RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.65 25.8197 0.922192
2 to 25 15.58 14.5746 0.373910
3 to 26 16.02 19.5168 0.700316
4 to 27 15.58 24.9827 0.904903
5 to 28 15.64 19.2351 0.684796
6 to 29 15.84 11.7242 0.183457
7 to 30 15.84 24.8603 0.902119
8 to 31 15.68 13.8152 0.319861
9 to 32 15.72 13.1029 0.270730
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.485503
Tough bday spacings test for dh-ranFile-2018-06-23_18:31: 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 12 31 72 95 98 76 57 28 19 10 2
(O-E)^2/E 0.9 0.9 0.0 0.1 0.0 0.1 0.5 0.1 1.1 1.7 1.0
Birthday Spacings: Sum(O-E)^2/E= 6.389, p= 0.218
RESULTS OF GCD FOR dh-ranFile-2018-06-23_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.257215
p-value, dist. of gcd's: 0.035909
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.943 0.816 0.702 0.401 0.967 0.609 0.854 0.443
Bits 8 to 15---> 0.837 0.026 0.503 0.181 0.906 0.398 0.494 0.443
Bits 16 to 23---> 0.734 0.064 0.216 0.625 0.809 0.054 0.053 0.793
Bits 24 to 31---> 0.849 0.482 0.899 0.635 0.332 0.623 0.575 0.659
KS test for the above 32 p values: 0.668
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_18:31,
p-values for 5 runs: 0.1641, 0.5297, 0.3980, 0.5847, 0.3838
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5147 5134.0 0.033 0.088
r= 30 23165 23103.0 0.166 0.254
r= 31 11480 11551.5 0.443 0.697
chi-square = 0.697 with df = 3; p-value = 0.126
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 212 211.4 0.002 0.002
r= 30 5107 5134.0 0.142 0.144
r= 31 23185 23103.0 0.291 0.434
r= 32 11496 11551.5 0.267 0.701
chi-square = 0.701 with df = 3; p-value = 0.127
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_18:31
b-rank test for bits 1 to 8, p=0.46909
b-rank test for bits 2 to 9, p=0.47096
b-rank test for bits 3 to 10, p=0.48794
b-rank test for bits 4 to 11, p=0.97206
b-rank test for bits 5 to 12, p=0.84752
b-rank test for bits 6 to 13, p=0.36638
b-rank test for bits 7 to 14, p=0.16296
b-rank test for bits 8 to 15, p=0.17630
b-rank test for bits 9 to 16, p=0.52252
b-rank test for bits 10 to 17, p=0.27753
b-rank test for bits 11 to 18, p=0.50691
b-rank test for bits 12 to 19, p=0.81240
b-rank test for bits 13 to 20, p=0.70174
b-rank test for bits 14 to 21, p=0.02791
b-rank test for bits 15 to 22, p=0.34487
b-rank test for bits 16 to 23, p=0.53881
b-rank test for bits 17 to 24, p=0.31793
b-rank test for bits 18 to 25, p=0.06843
b-rank test for bits 19 to 26, p=0.74836
b-rank test for bits 20 to 27, p=0.67440
b-rank test for bits 21 to 28, p=0.28683
b-rank test for bits 22 to 29, p=0.96755
b-rank test for bits 23 to 30, p=0.88061
b-rank test for bits 24 to 31, p=0.60531
b-rank test for bits 25 to 32, p=0.61158
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 = 0.942467
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_18:31
(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 141927 0.04 0.516466
2 141769 -0.33 0.371504
3 141825 -0.20 0.421901
4 141323 -1.37 0.085354
5 142639 1.70 0.955888
6 142303 0.92 0.821159
7 141778 -0.31 0.379480
8 141473 -1.02 0.153992
9 141607 -0.71 0.239976
10 141966 0.13 0.552669
11 141916 0.02 0.506217
12 141745 -0.38 0.350508
13 142131 0.52 0.697743
14 141283 -1.46 0.071681
15 140675 -2.88 0.001964
16 142054 0.34 0.632324
17 141967 0.13 0.553593
