RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.61 20.7197 0.760922
2 to 25 15.95 21.1107 0.778621
3 to 26 15.87 16.2066 0.490761
4 to 27 15.80 11.8138 0.188719
5 to 28 15.86 8.0500 0.034535
6 to 29 16.08 24.6352 0.896822
7 to 30 15.59 18.7482 0.656826
8 to 31 15.66 13.2922 0.283581
9 to 32 16.02 15.5541 0.444366
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.995715
Tough bday spacings test for dh-ranFile-2018-07-02_10:31: 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 2 32 64 110 101 74 61 23 27 4 2
(O-E)^2/E 5.6 0.6 1.2 1.6 0.1 0.2 1.5 1.5 9.9 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 24.242, p= 0.993
RESULTS OF GCD FOR dh-ranFile-2018-07-02_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.207949
p-value, dist. of gcd's: 0.333403
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.817 0.558 0.883 0.540 0.328 0.126 0.692 0.093
Bits 8 to 15---> 0.706 0.134 0.977 0.588 0.244 0.308 0.451 0.297
Bits 16 to 23---> 0.677 0.934 0.948 0.656 0.444 0.368 0.158 0.964
Bits 24 to 31---> 0.648 0.633 0.781 0.970 0.313 0.821 0.977 0.160
KS test for the above 32 p values: 0.773
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_10:31,
p-values for 5 runs: 0.4454, 0.2351, 0.8534, 0.6539, 0.1576
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 203 211.4 0.335 0.335
r= 29 5149 5134.0 0.044 0.379
r= 30 23155 23103.0 0.117 0.496
r= 31 11493 11551.5 0.297 0.792
chi-square = 0.792 with df = 3; p-value = 0.149
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 223 211.4 0.634 0.634
r= 30 5120 5134.0 0.038 0.673
r= 31 23029 23103.0 0.237 0.910
r= 32 11628 11551.5 0.506 1.416
chi-square = 1.416 with df = 3; p-value = 0.298
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_10:31
b-rank test for bits 1 to 8, p=0.77346
b-rank test for bits 2 to 9, p=0.36776
b-rank test for bits 3 to 10, p=0.14239
b-rank test for bits 4 to 11, p=0.60535
b-rank test for bits 5 to 12, p=0.54443
b-rank test for bits 6 to 13, p=0.31238
b-rank test for bits 7 to 14, p=0.78011
b-rank test for bits 8 to 15, p=0.74267
b-rank test for bits 9 to 16, p=0.58769
b-rank test for bits 10 to 17, p=0.59748
b-rank test for bits 11 to 18, p=0.62419
b-rank test for bits 12 to 19, p=0.08468
b-rank test for bits 13 to 20, p=0.05719
b-rank test for bits 14 to 21, p=0.33722
b-rank test for bits 15 to 22, p=0.82050
b-rank test for bits 16 to 23, p=0.95474
b-rank test for bits 17 to 24, p=0.25367
b-rank test for bits 18 to 25, p=0.30135
b-rank test for bits 19 to 26, p=0.45424
b-rank test for bits 20 to 27, p=0.05733
b-rank test for bits 21 to 28, p=0.21893
b-rank test for bits 22 to 29, p=0.55973
b-rank test for bits 23 to 30, p=0.53377
b-rank test for bits 24 to 31, p=0.81101
b-rank test for bits 25 to 32, p=0.08434
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 = 0.713864
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_10:31
(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 142401 1.15 0.874673
2 142664 1.76 0.961071
3 142313 0.94 0.827199
4 140957 -2.23 0.013038
5 142322 0.96 0.832523
6 140970 -2.19 0.014093
7 141447 -1.08 0.140024
8 141526 -0.90 0.185225
9 142127 0.51 0.694475
10 142651 1.73 0.958441
11 141565 -0.80 0.210551
12 141354 -1.30 0.097230
13 141898 -0.03 0.489440
14 142328 0.98 0.836013
15 142570 1.54 0.938660
16 142023 0.27 0.604720
