RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_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 15.87 7.6097 0.025803
2 to 25 15.45 34.2695 0.992252
3 to 26 15.59 18.8490 0.662734
4 to 27 15.79 8.4862 0.044982
5 to 28 15.98 19.8310 0.717037
6 to 29 15.81 16.7570 0.529054
7 to 30 15.83 18.6927 0.653549
8 to 31 15.89 20.3427 0.742923
9 to 32 15.64 14.7831 0.388899
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.529443
Tough bday spacings test for dh-ranFile-2018-06-21_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 6 38 63 106 105 68 66 33 11 3 1
(O-E)^2/E 1.1 0.1 1.4 0.7 0.5 1.3 3.7 0.4 1.0 2.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 14.513, p= 0.849
RESULTS OF GCD FOR dh-ranFile-2018-06-21_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.128096
p-value, dist. of gcd's: 0.757286
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.796 0.514 0.051 0.110 0.302 0.774 0.900 0.002
Bits 8 to 15---> 0.194 0.709 0.618 0.509 0.396 0.393 0.552 0.197
Bits 16 to 23---> 0.628 0.252 0.368 0.899 0.565 0.344 0.474 0.114
Bits 24 to 31---> 0.458 0.696 0.454 0.533 0.265 0.073 0.737 0.065
KS test for the above 32 p values: 0.726
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_08:31,
p-values for 5 runs: 0.2474, 0.1194, 0.2292, 0.3680, 0.5969
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 203 211.4 0.335 0.335
r= 29 5195 5134.0 0.725 1.060
r= 30 23061 23103.0 0.077 1.136
r= 31 11541 11551.5 0.010 1.146
chi-square = 1.146 with df = 3; p-value = 0.234
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 186 211.4 3.056 3.056
r= 30 5135 5134.0 0.000 3.056
r= 31 23112 23103.0 0.003 3.060
r= 32 11567 11551.5 0.021 3.080
chi-square = 3.080 with df = 3; p-value = 0.621
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_08:31
b-rank test for bits 1 to 8, p=0.38709
b-rank test for bits 2 to 9, p=0.52341
b-rank test for bits 3 to 10, p=0.73774
b-rank test for bits 4 to 11, p=0.02809
b-rank test for bits 5 to 12, p=0.62241
b-rank test for bits 6 to 13, p=0.23278
b-rank test for bits 7 to 14, p=0.75446
b-rank test for bits 8 to 15, p=0.11763
b-rank test for bits 9 to 16, p=0.27040
b-rank test for bits 10 to 17, p=0.36269
b-rank test for bits 11 to 18, p=0.73886
b-rank test for bits 12 to 19, p=0.81464
b-rank test for bits 13 to 20, p=0.61568
b-rank test for bits 14 to 21, p=0.17972
b-rank test for bits 15 to 22, p=0.45243
b-rank test for bits 16 to 23, p=0.36662
b-rank test for bits 17 to 24, p=0.81753
b-rank test for bits 18 to 25, p=0.92471
b-rank test for bits 19 to 26, p=0.13469
b-rank test for bits 20 to 27, p=0.95962
b-rank test for bits 21 to 28, p=0.06157
b-rank test for bits 22 to 29, p=0.27168
b-rank test for bits 23 to 30, p=0.82160
b-rank test for bits 24 to 31, p=0.08331
b-rank test for bits 25 to 32, p=0.67764
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 = 0.972405
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_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 142749 1.96 0.975110
2 141293 -1.44 0.074930
3 141561 -0.81 0.207864
4 141441 -1.09 0.136927
5 141955 0.11 0.542489
6 142281 0.87 0.807409
7 142225 0.74 0.769605
8 141297 -1.43 0.076261
9 142191 0.66 0.744765
10 141937 0.06 0.525774
11 141683 -0.53 0.298469
12 142129 0.51 0.696111
13 142152 0.57 0.714638
14 142805 2.09 0.981811
15 141603 -0.72 0.237081
16 141353 -1.30 0.096829
17 142203 0.69 0.753689