18 141721 -0.44 0.329960
19 141685 -0.52 0.300092
20 141264 -1.51 0.065805
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_18:31
Bits used No. missing words z-score p-value
23 to 32 141746 -0.5632 0.286647
22 to 31 141940 0.1058 0.542113
21 to 30 142002 0.3196 0.625346
20 to 29 141687 -0.7667 0.221643
19 to 28 141756 -0.5287 0.298498
18 to 27 142072 0.5609 0.712578
17 to 26 141642 -0.9218 0.178309
16 to 25 141915 0.0196 0.507800
15 to 24 141732 -0.6115 0.270440
14 to 23 141995 0.2954 0.616161
13 to 22 141849 -0.2080 0.417601
12 to 21 141711 -0.6839 0.247020
11 to 20 141857 -0.1804 0.428400
10 to 19 142056 0.5058 0.693487
9 to 18 141699 -0.7253 0.234141
8 to 17 141672 -0.8184 0.206570
7 to 16 141974 0.2230 0.588232
6 to 15 142026 0.4023 0.656272
5 to 14 142286 1.2989 0.903004
4 to 13 141564 -1.1908 0.116867
3 to 12 141675 -0.8080 0.209535
2 to 11 141785 -0.4287 0.334062
1 to 10 141767 -0.4908 0.311786
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_18:31
Bits used No. missing words z-score p-value
28 to 32 141810 -0.3367 0.368167
27 to 31 142247 1.1446 0.873822
26 to 30 141758 -0.5130 0.303982
25 to 29 141685 -0.7604 0.223496
24 to 28 142380 1.5955 0.944699
23 to 27 142166 0.8701 0.807868
22 to 26 142052 0.4836 0.685675
21 to 25 142224 1.0667 0.856941
20 to 24 141965 0.1887 0.574841
19 to 23 142580 2.2735 0.988501
18 to 22 142204 0.9989 0.841074
17 to 21 141938 0.0972 0.538711
16 to 20 142515 2.0531 0.979969
15 to 19 141716 -0.6554 0.256119
14 to 18 141967 0.1955 0.577496
13 to 17 141856 -0.1808 0.428270
12 to 16 141962 0.1785 0.570852
11 to 15 141337 -1.9401 0.026184
10 to 14 141784 -0.4248 0.335474
9 to 13 142093 0.6226 0.733230
8 to 12 142025 0.3921 0.652509
7 to 11 141809 -0.3401 0.366890
6 to 10 141607 -1.0248 0.152718
5 to 9 141638 -0.9198 0.178848
4 to 8 141805 -0.3537 0.361797
3 to 7 141917 0.0260 0.510371
2 to 6 141610 -1.0147 0.155130
1 to 5 142326 1.4124 0.921090
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_18:31
Bits used No. missing words z-score p-value
31 to 32 142428 1.5300 0.936992
30 to 31 142039 0.3825 0.648958
29 to 30 141385 -1.5467 0.060968
28 to 29 142363 1.3383 0.909594
27 to 28 141955 0.1347 0.553583
26 to 27 141941 0.0934 0.537216
25 to 26 141723 -0.5496 0.291281
24 to 25 141909 -0.0010 0.499612
23 to 24 142234 0.9577 0.830900
22 to 23 142263 1.0433 0.851589
21 to 22 141968 0.1731 0.568701
20 to 21 142223 0.9253 0.822590
19 to 20 141404 -1.4906 0.068027
18 to 19 141912 0.0079 0.503142
17 to 18 141797 -0.3314 0.370187
16 to 17 141642 -0.7886 0.215178
15 to 16 141055 -2.5201 0.005865
14 to 15 142217 0.9076 0.817950
13 to 14 142231 0.9489 0.828659
12 to 13 141976 0.1967 0.577956
11 to 12 142165 0.7542 0.774632
10 to 11 141832 -0.2281 0.409780
9 to 10 142593 2.0167 0.978138
8 to 9 142594 2.0197 0.978291
7 to 8 142741 2.4533 0.992922
6 to 7 142137 0.6716 0.749079
5 to 6 142066 0.4622 0.678014
4 to 5 142300 1.1524 0.875426
3 to 4 141884 -0.0747 0.470219
2 to 3 142517 1.7925 0.963477
1 to 2 141218 -2.0393 0.020709
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2455.23 -0.633 0.263319
Test results for specific bytes for dh-ranFile-2018-06-23_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2626.00 1.782 0.962622
2 to 9 2514.64 0.207 0.582004
3 to 10 2445.46 -0.771 0.220276
4 to 11 2534.91 0.494 0.689218
