RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.58 20.9535 0.771622
2 to 25 15.40 24.9115 0.903292
3 to 26 15.51 21.1142 0.778775
4 to 27 15.42 25.1838 0.909330
5 to 28 15.86 19.5573 0.702506
6 to 29 15.61 18.2313 0.625611
7 to 30 15.42 23.0931 0.853755
8 to 31 15.45 23.7762 0.874356
9 to 32 15.75 16.2529 0.494014
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.006228
Tough bday spacings test for dh-ranFile-2018-06-27_15:31: 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 14 39 72 93 99 78 51 34 10 4 6
(O-E)^2/E 2.6 0.2 0.0 0.2 0.0 0.0 0.0 0.6 1.6 1.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 7.159, p= 0.290
RESULTS OF GCD FOR dh-ranFile-2018-06-27_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.702494
p-value, dist. of gcd's: 0.419531
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.574 0.537 0.480 0.868 0.714 0.082 0.867 0.400
Bits 8 to 15---> 0.944 0.603 0.110 0.904 0.411 0.119 0.595 0.743
Bits 16 to 23---> 0.490 0.144 0.040 0.393 0.930 0.721 0.969 0.985
Bits 24 to 31---> 0.414 0.414 0.046 0.621 0.946 0.217 0.553 0.167
KS test for the above 32 p values: 0.326
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_15:31,
p-values for 5 runs: 0.1248, 0.2207, 0.2792, 0.9062, 0.0001
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5091 5134.0 0.360 1.212
r= 30 22937 23103.0 1.193 2.405
r= 31 11774 11551.5 4.285 6.690
chi-square = 6.690 with df = 3; p-value = 0.918
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5075 5134.0 0.678 0.883
r= 31 23167 23103.0 0.177 1.060
r= 32 11540 11551.5 0.011 1.072
chi-square = 1.072 with df = 3; p-value = 0.216
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_15:31
b-rank test for bits 1 to 8, p=0.86756
b-rank test for bits 2 to 9, p=0.42905
b-rank test for bits 3 to 10, p=0.85358
b-rank test for bits 4 to 11, p=0.58822
b-rank test for bits 5 to 12, p=0.47292
b-rank test for bits 6 to 13, p=0.34423
b-rank test for bits 7 to 14, p=0.03683
b-rank test for bits 8 to 15, p=0.68691
b-rank test for bits 9 to 16, p=0.26782
b-rank test for bits 10 to 17, p=0.13716
b-rank test for bits 11 to 18, p=0.75122
b-rank test for bits 12 to 19, p=0.94852
b-rank test for bits 13 to 20, p=0.44799
b-rank test for bits 14 to 21, p=0.90944
b-rank test for bits 15 to 22, p=0.42012
b-rank test for bits 16 to 23, p=0.40953
b-rank test for bits 17 to 24, p=0.75157
b-rank test for bits 18 to 25, p=0.66536
b-rank test for bits 19 to 26, p=0.92642
b-rank test for bits 20 to 27, p=0.20236
b-rank test for bits 21 to 28, p=0.49563
b-rank test for bits 22 to 29, p=0.02099
b-rank test for bits 23 to 30, p=0.20262
b-rank test for bits 24 to 31, p=0.78488
b-rank test for bits 25 to 32, p=0.80737
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 = 0.847943
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_15:31
(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 142106 0.46 0.677066
2 142195 0.67 0.747759
3 142161 0.59 0.721739
4 141140 -1.80 0.036128
5 142217 0.72 0.763885
6 141570 -0.79 0.213939
7 142523 1.43 0.924187
8 142103 0.45 0.674546
9 141968 0.14 0.554516
10 141627 -0.66 0.254739
11 142386 1.11 0.867299
12 142728 1.91 0.972112
13 141228 -1.59 0.055704
14 141941 0.07 0.529493
15 142483 1.34 0.909934
16 141909 -0.00 0.499692
17 141775 -0.31 0.376816
18 142452 1.27 0.897587
