RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.98 24.1744 0.885225
2 to 25 15.54 24.8824 0.902627
3 to 26 15.60 10.3927 0.113661
4 to 27 15.65 18.7463 0.656715
5 to 28 15.79 11.3126 0.160141
6 to 29 15.76 18.5000 0.642024
7 to 30 15.75 10.9246 0.139545
8 to 31 15.61 20.5550 0.753169
9 to 32 15.49 18.1370 0.619751
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.667200
Tough bday spacings test for dh-ranFile-2018-06-27_17:31: 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 10 38 68 101 105 76 44 32 18 4 4
(O-E)^2/E 0.1 0.1 0.4 0.1 0.5 0.1 1.3 0.2 0.7 1.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 4.339, p= 0.069
RESULTS OF GCD FOR dh-ranFile-2018-06-27_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.820372
p-value, dist. of gcd's: 0.062307
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.855 0.155 0.685 0.975 0.520 0.944 0.853 0.288
Bits 8 to 15---> 0.131 0.151 0.579 0.321 0.733 0.637 0.006 0.704
Bits 16 to 23---> 0.271 0.044 0.290 0.252 0.467 0.182 0.860 0.294
Bits 24 to 31---> 0.487 0.570 0.193 0.637 0.623 0.793 0.690 0.439
KS test for the above 32 p values: 0.037
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_17:31,
p-values for 5 runs: 0.8859, 0.8247, 0.3719, 0.5454, 0.1670
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 217 211.4 0.147 0.147
r= 29 5060 5134.0 1.067 1.214
r= 30 23159 23103.0 0.136 1.350
r= 31 11564 11551.5 0.013 1.363
chi-square = 1.363 with df = 3; p-value = 0.286
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 225 211.4 0.873 0.873
r= 30 5180 5134.0 0.412 1.285
r= 31 23061 23103.0 0.077 1.361
r= 32 11534 11551.5 0.027 1.388
chi-square = 1.388 with df = 3; p-value = 0.292
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_17:31
b-rank test for bits 1 to 8, p=0.84653
b-rank test for bits 2 to 9, p=0.54893
b-rank test for bits 3 to 10, p=0.83105
b-rank test for bits 4 to 11, p=0.57900
b-rank test for bits 5 to 12, p=0.13291
b-rank test for bits 6 to 13, p=0.22582
b-rank test for bits 7 to 14, p=0.86480
b-rank test for bits 8 to 15, p=0.93002
b-rank test for bits 9 to 16, p=0.80244
b-rank test for bits 10 to 17, p=0.41860
b-rank test for bits 11 to 18, p=0.11845
b-rank test for bits 12 to 19, p=0.39768
b-rank test for bits 13 to 20, p=0.83610
b-rank test for bits 14 to 21, p=0.46978
b-rank test for bits 15 to 22, p=0.16316
b-rank test for bits 16 to 23, p=0.42870
b-rank test for bits 17 to 24, p=0.00458
b-rank test for bits 18 to 25, p=0.60742
b-rank test for bits 19 to 26, p=0.48594
b-rank test for bits 20 to 27, p=0.01112
b-rank test for bits 21 to 28, p=0.82923
b-rank test for bits 22 to 29, p=0.71876
b-rank test for bits 23 to 30, p=0.75305
b-rank test for bits 24 to 31, p=0.53300
b-rank test for bits 25 to 32, p=0.79827
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 = 0.504064
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_17:31
(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 142068 0.37 0.644579
2 142101 0.45 0.672861
3 140680 -2.87 0.002038
4 141607 -0.71 0.239976
5 142184 0.64 0.739483
6 141843 -0.15 0.438420
7 141416 -1.15 0.124529
8 142525 1.44 0.924851
9 142290 0.89 0.813110
10 141674 -0.55 0.291216
11 141933 0.06 0.522052
12 141622 -0.67 0.251005
13 141762 -0.34 0.365337
14 141871 -0.09 0.464320
15 142161 0.59 0.721739
16 141393 -1.21 0.113836