17 142185 0.64 0.740241
18 141385 -1.23 0.110274
19 142376 1.09 0.862221
20 141940 0.07 0.528563
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_10:31
Bits used No. missing words z-score p-value
23 to 32 141848 -0.2115 0.416255
22 to 31 141747 -0.5598 0.287822
21 to 30 142069 0.5506 0.709041
20 to 29 142193 0.9782 0.836006
19 to 28 142168 0.8920 0.813794
18 to 27 141921 0.0402 0.516050
17 to 26 141980 0.2437 0.596264
16 to 25 141915 0.0196 0.507800
15 to 24 141894 -0.0529 0.478921
14 to 23 142286 1.2989 0.903004
13 to 22 142498 2.0299 0.978816
12 to 21 141613 -1.0218 0.153431
11 to 20 141271 -2.2011 0.013863
10 to 19 141900 -0.0322 0.487167
9 to 18 141812 -0.3356 0.368579
8 to 17 141982 0.2506 0.598933
7 to 16 141941 0.1092 0.543481
6 to 15 141754 -0.5356 0.296110
5 to 14 141267 -2.2149 0.013382
4 to 13 141792 -0.4046 0.342891
3 to 12 142391 1.6609 0.951636
2 to 11 141612 -1.0253 0.152617
1 to 10 142401 1.6954 0.955002
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_10:31
Bits used No. missing words z-score p-value
28 to 32 142091 0.6158 0.730997
27 to 31 142249 1.1514 0.875221
26 to 30 142312 1.3650 0.913871
25 to 29 141920 0.0362 0.514426
24 to 28 141816 -0.3164 0.375860
23 to 27 142154 0.8294 0.796558
22 to 26 141925 0.0531 0.521181
21 to 25 142191 0.9548 0.830164
20 to 24 141739 -0.5774 0.281838
19 to 23 142955 3.5446 0.999803
18 to 22 142393 1.6396 0.949452
17 to 21 141684 -0.7638 0.222484
16 to 20 142410 1.6972 0.955169
15 to 19 142184 0.9311 0.824095
14 to 18 141631 -0.9435 0.172715
13 to 17 142070 0.5446 0.707001
12 to 16 141711 -0.6723 0.250695
11 to 15 141832 -0.2621 0.396609
10 to 14 141481 -1.4520 0.073256
9 to 13 142600 2.3413 0.990390
8 to 12 142650 2.5107 0.993976
7 to 11 142014 0.3548 0.638635
6 to 10 142246 1.1413 0.873118
5 to 9 142124 0.7277 0.766600
4 to 8 141780 -0.4384 0.330546
3 to 7 142126 0.7345 0.768670
2 to 6 142206 1.0057 0.842711
1 to 5 142123 0.7243 0.765561
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_10:31
Bits used No. missing words z-score p-value
31 to 32 141432 -1.4081 0.079558
30 to 31 142035 0.3707 0.644573
29 to 30 141773 -0.4022 0.343786
28 to 29 141880 -0.0865 0.465527
27 to 28 141641 -0.7915 0.214316
26 to 27 141683 -0.6676 0.252182
25 to 26 141979 0.2055 0.581416
24 to 25 141435 -1.3992 0.080876
23 to 24 141773 -0.4022 0.343786
22 to 23 141910 0.0020 0.500789
21 to 22 142126 0.6391 0.738636
20 to 21 141580 -0.9715 0.165656
19 to 20 141757 -0.4494 0.326589
18 to 19 141387 -1.5408 0.061683
17 to 18 141142 -2.2635 0.011802
16 to 17 142586 1.9961 0.977037
15 to 16 141788 -0.3579 0.360207
14 to 15 141809 -0.2960 0.383631
13 to 14 141970 0.1790 0.571018
12 to 13 141835 -0.2193 0.413223
11 to 12 142269 1.0610 0.855649
10 to 11 142414 1.4887 0.931717
9 to 10 141249 -1.9479 0.025715
8 to 9 141767 -0.4199 0.337297
7 to 8 141748 -0.4759 0.317073
6 to 7 141306 -1.7797 0.037560
5 to 6 141998 0.2616 0.603171
4 to 5 141990 0.2380 0.594046
3 to 4 142001 0.2704 0.606579
2 to 3 141721 -0.5555 0.289261
1 to 2 141466 -1.3078 0.095478
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2563.87 0.903 0.816812
Test results for specific bytes for dh-ranFile-2018-07-02_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2520.52 0.290 0.614165
2 to 9 2571.28 1.008 0.843296
3 to 10 2592.02 1.301 0.903429