19 141746 -0.38 0.351375
20 142286 0.88 0.810589
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_15:31
Bits used No. missing words z-score p-value
23 to 32 142498 2.0299 0.978816
22 to 31 142221 1.0747 0.858751
21 to 30 142527 2.1299 0.983410
20 to 29 142040 0.4506 0.673856
19 to 28 142028 0.4092 0.658806
18 to 27 141996 0.2989 0.617477
17 to 26 141897 -0.0425 0.483043
16 to 25 142364 1.5678 0.941539
15 to 24 141959 0.1713 0.567997
14 to 23 141755 -0.5322 0.297303
13 to 22 142170 0.8989 0.815637
12 to 21 141711 -0.6839 0.247020
11 to 20 141174 -2.5356 0.005612
10 to 19 141567 -1.1804 0.118911
9 to 18 141718 -0.6598 0.254704
8 to 17 141750 -0.5494 0.291361
7 to 16 141380 -1.8253 0.033980
6 to 15 141377 -1.8356 0.033207
5 to 14 141713 -0.6770 0.249203
4 to 13 141903 -0.0218 0.491293
3 to 12 142440 1.8299 0.966367
2 to 11 141971 0.2127 0.584202
1 to 10 142163 0.8747 0.809138
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_15:31
Bits used No. missing words z-score p-value
28 to 32 141618 -0.9876 0.161684
27 to 31 141545 -1.2350 0.108412
26 to 30 141987 0.2633 0.603836
25 to 29 142352 1.5006 0.933267
24 to 28 141935 0.0870 0.534671
23 to 27 142219 1.0497 0.853079
22 to 26 141987 0.2633 0.603836
21 to 25 141921 0.0396 0.515778
20 to 24 142394 1.6429 0.949803
19 to 23 141546 -1.2316 0.109044
18 to 22 141975 0.2226 0.588081
17 to 21 141996 0.2938 0.615543
16 to 20 141803 -0.3604 0.359259
15 to 19 141143 -2.5977 0.004692
14 to 18 142210 1.0192 0.845951
13 to 17 141857 -0.1774 0.429601
12 to 16 141836 -0.2486 0.401844
11 to 15 141787 -0.4147 0.339189
10 to 14 141363 -1.8520 0.032015
9 to 13 141656 -0.8587 0.195240
8 to 12 141665 -0.8282 0.203768
7 to 11 141993 0.2836 0.611652
6 to 10 142049 0.4735 0.682057
5 to 9 142171 0.8870 0.812465
4 to 8 142342 1.4667 0.928768
3 to 7 141895 -0.0486 0.480629
2 to 6 141429 -1.6282 0.051737
1 to 5 142505 2.0192 0.978268
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_15:31
Bits used No. missing words z-score p-value
31 to 32 141991 0.2409 0.595189
30 to 31 140990 -2.7119 0.003345
29 to 30 141633 -0.8151 0.207498
28 to 29 141950 0.1200 0.547747
27 to 28 142830 2.7158 0.996695
26 to 27 141390 -1.5319 0.062768
25 to 26 141718 -0.5644 0.286243
24 to 25 142124 0.6332 0.736713
23 to 24 141909 -0.0010 0.499612
22 to 23 142698 2.3265 0.990003
21 to 22 141746 -0.4818 0.314974
20 to 21 141836 -0.2163 0.414372
19 to 20 142024 0.3383 0.632416
18 to 19 142192 0.8338 0.797813
17 to 18 141901 -0.0246 0.490198
16 to 17 142793 2.6067 0.995429
15 to 16 141795 -0.3373 0.367962
14 to 15 141840 -0.2045 0.418976
13 to 14 142054 0.4268 0.665221
12 to 13 141650 -0.7650 0.222140
11 to 12 141313 -1.7591 0.039282
10 to 11 142187 0.8191 0.793631
9 to 10 142016 0.3147 0.623490
8 to 9 141686 -0.6588 0.255015
7 to 8 142606 2.0551 0.980064
6 to 7 142250 1.0049 0.842534
5 to 6 141473 -1.2871 0.099028
4 to 5 141968 0.1731 0.568701
3 to 4 142954 3.0816 0.998971
2 to 3 142234 0.9577 0.830900
1 to 2 141873 -0.1072 0.457328
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2463.98 -0.509 0.305212
Test results for specific bytes for dh-ranFile-2018-06-27_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2417.39 -1.168 0.121344
2 to 9 2417.95 -1.160 0.122952
3 to 10 2550.77 0.718 0.763599
4 to 11 2410.18 -1.270 0.101990