17 141651 -0.60 0.273063
18 141691 -0.51 0.304985
19 141379 -1.24 0.107656
20 142407 1.16 0.877541
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_17:31
Bits used No. missing words z-score p-value
23 to 32 142132 0.7678 0.778705
22 to 31 141434 -1.6391 0.050599
21 to 30 141538 -1.2804 0.100194
20 to 29 142050 0.4851 0.686186
19 to 28 142017 0.3713 0.644784
18 to 27 142198 0.9954 0.840233
17 to 26 142279 1.2747 0.898797
16 to 25 141920 0.0368 0.514675
15 to 24 141939 0.1023 0.540745
14 to 23 142313 1.3920 0.918034
13 to 22 141757 -0.5253 0.299696
12 to 21 141766 -0.4942 0.310568
11 to 20 141370 -1.8598 0.031460
10 to 19 141646 -0.9080 0.181930
9 to 18 141648 -0.9011 0.183758
8 to 17 142239 1.1368 0.872188
7 to 16 141566 -1.1839 0.118227
6 to 15 141896 -0.0460 0.481669
5 to 14 141560 -1.2046 0.114182
4 to 13 141943 0.1161 0.546215
3 to 12 141917 0.0264 0.510550
2 to 11 141733 -0.6080 0.271582
1 to 10 142109 0.6885 0.754436
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_17:31
Bits used No. missing words z-score p-value
28 to 32 142133 0.7582 0.775835
27 to 31 141807 -0.3469 0.364340
26 to 30 142274 1.2362 0.891802
25 to 29 141950 0.1379 0.554826
24 to 28 141452 -1.5503 0.060538
23 to 27 141823 -0.2926 0.384897
22 to 26 142465 1.8836 0.970192
21 to 25 142283 1.2667 0.897365
20 to 24 141267 -2.1774 0.014726
19 to 23 141372 -1.8215 0.034269
18 to 22 141496 -1.4011 0.080589
17 to 21 141894 -0.0520 0.479278
16 to 20 142120 0.7141 0.762428
15 to 19 141810 -0.3367 0.368167
14 to 18 142065 0.5277 0.701145
13 to 17 141539 -1.2554 0.104675
12 to 16 141243 -2.2587 0.011950
11 to 15 141742 -0.5672 0.285282
10 to 14 141696 -0.7232 0.234793
9 to 13 141626 -0.9604 0.168417
8 to 12 141848 -0.2079 0.417654
7 to 11 141730 -0.6079 0.271628
6 to 10 141782 -0.4316 0.333006
5 to 9 141731 -0.6045 0.272753
4 to 8 142225 1.0701 0.857706
3 to 7 141702 -0.7028 0.241086
2 to 6 142056 0.4972 0.690471
1 to 5 141970 0.2057 0.581472
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_17:31
Bits used No. missing words z-score p-value
31 to 32 141901 -0.0246 0.490198
30 to 31 141882 -0.0806 0.467872
29 to 30 141869 -0.1190 0.452651
28 to 29 141381 -1.5585 0.059558
27 to 28 142167 0.7601 0.776399
26 to 27 141068 -2.4818 0.006536
25 to 26 141871 -0.1131 0.454988
24 to 25 141697 -0.6263 0.265545
23 to 24 142488 1.7070 0.956088
22 to 23 142200 0.8574 0.804397
21 to 22 141531 -1.1160 0.132207
20 to 21 141699 -0.6204 0.267483
19 to 20 142285 1.1082 0.866106
18 to 19 142168 0.7630 0.777280
17 to 18 141697 -0.6263 0.265545
16 to 17 141992 0.2439 0.596332
15 to 16 141577 -0.9803 0.163463
14 to 15 142108 0.5860 0.721078
13 to 14 141878 -0.0924 0.463183
12 to 13 141865 -0.1308 0.447980
11 to 12 142083 0.5123 0.695780
10 to 11 142803 2.6362 0.995808
9 to 10 141971 0.1819 0.572176
8 to 9 142316 1.1996 0.884856
7 to 8 142143 0.6893 0.754680
6 to 7 141640 -0.7945 0.213457
5 to 6 142031 0.3589 0.640168
4 to 5 142595 2.0226 0.978444
3 to 4 141689 -0.6499 0.257865
2 to 3 142062 0.4504 0.673772
1 to 2 142103 0.5713 0.716101
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2584.88 1.200 0.885011
Test results for specific bytes for dh-ranFile-2018-06-27_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2510.66 0.151 0.559919
2 to 9 2556.57 0.800 0.788151
3 to 10 2529.69 0.420 0.662724