18 142068 0.37 0.644579
19 141978 0.16 0.563734
20 142700 1.85 0.967653
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_08:31
Bits used No. missing words z-score p-value
23 to 32 141893 -0.0563 0.477547
22 to 31 142261 1.2127 0.887369
21 to 30 142580 2.3127 0.989629
20 to 29 142135 0.7782 0.781766
19 to 28 142035 0.4333 0.667618
18 to 27 142176 0.9196 0.821097
17 to 26 141827 -0.2839 0.388245
16 to 25 142121 0.7299 0.767273
15 to 24 141850 -0.2046 0.418948
14 to 23 141766 -0.4942 0.310568
13 to 22 142134 0.7747 0.780749
12 to 21 142101 0.6609 0.745672
11 to 20 142096 0.6437 0.740112
10 to 19 141925 0.0540 0.521546
9 to 18 141848 -0.2115 0.416255
8 to 17 142447 1.8540 0.968133
7 to 16 141386 -1.8046 0.035570
6 to 15 141846 -0.2184 0.413567
5 to 14 141624 -0.9839 0.162583
4 to 13 142299 1.3437 0.910476
3 to 12 141968 0.2023 0.580163
2 to 11 141851 -0.2011 0.420295
1 to 10 142242 1.1471 0.874338
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_08:31
Bits used No. missing words z-score p-value
28 to 32 142269 1.2192 0.888620
27 to 31 141842 -0.2282 0.409731
26 to 30 141874 -0.1198 0.452336
25 to 29 142246 1.1413 0.873118
24 to 28 141711 -0.6723 0.250695
23 to 27 141234 -2.2893 0.011032
22 to 26 141636 -0.9265 0.177082
21 to 25 141266 -2.1808 0.014600
20 to 24 142355 1.5107 0.934573
19 to 23 141749 -0.5435 0.293396
18 to 22 142232 1.0938 0.862978
17 to 21 141684 -0.7638 0.222484
16 to 20 142091 0.6158 0.730997
15 to 19 141819 -0.3062 0.379725
14 to 18 141822 -0.2960 0.383602
13 to 17 142112 0.6870 0.753964
12 to 16 141805 -0.3537 0.361797
11 to 15 141928 0.0633 0.525232
10 to 14 142118 0.7074 0.760327
9 to 13 142019 0.3718 0.644965
8 to 12 141833 -0.2587 0.397916
7 to 11 142340 1.4599 0.927841
6 to 10 141888 -0.0723 0.471180
5 to 9 142007 0.3311 0.629710
4 to 8 141945 0.1209 0.548121
3 to 7 142042 0.4497 0.673547
2 to 6 142304 1.3379 0.909530
1 to 5 142078 0.5718 0.716259
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_08:31
Bits used No. missing words z-score p-value
31 to 32 142133 0.6598 0.745307
30 to 31 142548 1.8840 0.970216
29 to 30 141826 -0.2458 0.402914
28 to 29 141575 -0.9862 0.162012
27 to 28 141560 -1.0305 0.151394
26 to 27 141257 -1.9243 0.027160
25 to 26 141580 -0.9715 0.165656
24 to 25 141426 -1.4258 0.076970
23 to 24 142265 1.0492 0.852951
22 to 23 141308 -1.7738 0.038045
21 to 22 141811 -0.2901 0.385886
20 to 21 141442 -1.3786 0.084016
19 to 20 142282 1.0993 0.864186
18 to 19 141631 -0.8210 0.205814
17 to 18 142573 1.9577 0.974869
16 to 17 142060 0.4445 0.671643
15 to 16 142140 0.6804 0.751888
14 to 15 140921 -2.9154 0.001776
13 to 14 142483 1.6922 0.954700
12 to 13 141845 -0.1898 0.424747
11 to 12 142158 0.7335 0.768385
10 to 11 142517 1.7925 0.963477
9 to 10 141400 -1.5024 0.066491
8 to 9 141643 -0.7856 0.216041
7 to 8 141967 0.1701 0.567541
6 to 7 141796 -0.3343 0.369074
5 to 6 141803 -0.3137 0.376891
4 to 5 142158 0.7335 0.768385
3 to 4 141757 -0.4494 0.326589
2 to 3 142135 0.6657 0.747196
1 to 2 141780 -0.3815 0.351415
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2462.43 -0.531 0.297590
Test results for specific bytes for dh-ranFile-2018-06-21_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2384.50 -1.633 0.051189
2 to 9 2533.70 0.477 0.683179
3 to 10 2518.33 0.259 0.602284
4 to 11 2408.07 -1.300 0.096790
5 to 12 2497.18 -0.040 0.484069
6 to 13 2532.87 0.465 0.678990
7 to 14 2455.40 -0.631 0.264086