5 to 12 2424.55 -1.067 0.142986
6 to 13 2535.58 0.503 0.692597
7 to 14 2537.73 0.534 0.703161
8 to 15 2456.64 -0.613 0.269861
9 to 16 2560.31 0.853 0.803136
10 to 17 2559.28 0.838 0.799095
11 to 18 2344.54 -2.198 0.013957
12 to 19 2508.00 0.113 0.545047
13 to 20 2558.46 0.827 0.795819
14 to 21 2500.81 0.011 0.504558
15 to 22 2529.94 0.423 0.663983
16 to 23 2450.38 -0.702 0.241433
17 to 24 2487.17 -0.181 0.428001
18 to 25 2468.75 -0.442 0.329289
19 to 26 2590.00 1.273 0.898444
20 to 27 2479.60 -0.289 0.386461
21 to 28 2412.37 -1.239 0.107614
22 to 29 2583.44 1.180 0.881014
23 to 30 2511.49 0.163 0.564554
24 to 31 2453.74 -0.654 0.256481
25 to 32 2471.05 -0.409 0.341143
CDPARK for dh-ranFile-2018-06-27_15:31: 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
3537 0.6393 0.738676
3498 -1.1416 0.126820
3530 0.3196 0.625377
3507 -0.7306 0.232514
3525 0.0913 0.536383
3487 -1.6438 0.050105
3519 -0.1826 0.427537
3550 1.2329 0.891189
3506 -0.7763 0.218799
3501 -1.0046 0.157553
Square side=100, avg. no. parked=3516.00 sample std.=18.58
p-value of the KSTEST for those 10 p-values: 0.514716
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_15:31
0.0055,0.2088,0.2559,0.2561,0.5156,0.3485,0.3128,0.6276,0.1479,0.7650,
The KS test for those 10 p-values: 0.120681
The 3DSPHERES test for dh-ranFile-2018-06-27_15:31
sample no r^3 equiv. uni.
1 3.782 0.118454
2 61.226 0.870083
3 19.108 0.471092
4 7.078 0.210169
5 14.369 0.380579
6 73.576 0.913924
7 67.700 0.895302
8 0.947 0.031060
9 11.034 0.307749
10 38.098 0.719153
11 62.828 0.876841
12 62.344 0.874837
13 19.289 0.474271
14 12.786 0.347009
15 33.016 0.667311
16 55.907 0.844880
17 34.539 0.683779
18 36.597 0.704744
19 78.115 0.926011
20 6.662 0.199127
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.313624
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.3 -1.1 -0.4 0.9 0.0
-0.2 -1.6 1.1 -0.3 -1.2 1.0
-0.2 3.7 -0.6 0.3 -0.4 -0.2
-0.0 0.7 -0.8 -2.0 -1.0 -0.1
0.6 1.7 0.2 -0.7 -0.4 -0.7
-0.5 -0.2 -0.5 1.0 0.8 -0.5
-0.5 0.2 0.9 -0.1 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:41.623911
z-score=-0.041035, p-value=0.512651
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_15:31
Test no p-value
1 0.651906
2 0.014328
3 0.114980
4 0.524187
5 0.042477
6 0.036188
7 0.121511
8 0.519091
9 0.004636
10 0.208469
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000837
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_15:31:
(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 66753 0.11 66419 0.92
3 25000.00 24971 0.03 25096 0.37
4 6666.67 6674 0.01 6689 0.07
5 1388.89 1353 0.93 1501 9.05
6 238.10 231 0.21 262 2.40
7 34.72 16 10.09 30 0.64
8 4.96 1 3.16 2 1.77
p=0.97591 p=0.98140
Number of rngs required: 688845, p-value: 0.695
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_15:31
No. of wins: Observed Expected
98710 98585.9
z-score= 0.555, pvalue=0.71063
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66812 66666.7 0.317 0.317
2 37496 37654.3 0.666 0.983
3 27022 26954.7 0.168 1.150
4 19423 19313.5 0.621 1.772
5 13866 13851.4 0.015 1.787
6 9779 9943.5 2.723 4.510
7 7282 7145.0 2.626 7.136
8 5072 5139.1 0.875 8.011
9 3670 3699.9 0.241 8.252
10 2686 2666.3 0.146 8.398
11 1885 1923.3 0.764 9.162
12 1432 1388.7 1.348 10.509
13 1004 1003.7 0.000 10.509
14 727 726.1 0.001 10.510