5 to 12 2449.72 -0.711 0.238537
6 to 13 2513.92 0.197 0.578054
7 to 14 2427.71 -1.022 0.153316
8 to 15 2538.87 0.550 0.708739
9 to 16 2488.89 -0.157 0.437549
10 to 17 2491.24 -0.124 0.450729
11 to 18 2660.82 2.274 0.988529
12 to 19 2572.82 1.030 0.848451
13 to 20 2710.60 2.978 0.998551
14 to 21 2655.90 2.205 0.986265
15 to 22 2441.87 -0.822 0.205528
16 to 23 2570.48 0.997 0.840543
17 to 24 2465.68 -0.485 0.313731
18 to 25 2485.72 -0.202 0.419961
19 to 26 2364.57 -1.915 0.027732
20 to 27 2526.48 0.374 0.645966
21 to 28 2465.95 -0.481 0.315091
22 to 29 2620.28 1.701 0.955536
23 to 30 2423.08 -1.088 0.138347
24 to 31 2405.55 -1.336 0.090823
25 to 32 2559.26 0.838 0.799013
CDPARK for dh-ranFile-2018-06-23_18:31: 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
3527 0.1826 0.572463
3535 0.5479 0.708135
3525 0.0913 0.536383
3497 -1.1872 0.117571
3475 -2.1918 0.014198
3567 2.0091 0.977738
3522 -0.0457 0.481790
3522 -0.0457 0.481790
3541 0.8219 0.794438
3503 -0.9132 0.180558
Square side=100, avg. no. parked=3521.40 sample std.=24.04
p-value of the KSTEST for those 10 p-values: 0.916080
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_18:31
0.2952,0.6476,0.7542,0.0738,0.4687,0.4778,0.8894,0.0262,0.2075,0.0353,
The KS test for those 10 p-values: 0.300900
The 3DSPHERES test for dh-ranFile-2018-06-23_18:31
sample no r^3 equiv. uni.
1 15.557 0.404634
2 10.269 0.289872
3 16.103 0.415364
4 46.463 0.787487
5 58.929 0.859748
6 62.524 0.875586
7 44.189 0.770753
8 81.700 0.934344
9 196.182 0.998555
10 3.840 0.120158
11 33.073 0.667933
12 18.865 0.466778
13 57.107 0.850963
14 107.036 0.971784
15 0.885 0.029063
16 39.051 0.727933
17 6.328 0.190179
18 19.853 0.484058
19 26.238 0.582966
20 134.995 0.988889
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.064975
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.7 3.0 -0.4 0.5 -1.5
-0.3 0.4 0.2 -0.1 2.1 -0.8
-1.8 -0.9 1.7 1.2 0.9 1.0
-0.4 -0.4 -0.3 0.3 -1.7 0.3
-2.2 0.2 0.4 -1.0 0.9 -0.4
0.7 -1.0 -0.6 0.5 1.2 0.8
-0.7 0.8 -0.8 -0.1 -1.3 -1.0
-0.1
Chi-square with 42 degrees of freedom:51.334975
z-score=1.018529, p-value=0.846875
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_18:31
Test no p-value
1 0.327165
2 0.701604
3 0.271729
4 0.041745
5 0.107459
6 0.285781
7 0.085522
8 0.000798
9 0.602059
10 0.032625
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.003542
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_18:31:
(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 66369 1.33 66701 0.02
3 25000.00 25364 5.30 25037 0.05
4 6666.67 6619 0.34 6589 0.90
5 1388.89 1367 0.35 1402 0.12
6 238.10 244 0.15 229 0.35
7 34.72 29 0.94 34 0.01
8 4.96 7 0.84 7 0.84
p=0.83962 p=0.11011
Number of rngs required: 687597, p-value: 0.175
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_18:31
No. of wins: Observed Expected
98604 98585.9
z-score= 0.081, pvalue=0.53233
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66749 66666.7 0.102 0.102
2 37737 37654.3 0.182 0.283
3 27094 26954.7 0.720 1.003
4 19111 19313.5 2.122 3.125
5 13923 13851.4 0.370 3.495
6 9831 9943.5 1.274 4.769
7 7196 7145.0 0.364 5.133
8 5123 5139.1 0.050 5.183
9 3702 3699.9 0.001 5.184
10 2678 2666.3 0.051 5.235
11 1833 1923.3 4.242 9.478
12 1396 1388.7 0.038 9.516
13 969 1003.7 1.201 10.716
14 725 726.1 0.002 10.718