4 to 11 2542.17 0.596 0.724537
5 to 12 2580.55 1.139 0.872673
6 to 13 2573.00 1.032 0.849037
7 to 14 2430.64 -0.981 0.163330
8 to 15 2429.50 -0.997 0.159362
9 to 16 2463.61 -0.515 0.303399
10 to 17 2519.47 0.275 0.608494
11 to 18 2417.26 -1.170 0.120988
12 to 19 2571.90 1.017 0.845383
13 to 20 2406.44 -1.323 0.092892
14 to 21 2617.56 1.663 0.951798
15 to 22 2482.05 -0.254 0.399802
16 to 23 2589.26 1.262 0.896587
17 to 24 2533.59 0.475 0.682635
18 to 25 2492.31 -0.109 0.456677
19 to 26 2343.75 -2.210 0.013562
20 to 27 2526.31 0.372 0.645079
21 to 28 2500.87 0.012 0.504894
22 to 29 2435.59 -0.911 0.181178
23 to 30 2596.56 1.366 0.913968
24 to 31 2654.14 2.180 0.985365
25 to 32 2564.79 0.916 0.820237
CDPARK for dh-ranFile-2018-07-02_10:31: 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
3530 0.3196 0.625377
3516 -0.3196 0.374623
3521 -0.0913 0.463617
3555 1.4612 0.928018
3472 -2.3288 0.009936
3469 -2.4658 0.006836
3527 0.1826 0.572463
3531 0.3653 0.642555
3553 1.3699 0.914635
3502 -0.9589 0.168804
Square side=100, avg. no. parked=3517.60 sample std.=27.88
p-value of the KSTEST for those 10 p-values: 0.412857
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_10:31
0.6941,0.3505,0.2247,0.0297,0.9786,0.7964,0.8882,0.2493,0.9472,0.6074,
The KS test for those 10 p-values: 0.528108
The 3DSPHERES test for dh-ranFile-2018-07-02_10:31
sample no r^3 equiv. uni.
1 86.210 0.943508
2 19.222 0.473093
3 43.414 0.764755
4 8.888 0.256410
5 68.387 0.897673
6 13.530 0.363002
7 69.583 0.901670
8 136.101 0.989291
9 18.812 0.465841
10 8.309 0.241913
11 28.114 0.608250
12 6.876 0.204843
13 5.912 0.178864
14 33.195 0.669286
15 3.140 0.099367
16 23.495 0.543044
17 10.384 0.292585
18 26.634 0.588442
19 30.761 0.641338
20 3.724 0.116746
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.944761
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -0.4 0.8 0.2 -0.8
-1.3 1.4 0.2 0.4 -0.3 -0.9
-0.2 1.1 -1.7 0.1 1.3 2.7
-0.1 -0.7 -0.7 0.1 0.5 -0.7
0.3 -2.1 -1.0 -0.5 -0.5 1.2
-0.6 0.1 0.7 -0.4 -0.2 1.0
0.7 0.2 0.5 -1.3 0.1 1.0
0.8
Chi-square with 42 degrees of freedom:35.459396
z-score=-0.713638, p-value=0.248045
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_10:31
Test no p-value
1 0.099938
2 0.006317
3 0.027095
4 0.482257
5 0.946014
6 0.130256
7 0.901187
8 0.482511
9 0.129098
10 0.924367
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.093921
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_10:31:
(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 66710 0.03 66757 0.12
3 25000.00 24951 0.10 24904 0.37
4 6666.67 6655 0.02 6680 0.03
5 1388.89 1390 0.00 1381 0.04
6 238.10 254 1.06 240 0.02
7 34.72 36 0.05 30 0.64
8 4.96 3 0.77 7 0.84
p=0.08305 p=0.08575
Number of rngs required: 689008, p-value: 0.758
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_10:31
No. of wins: Observed Expected
99058 98585.9
z-score= 2.112, pvalue=0.98264
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66477 66666.7 0.540 0.540
2 37355 37654.3 2.379 2.919
3 26984 26954.7 0.032 2.951
4 19490 19313.5 1.614 4.564
5 13760 13851.4 0.603 5.168
6 9972 9943.5 0.081 5.249
7 7221 7145.0 0.808 6.057
8 5178 5139.1 0.295 6.352
9 3710 3699.9 0.028 6.380
10 2786 2666.3 5.374 11.754
11 1964 1923.3 0.860 12.614
12 1480 1388.7 5.997 18.611
13 974 1003.7 0.880 19.491
