to 13 2494.69 -0.075 0.470064
7 to 14 2502.25 0.032 0.512690
8 to 15 2507.16 0.101 0.540347
9 to 16 2465.11 -0.493 0.310882
10 to 17 2461.84 -0.540 0.294705
11 to 18 2426.41 -1.041 0.149018
12 to 19 2488.25 -0.166 0.434027
13 to 20 2552.49 0.742 0.771052
14 to 21 2440.97 -0.835 0.201894
15 to 22 2583.90 1.187 0.882303
16 to 23 2474.20 -0.365 0.357624
17 to 24 2574.59 1.055 0.854251
18 to 25 2536.95 0.523 0.699348
19 to 26 2499.87 -0.002 0.499279
20 to 27 2607.40 1.519 0.935609
21 to 28 2554.13 0.766 0.778027
22 to 29 2478.24 -0.308 0.379124
23 to 30 2555.70 0.788 0.784560
24 to 31 2614.92 1.625 0.947939
25 to 32 2535.96 0.509 0.694483
CDPARK for dh-ranFile-2018-07-08_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
3513 -0.4566 0.323972
3527 0.1826 0.572463
3539 0.7306 0.767486
3490 -1.5068 0.065925
3507 -0.7306 0.232514
3534 0.5023 0.692266
3503 -0.9132 0.180558
3510 -0.5936 0.276387
3546 1.0502 0.853193
3530 0.3196 0.625377
Square side=100, avg. no. parked=3519.90 sample std.=17.00
p-value of the KSTEST for those 10 p-values: 0.902273
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_08:31
0.2152,0.2150,0.2271,0.9983,0.7375,0.5174,0.5766,0.1248,0.7460,0.5478,
The KS test for those 10 p-values: 0.647743
The 3DSPHERES test for dh-ranFile-2018-07-08_08:31
sample no r^3 equiv. uni.
1 33.863 0.676568
2 47.840 0.797021
3 24.822 0.562815
4 48.980 0.804590
5 40.836 0.743649
6 47.214 0.792746
7 4.494 0.139124
8 29.331 0.623826
9 16.376 0.420661
10 15.394 0.401392
11 32.011 0.655973
12 22.142 0.521956
13 13.491 0.362186
14 8.519 0.247200
15 44.669 0.774397
16 2.127 0.068436
17 15.386 0.401222
18 13.014 0.351962
19 43.714 0.767098
20 33.539 0.673058
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.279170
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -2.0 -2.0 -0.7 1.2
-0.8 -0.2 -2.2 -0.1 1.5 0.2
0.7 2.0 -1.4 -1.5 1.1 -0.1
-0.3 0.0 1.8 -0.4 -0.5 2.2
-1.0 -1.7 0.2 -1.6 -1.3 0.5
-1.6 0.1 1.2 0.4 -0.1 0.1
-0.9 -0.7 0.1 -1.3 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:55.110590
z-score=1.430483, p-value=0.915446
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_08:31
Test no p-value
1 0.356845
2 0.143593
3 0.435576
4 0.246109
5 0.120693
6 0.351943
7 0.390875
8 0.342856
9 0.021818
10 0.455480
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.020749
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_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 66342 1.58 66600 0.07
3 25000.00 25191 1.46 25025 0.03
4 6666.67 6734 0.68 6679 0.02
5 1388.89 1469 4.62 1414 0.45
6 238.10 221 1.23 231 0.21
7 34.72 37 0.15 42 1.53
8 4.96 5 0.00 8 1.86
p=0.86298 p=0.34626
Number of rngs required: 688404, p-value: 0.500
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_08:31
No. of wins: Observed Expected
98558 98585.9
z-score=-0.125, pvalue=0.45042
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66951 66666.7 1.213 1.213
2 37394 37654.3 1.800 3.012
3 26700 26954.7 2.407 5.420
4 19200 19313.5 0.667 6.086
5 13974 13851.4 1.085 7.171
6 9956 9943.5 0.016 7.187
7 7225 7145.0 0.895 8.082
8 5211 5139.1 1.007 9.089
9 3818 3699.9 3.772 12.861
10 2725 2666.3 1.292 14.153
11 1883 1923.3 0.846 14.999
12 1391 1388.7 0.004 15.002
13 957 1003.7 2.174 17.177
14 723 726.1 0.014 17.190
15 562 525.8 2.487 19.677