4 to 11 2577.17 1.091 0.862450
5 to 12 2531.55 0.446 0.672269
6 to 13 2380.87 -1.685 0.046014
7 to 14 2567.53 0.955 0.830226
8 to 15 2328.12 -2.431 0.007534
9 to 16 2530.78 0.435 0.668300
10 to 17 2517.93 0.254 0.600091
11 to 18 2442.93 -0.807 0.209799
12 to 19 2557.09 0.807 0.790291
13 to 20 2594.65 1.339 0.909649
14 to 21 2463.29 -0.519 0.301831
15 to 22 2554.14 0.766 0.778047
16 to 23 2592.99 1.315 0.905770
17 to 24 2453.06 -0.664 0.253398
18 to 25 2595.31 1.348 0.911144
19 to 26 2453.40 -0.659 0.254929
20 to 27 2349.00 -2.135 0.016363
21 to 28 2507.92 0.112 0.544603
22 to 29 2412.92 -1.231 0.109072
23 to 30 2296.13 -2.883 0.001968
24 to 31 2574.69 1.056 0.854592
25 to 32 2488.51 -0.163 0.435434
CDPARK for dh-ranFile-2018-06-27_17:31: 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
3547 1.0959 0.863437
3541 0.8219 0.794438
3518 -0.2283 0.409702
3552 1.3242 0.907282
3561 1.7352 0.958644
3514 -0.4110 0.340551
3524 0.0457 0.518210
3553 1.3699 0.914635
3534 0.5023 0.692266
3524 0.0457 0.518210
Square side=100, avg. no. parked=3536.80 sample std.=15.52
p-value of the KSTEST for those 10 p-values: 0.055342
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_17:31
0.9404,0.6801,0.8869,0.6250,0.6506,0.6259,0.1727,0.0890,0.0480,0.2237,
The KS test for those 10 p-values: 0.825557
The 3DSPHERES test for dh-ranFile-2018-06-27_17:31
sample no r^3 equiv. uni.
1 30.079 0.633094
2 7.101 0.210768
3 21.100 0.505068
4 85.344 0.941854
5 39.352 0.730644
6 2.905 0.092287
7 9.396 0.268908
8 1.020 0.033425
9 62.909 0.877171
10 23.175 0.538147
11 56.431 0.847568
12 32.572 0.662345
13 4.251 0.132115
14 22.880 0.533579
15 56.986 0.850363
16 4.946 0.152003
17 5.724 0.173693
18 3.174 0.100409
19 51.689 0.821464
20 8.862 0.255763
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.740622
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 2.0 -1.6 -0.5 -1.9
-1.3 0.4 0.4 0.1 -1.8 0.9
1.0 -0.5 -1.0 1.0 0.9 -0.5
1.2 -0.1 -0.1 -1.0 0.9 -1.1
0.3 -1.0 0.5 -0.1 -1.2 0.5
2.0 0.3 -0.2 -0.8 1.0 -0.1
1.2 -1.0 -0.8 -1.3 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:41.123232
z-score=-0.095663, p-value=0.490670
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_17:31
Test no p-value
1 0.323892
2 0.021298
3 0.955619
4 0.090225
5 0.032906
6 0.005702
7 0.142031
8 0.850278
9 0.154739
10 0.082671
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001558
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_17:31:
(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 66643 0.01 66489 0.47
3 25000.00 25034 0.05 25227 2.06
4 6666.67 6669 0.00 6550 2.04
5 1388.89 1401 0.11 1427 1.05
6 238.10 213 2.65 264 2.82
7 34.72 33 0.09 39 0.53
8 4.96 6 0.22 3 0.77
p=0.20500 p=0.86409
Number of rngs required: 688483, p-value: 0.537
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_17:31
No. of wins: Observed Expected
98882 98585.9
z-score= 1.325, pvalue=0.90733
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66563 66666.7 0.161 0.161
2 37661 37654.3 0.001 0.162
3 27115 26954.7 0.953 1.115
4 19392 19313.5 0.319 1.435
5 13646 13851.4 3.046 4.481
6 9771 9943.5 2.994 7.475
7 7160 7145.0 0.031 7.507
8 5211 5139.1 1.007 8.513
9 3792 3699.9 2.294 10.808
10 2760 2666.3 3.293 14.101
11 1879 1923.3 1.022 15.122
12 1365 1388.7 0.406 15.528
13 1025 1003.7 0.451 15.980