15 547 525.8 0.852 11.570
16 398 381.2 0.745 12.315
17 276 276.5 0.001 12.316
18 176 200.8 3.070 15.386
19 138 146.0 0.437 15.822
20 112 106.2 0.315 16.137
21 286 287.1 0.004 16.142
Chisq= 16.14 for 20 degrees of freedom, p= 0.29221
SUMMARY of craptest
p-value for no. of wins: 0.532334
p-value for throws/game: 0.292211
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_18:31
No. of wins: Observed Expected
98296 98585.9
z-score=-1.296, pvalue=0.09742
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66544 66666.7 0.226 0.226
2 37760 37654.3 0.297 0.522
3 27023 26954.7 0.173 0.695
4 19065 19313.5 3.196 3.892
5 13780 13851.4 0.368 4.260
6 9926 9943.5 0.031 4.291
7 7192 7145.0 0.309 4.600
8 5267 5139.1 3.185 7.784
9 3767 3699.9 1.218 9.002
10 2664 2666.3 0.002 9.004
11 1864 1923.3 1.830 10.834
12 1432 1388.7 1.348 12.182
13 1027 1003.7 0.540 12.722
14 743 726.1 0.391 13.114
15 537 525.8 0.237 13.351
16 388 381.2 0.123 13.474
17 257 276.5 1.381 14.854
18 213 200.8 0.737 15.592
19 157 146.0 0.831 16.423
20 99 106.2 0.490 16.913
21 295 287.1 0.217 17.130
Chisq= 17.13 for 20 degrees of freedom, p= 0.35547
SUMMARY of craptest
p-value for no. of wins: 0.097416
p-value for throws/game: 0.355469
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0020,0.0035,0.0059,0.0142,0.0207,0.0260,0.0262,0.0262,0.0277,
0.0279,0.0291,0.0326,0.0353,0.0359,0.0417,0.0531,0.0542,0.0610,0.0638,
0.0650,0.0658,0.0680,0.0684,0.0717,0.0738,0.0854,0.0855,0.0908,0.0974,
0.1075,0.1101,0.1169,0.1176,0.1202,0.1261,0.1271,0.1383,0.1527,0.1533,
0.1540,0.1551,0.1630,0.1641,0.1754,0.1763,0.1783,0.1788,0.1806,0.1809,
0.1835,0.1902,0.2055,0.2066,0.2075,0.2095,0.2152,0.2159,0.2184,0.2203,
0.2216,0.2235,0.2341,0.2385,0.2400,0.2470,0.2561,0.2572,0.2633,0.2704,
0.2707,0.2717,0.2775,0.2858,0.2866,0.2868,0.2899,0.2913,0.2922,0.2952,
0.2985,0.3001,0.3009,0.3040,0.3118,0.3137,0.3151,0.3179,0.3199,0.3272,
0.3300,0.3320,0.3341,0.3355,0.3449,0.3505,0.3555,0.3618,0.3664,0.3669,
0.3682,0.3702,0.3715,0.3739,0.3795,0.3838,0.3979,0.3980,0.4009,0.4046,
0.4098,0.4154,0.4176,0.4200,0.4219,0.4283,0.4284,0.4375,0.4425,0.4431,
0.4507,0.4668,0.4687,0.4691,0.4702,0.4710,0.4778,0.4818,0.4818,0.4819,
0.4841,0.4855,0.4879,0.4936,0.4996,0.5031,0.5031,0.5062,0.5069,0.5078,
0.5104,0.5165,0.5225,0.5297,0.5323,0.5364,0.5372,0.5387,0.5388,0.5421,
0.5527,0.5536,0.5536,0.5687,0.5709,0.5725,0.5748,0.5751,0.5775,0.5780,
0.5781,0.5820,0.5830,0.5847,0.5882,0.6021,0.6053,0.6085,0.6116,0.6162,
0.6235,0.6250,0.6253,0.6323,0.6351,0.6460,0.6476,0.6490,0.6525,0.6563,
0.6592,0.6678,0.6679,0.6744,0.6780,0.6848,0.6857,0.6892,0.6935,0.6977,
0.7003,0.7016,0.7017,0.7024,0.7081,0.7087,0.7126,0.7279,0.7332,0.7342,
0.7484,0.7491,0.7542,0.7708,0.7746,0.7875,0.7932,0.7944,0.7990,0.8079,
0.8085,0.8124,0.8158,0.8180,0.8212,0.8226,0.8287,0.8309,0.8375,0.8396,
0.8405,0.8411,0.8469,0.8475,0.8485,0.8494,0.8510,0.8516,0.8544,0.8569,
0.8597,0.8738,0.8754,0.8756,0.8806,0.8894,0.8991,0.9021,0.9030,0.9049,
0.9056,0.9096,0.9161,0.9211,0.9222,0.9343,0.9370,0.9425,0.9427,0.9447,
0.9555,0.9559,0.9626,0.9635,0.9674,0.9676,0.9718,0.9721,0.9777,0.9781,
0.9783,0.9800,0.9863,0.9885,0.9885,0.9889,0.9929,0.9986,0.9986,
Overall p-value after applying KStest on 269 p-values = 0.819135
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.