15 478 525.8 4.352 14.862
16 369 381.2 0.387 15.249
17 293 276.5 0.980 16.229
18 190 200.8 0.584 16.813
19 128 146.0 2.216 19.029
20 111 106.2 0.216 19.244
21 275 287.1 0.511 19.755
Chisq= 19.76 for 20 degrees of freedom, p= 0.52667
SUMMARY of craptest
p-value for no. of wins: 0.710632
p-value for throws/game: 0.526669
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_15:31
No. of wins: Observed Expected
98859 98585.9
z-score= 1.222, pvalue=0.88908
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66626 66666.7 0.025 0.025
2 37588 37654.3 0.117 0.142
3 27118 26954.7 0.989 1.131
4 19558 19313.5 3.096 4.227
5 13677 13851.4 2.196 6.423
6 9906 9943.5 0.142 6.565
7 7108 7145.0 0.192 6.757
8 5162 5139.1 0.102 6.859
9 3722 3699.9 0.132 6.991
10 2664 2666.3 0.002 6.993
11 1843 1923.3 3.355 10.348
12 1413 1388.7 0.424 10.772
13 968 1003.7 1.271 12.043
14 737 726.1 0.162 12.205
15 489 525.8 2.580 14.786
16 405 381.2 1.492 16.278
17 275 276.5 0.009 16.287
18 201 200.8 0.000 16.287
19 145 146.0 0.007 16.294
20 120 106.2 1.789 18.083
21 275 287.1 0.511 18.594
Chisq= 18.59 for 20 degrees of freedom, p= 0.45164
SUMMARY of craptest
p-value for no. of wins: 0.889080
p-value for throws/game: 0.451638
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0008,0.0033,0.0046,0.0047,0.0055,0.0056,0.0062,0.0140,0.0143,
0.0210,0.0311,0.0320,0.0332,0.0340,0.0361,0.0362,0.0368,0.0393,0.0398,
0.0425,0.0457,0.0501,0.0517,0.0557,0.0628,0.0819,0.0990,0.1020,0.1076,
0.1084,0.1090,0.1099,0.1150,0.1185,0.1188,0.1189,0.1207,0.1213,0.1215,
0.1230,0.1248,0.1268,0.1372,0.1430,0.1440,0.1479,0.1576,0.1617,0.1675,
0.1952,0.1991,0.2024,0.2026,0.2038,0.2075,0.2085,0.2088,0.2102,0.2139,
0.2161,0.2170,0.2188,0.2207,0.2221,0.2325,0.2414,0.2470,0.2492,0.2547,
0.2547,0.2550,0.2559,0.2561,0.2565,0.2678,0.2699,0.2792,0.2862,0.2896,
0.2914,0.2973,0.3052,0.3077,0.3128,0.3136,0.3150,0.3263,0.3293,0.3392,
0.3411,0.3442,0.3470,0.3485,0.3514,0.3593,0.3680,0.3768,0.3806,0.3865,
0.3928,0.4001,0.4018,0.4095,0.4107,0.4142,0.4144,0.4144,0.4190,0.4195,
0.4201,0.4275,0.4280,0.4291,0.4296,0.4480,0.4516,0.4573,0.4711,0.4729,
0.4743,0.4802,0.4806,0.4830,0.4900,0.4902,0.4913,0.4940,0.4956,0.4996,
0.4997,0.5046,0.5127,0.5147,0.5156,0.5158,0.5191,0.5242,0.5267,0.5295,
0.5347,0.5364,0.5367,0.5450,0.5477,0.5528,0.5545,0.5646,0.5680,0.5687,
0.5744,0.5842,0.5881,0.5882,0.5949,0.5952,0.6026,0.6038,0.6038,0.6117,
0.6155,0.6175,0.6210,0.6235,0.6254,0.6256,0.6276,0.6324,0.6519,0.6588,
0.6640,0.6652,0.6654,0.6673,0.6739,0.6745,0.6771,0.6821,0.6838,0.6869,
0.6926,0.6948,0.7025,0.7025,0.7032,0.7047,0.7106,0.7141,0.7192,0.7207,
0.7217,0.7367,0.7387,0.7429,0.7478,0.7512,0.7516,0.7636,0.7639,0.7650,
0.7716,0.7788,0.7849,0.7936,0.7958,0.7978,0.7991,0.8031,0.8074,0.8091,
0.8106,0.8125,0.8156,0.8309,0.8425,0.8449,0.8460,0.8479,0.8531,0.8536,
0.8538,0.8588,0.8670,0.8673,0.8676,0.8680,0.8701,0.8744,0.8748,0.8768,
0.8810,0.8891,0.8912,0.8953,0.8976,0.8984,0.9033,0.9035,0.9062,0.9093,
0.9094,0.9099,0.9139,0.9175,0.9242,0.9260,0.9264,0.9288,0.9295,0.9333,
0.9415,0.9438,0.9462,0.9485,0.9498,0.9664,0.9691,0.9721,0.9759,0.9783,
0.9788,0.9801,0.9814,0.9834,0.9846,0.9900,0.9954,0.9967,0.9990,
Overall p-value after applying KStest on 269 p-values = 0.317296
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.