14 711 726.1 0.316 16.295
15 536 525.8 0.196 16.492
16 402 381.2 1.140 17.632
17 264 276.5 0.569 18.201
18 202 200.8 0.007 18.208
19 171 146.0 4.287 22.494
20 97 106.2 0.800 23.294
21 277 287.1 0.356 23.650
Chisq= 23.65 for 20 degrees of freedom, p= 0.74199
SUMMARY of craptest
p-value for no. of wins: 0.907334
p-value for throws/game: 0.741985
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_17:31
No. of wins: Observed Expected
98355 98585.9
z-score=-1.033, pvalue=0.15091
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66523 66666.7 0.310 0.310
2 37884 37654.3 1.401 1.711
3 27055 26954.7 0.373 2.084
4 19120 19313.5 1.938 4.021
5 13865 13851.4 0.013 4.035
6 9891 9943.5 0.278 4.312
7 7241 7145.0 1.289 5.602
8 5269 5139.1 3.285 8.886
9 3761 3699.9 1.010 9.897
10 2608 2666.3 1.275 11.171
11 1825 1923.3 5.027 16.198
12 1337 1388.7 1.928 18.126
13 1040 1003.7 1.312 19.438
14 685 726.1 2.331 21.769
15 504 525.8 0.907 22.675
16 383 381.2 0.009 22.684
17 271 276.5 0.111 22.795
18 217 200.8 1.302 24.097
19 129 146.0 1.976 26.073
20 91 106.2 2.180 28.253
21 301 287.1 0.672 28.924
Chisq= 28.92 for 20 degrees of freedom, p= 0.91074
SUMMARY of craptest
p-value for no. of wins: 0.150911
p-value for throws/game: 0.910742
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0020,0.0020,0.0046,0.0057,0.0059,0.0065,0.0075,0.0111,0.0119,
0.0147,0.0164,0.0213,0.0315,0.0329,0.0334,0.0343,0.0370,0.0438,0.0460,
0.0480,0.0506,0.0553,0.0596,0.0605,0.0623,0.0692,0.0806,0.0827,0.0890,
0.0902,0.0923,0.1002,0.1004,0.1047,0.1077,0.1091,0.1137,0.1138,0.1142,
0.1182,0.1185,0.1245,0.1311,0.1321,0.1322,0.1329,0.1395,0.1420,0.1509,
0.1513,0.1520,0.1547,0.1554,0.1601,0.1632,0.1635,0.1670,0.1684,0.1727,
0.1737,0.1819,0.1823,0.1838,0.1931,0.2050,0.2098,0.2108,0.2135,0.2237,
0.2258,0.2348,0.2400,0.2411,0.2510,0.2518,0.2534,0.2549,0.2558,0.2579,
0.2655,0.2655,0.2675,0.2689,0.2715,0.2716,0.2716,0.2728,0.2731,0.2853,
0.2858,0.2879,0.2899,0.2912,0.2916,0.2935,0.2997,0.3018,0.3050,0.3106,
0.3209,0.3239,0.3330,0.3406,0.3643,0.3653,0.3682,0.3719,0.3849,0.3977,
0.4097,0.4177,0.4186,0.4287,0.4354,0.4384,0.4388,0.4480,0.4527,0.4550,
0.4632,0.4643,0.4672,0.4679,0.4698,0.4793,0.4817,0.4859,0.4871,0.4902,
0.4907,0.5041,0.5051,0.5106,0.5147,0.5182,0.5182,0.5205,0.5221,0.5330,
0.5336,0.5367,0.5381,0.5407,0.5446,0.5454,0.5462,0.5489,0.5548,0.5599,
0.5696,0.5722,0.5789,0.5790,0.5815,0.5963,0.6001,0.6074,0.6198,0.6234,
0.6250,0.6259,0.6331,0.6365,0.6366,0.6402,0.6420,0.6446,0.6448,0.6506,
0.6567,0.6623,0.6627,0.6672,0.6683,0.6723,0.6729,0.6738,0.6801,0.6847,
0.6862,0.6899,0.6905,0.6923,0.6958,0.7011,0.7038,0.7161,0.7188,0.7211,
0.7217,0.7306,0.7330,0.7395,0.7406,0.7420,0.7531,0.7532,0.7544,0.7547,
0.7624,0.7758,0.7764,0.7773,0.7780,0.7787,0.7882,0.7903,0.7934,0.7944,
0.7983,0.8024,0.8044,0.8131,0.8204,0.8215,0.8247,0.8256,0.8292,0.8302,
0.8310,0.8361,0.8402,0.8465,0.8476,0.8503,0.8504,0.8534,0.8546,0.8554,
0.8577,0.8597,0.8625,0.8634,0.8641,0.8648,0.8661,0.8722,0.8772,0.8775,
0.8849,0.8850,0.8852,0.8859,0.8869,0.8918,0.8974,0.8988,0.9026,0.9058,
0.9073,0.9073,0.9096,0.9107,0.9111,0.9146,0.9180,0.9249,0.9300,0.9404,
0.9419,0.9440,0.9556,0.9561,0.9586,0.9702,0.9751,0.9784,0.9958,
Overall p-value after applying KStest on 269 p-values = 0.129105
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.