14 745 726.1 0.490 19.980
15 519 525.8 0.089 20.069
16 377 381.2 0.045 20.114
17 277 276.5 0.001 20.115
18 200 200.8 0.003 20.119
19 142 146.0 0.109 20.227
20 95 106.2 1.184 21.412
21 294 287.1 0.165 21.577
Chisq= 21.58 for 20 degrees of freedom, p= 0.63609
SUMMARY of craptest
p-value for no. of wins: 0.982644
p-value for throws/game: 0.636086
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_10:31
No. of wins: Observed Expected
98512 98585.9
z-score=-0.330, pvalue=0.37057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66533 66666.7 0.268 0.268
2 37541 37654.3 0.341 0.609
3 27098 26954.7 0.761 1.371
4 19244 19313.5 0.250 1.620
5 13971 13851.4 1.032 2.653
6 9993 9943.5 0.246 2.899
7 7112 7145.0 0.153 3.051
8 5189 5139.1 0.485 3.536
9 3700 3699.9 0.000 3.536
10 2637 2666.3 0.322 3.858
11 1935 1923.3 0.071 3.929
12 1375 1388.7 0.136 4.065
13 1035 1003.7 0.975 5.040
14 710 726.1 0.359 5.399
15 505 525.8 0.826 6.225
16 398 381.2 0.745 6.969
17 246 276.5 3.373 10.342
18 211 200.8 0.515 10.857
19 151 146.0 0.172 11.029
20 114 106.2 0.571 11.600
21 302 287.1 0.772 12.372
Chisq= 12.37 for 20 degrees of freedom, p= 0.09731
SUMMARY of craptest
p-value for no. of wins: 0.370572
p-value for throws/game: 0.097314
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0063,0.0068,0.0099,0.0118,0.0130,0.0134,0.0136,0.0139,0.0141,0.0257,
0.0271,0.0297,0.0345,0.0376,0.0572,0.0573,0.0617,0.0733,0.0796,0.0809,
0.0830,0.0843,0.0847,0.0858,0.0929,0.0932,0.0939,0.0955,0.0972,0.0973,
0.0994,0.0999,0.1103,0.1167,0.1210,0.1258,0.1291,0.1303,0.1341,0.1400,
0.1424,0.1487,0.1526,0.1534,0.1576,0.1580,0.1594,0.1598,0.1633,0.1657,
0.1688,0.1727,0.1789,0.1812,0.1852,0.1887,0.2048,0.2079,0.2106,0.2143,
0.2189,0.2225,0.2247,0.2351,0.2419,0.2440,0.2480,0.2493,0.2507,0.2522,
0.2537,0.2564,0.2818,0.2836,0.2878,0.2893,0.2926,0.2961,0.2968,0.2983,
0.3013,0.3034,0.3077,0.3124,0.3125,0.3171,0.3266,0.3282,0.3305,0.3334,
0.3372,0.3373,0.3429,0.3438,0.3438,0.3505,0.3602,0.3630,0.3678,0.3678,
0.3686,0.3706,0.3746,0.3759,0.3836,0.3966,0.3998,0.4129,0.4132,0.4163,
0.4436,0.4444,0.4454,0.4506,0.4542,0.4567,0.4636,0.4655,0.4658,0.4731,
0.4789,0.4823,0.4825,0.4872,0.4894,0.4908,0.5008,0.5049,0.5078,0.5144,
0.5160,0.5212,0.5281,0.5286,0.5338,0.5397,0.5430,0.5435,0.5444,0.5576,
0.5597,0.5710,0.5725,0.5814,0.5877,0.5878,0.5884,0.5940,0.5963,0.5975,
0.5989,0.6032,0.6047,0.6053,0.6066,0.6074,0.6082,0.6085,0.6142,0.6242,
0.6254,0.6327,0.6361,0.6386,0.6413,0.6426,0.6446,0.6451,0.6479,0.6539,
0.6559,0.6568,0.6693,0.6765,0.6826,0.6923,0.6941,0.6945,0.7062,0.7070,
0.7090,0.7139,0.7245,0.7310,0.7386,0.7402,0.7427,0.7575,0.7609,0.7648,
0.7656,0.7666,0.7687,0.7726,0.7735,0.7786,0.7801,0.7808,0.7964,0.7966,
0.8110,0.8138,0.8166,0.8168,0.8202,0.8205,0.8206,0.8241,0.8272,0.8302,
0.8325,0.8360,0.8360,0.8427,0.8433,0.8454,0.8490,0.8534,0.8556,0.8622,
0.8727,0.8731,0.8747,0.8752,0.8832,0.8882,0.8966,0.8968,0.8977,0.9012,
0.9017,0.9030,0.9034,0.9139,0.9140,0.9146,0.9244,0.9280,0.9317,0.9338,
0.9387,0.9435,0.9448,0.9460,0.9472,0.9478,0.9495,0.9516,0.9518,0.9547,
0.9550,0.9552,0.9584,0.9611,0.9643,0.9703,0.9766,0.9769,0.9770,0.9786,
0.9788,0.9826,0.9854,0.9893,0.9904,0.9930,0.9940,0.9957,0.9998,
Overall p-value after applying KStest on 269 p-values = 0.102705
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.