16 352 381.2 2.229 21.907
17 286 276.5 0.324 22.230
18 197 200.8 0.073 22.303
19 134 146.0 0.984 23.287
20 81 106.2 5.986 29.273
21 280 287.1 0.176 29.450
Chisq= 29.45 for 20 degrees of freedom, p= 0.92072
SUMMARY of craptest
p-value for no. of wins: 0.450420
p-value for throws/game: 0.920722
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_08:31
No. of wins: Observed Expected
98524 98585.9
z-score=-0.277, pvalue=0.39102
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66695 66666.7 0.012 0.012
2 37807 37654.3 0.619 0.631
3 26960 26954.7 0.001 0.632
4 19204 19313.5 0.620 1.253
5 13743 13851.4 0.849 2.101
6 10095 9943.5 2.307 4.408
7 7093 7145.0 0.379 4.787
8 5244 5139.1 2.142 6.929
9 3636 3699.9 1.102 8.032
10 2651 2666.3 0.088 8.119
11 1883 1923.3 0.846 8.965
12 1344 1388.7 1.441 10.407
13 1007 1003.7 0.011 10.417
14 702 726.1 0.803 11.220
15 519 525.8 0.089 11.309
16 402 381.2 1.140 12.449
17 285 276.5 0.259 12.708
18 212 200.8 0.621 13.329
19 154 146.0 0.440 13.769
20 90 106.2 2.475 16.245
21 274 287.1 0.599 16.844
Chisq= 16.84 for 20 degrees of freedom, p= 0.33691
SUMMARY of craptest
p-value for no. of wins: 0.391018
p-value for throws/game: 0.336912
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0055,0.0123,0.0207,0.0218,0.0221,0.0222,0.0249,0.0249,0.0281,0.0298,
0.0333,0.0343,0.0359,0.0453,0.0511,0.0566,0.0659,0.0684,0.0694,0.0791,
0.0831,0.0868,0.0931,0.0941,0.0955,0.0981,0.1044,0.1071,0.1102,0.1113,
0.1121,0.1144,0.1207,0.1225,0.1248,0.1341,0.1343,0.1373,0.1391,0.1433,
0.1436,0.1444,0.1490,0.1542,0.1634,0.1634,0.1642,0.1684,0.1806,0.1880,
0.1905,0.1912,0.1961,0.2019,0.2039,0.2066,0.2102,0.2114,0.2150,0.2152,
0.2206,0.2261,0.2271,0.2288,0.2325,0.2405,0.2438,0.2461,0.2472,0.2593,
0.2636,0.2671,0.2756,0.2764,0.2780,0.2792,0.2794,0.2831,0.2840,0.2947,
0.3015,0.3109,0.3159,0.3240,0.3369,0.3388,0.3404,0.3418,0.3429,0.3460,
0.3463,0.3467,0.3519,0.3520,0.3525,0.3568,0.3576,0.3591,0.3622,0.3682,
0.3702,0.3719,0.3791,0.3791,0.3813,0.3863,0.3909,0.3910,0.3910,0.3919,
0.3920,0.4012,0.4014,0.4067,0.4101,0.4109,0.4207,0.4213,0.4219,0.4340,
0.4356,0.4393,0.4504,0.4555,0.4588,0.4644,0.4701,0.4725,0.4727,0.4755,
0.4803,0.4806,0.4967,0.4993,0.5005,0.5008,0.5024,0.5102,0.5127,0.5174,
0.5220,0.5229,0.5302,0.5336,0.5337,0.5403,0.5443,0.5478,0.5503,0.5543,
0.5562,0.5628,0.5635,0.5672,0.5725,0.5744,0.5766,0.5882,0.5882,0.5885,
0.5966,0.6130,0.6135,0.6179,0.6194,0.6222,0.6227,0.6238,0.6254,0.6284,
0.6415,0.6435,0.6437,0.6477,0.6504,0.6525,0.6533,0.6560,0.6568,0.6574,
0.6639,0.6718,0.6731,0.6766,0.6812,0.6870,0.6923,0.6937,0.6945,0.6987,
0.6993,0.7008,0.7028,0.7249,0.7341,0.7375,0.7380,0.7433,0.7436,0.7460,
0.7463,0.7519,0.7555,0.7584,0.7636,0.7671,0.7675,0.7707,0.7711,0.7744,
0.7764,0.7780,0.7787,0.7846,0.7911,0.7927,0.7946,0.7970,0.7986,0.8013,
0.8046,0.8120,0.8128,0.8156,0.8170,0.8189,0.8250,0.8403,0.8423,0.8457,
0.8532,0.8543,0.8577,0.8588,0.8592,0.8611,0.8630,0.8680,0.8712,0.8773,
0.8823,0.8837,0.8877,0.8938,0.9023,0.9087,0.9133,0.9154,0.9160,0.9206,
0.9207,0.9242,0.9304,0.9356,0.9364,0.9453,0.9479,0.9482,0.9488,0.9526,
0.9531,0.9669,0.9724,0.9749,0.9825,0.9830,0.9846,0.9971,0.9983,
Overall p-value after applying KStest on 269 p-values = 0.998112
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.