8 to 15 2358.27 -2.004 0.022518
9 to 16 2472.89 -0.383 0.350728
10 to 17 2529.08 0.411 0.659562
11 to 18 2422.94 -1.090 0.137913
12 to 19 2415.19 -1.199 0.115183
13 to 20 2512.17 0.172 0.568319
14 to 21 2449.42 -0.715 0.237210
15 to 22 2423.56 -1.081 0.139844
16 to 23 2479.25 -0.293 0.384597
17 to 24 2466.31 -0.476 0.316872
18 to 25 2466.62 -0.472 0.318417
19 to 26 2422.22 -1.100 0.135662
20 to 27 2490.53 -0.134 0.446754
21 to 28 2411.60 -1.250 0.105612
22 to 29 2442.76 -0.810 0.209108
23 to 30 2432.84 -0.950 0.171108
24 to 31 2512.32 0.174 0.569170
25 to 32 2570.93 1.003 0.842106
CDPARK for dh-ranFile-2018-06-21_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
3566 1.9635 0.975204
3514 -0.4110 0.340551
3543 0.9132 0.819442
3551 1.2785 0.899470
3477 -2.1005 0.017844
3534 0.5023 0.692266
3548 1.1416 0.873180
3551 1.2785 0.899470
3500 -1.0502 0.146807
3576 2.4201 0.992242
Square side=100, avg. no. parked=3536.00 sample std.=29.00
p-value of the KSTEST for those 10 p-values: 0.027025
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_08:31
0.1029,0.3545,0.8925,0.6698,0.9600,0.8665,0.4827,0.9614,0.7383,0.2789,
The KS test for those 10 p-values: 0.216325
The 3DSPHERES test for dh-ranFile-2018-06-21_08:31
sample no r^3 equiv. uni.
1 42.011 0.753497
2 38.255 0.720617
3 8.809 0.254460
4 8.837 0.255151
5 32.598 0.662640
6 20.157 0.489261
7 13.357 0.359336
8 31.258 0.647224
9 7.844 0.230079
10 112.718 0.976653
11 14.852 0.390461
12 26.007 0.579754
13 8.383 0.243786
14 44.074 0.769872
15 6.517 0.195257
16 143.702 0.991688
17 24.100 0.552167
18 56.483 0.847832
19 7.997 0.234004
20 76.851 0.922827
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.461910
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 1.5 -0.7 0.8 1.7
1.0 -0.7 -0.9 1.6 -1.1 -2.1
0.3 0.9 -0.2 -0.2 0.4 0.1
0.4 1.2 -0.0 -0.4 -0.5 -0.4
-1.4 0.7 -0.1 0.1 0.4 1.0
-1.3 -0.5 0.7 0.3 -0.1 0.2
0.3 -0.7 -0.4 -0.1 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:29.220654
z-score=-1.394341, p-value=0.067726
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_08:31
Test no p-value
1 0.055438
2 0.661217
3 0.012478
4 0.517844
5 0.148473
6 0.275390
7 0.060658
8 0.107262
9 0.567844
10 0.065888
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004213
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_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 66499 0.42 66741 0.08
3 25000.00 25251 2.52 24929 0.20
4 6666.67 6596 0.75 6631 0.19
5 1388.89 1365 0.41 1380 0.06
6 238.10 251 0.70 273 5.12
7 34.72 31 0.40 40 0.80
8 4.96 6 0.22 5 0.00
p=0.50856 p=0.62556
Number of rngs required: 688752, p-value: 0.656
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_08:31
No. of wins: Observed Expected
98518 98585.9
z-score=-0.304, pvalue=0.38075
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66615 66666.7 0.040 0.040
2 37885 37654.3 1.413 1.453
3 27073 26954.7 0.519 1.972
4 19011 19313.5 4.737 6.709
5 13983 13851.4 1.250 7.959
6 9698 9943.5 6.063 14.022
7 7156 7145.0 0.017 14.039
8 5133 5139.1 0.007 14.046
9 3701 3699.9 0.000 14.047
10 2793 2666.3 6.021 20.068
11 1877 1923.3 1.116 21.183
12 1415 1388.7 0.497 21.680
13 989 1003.7 0.216 21.896
14 716 726.1 0.142 22.037
15 510 525.8 0.477 22.514
16 382 381.2 0.002 22.516
17 288 276.5 0.475 22.991
18 187 200.8 0.952 23.944
19 164 146.0 2.223 26.167
20 106 106.2 0.000 26.167
21 318 287.1 3.323 29.490
Chisq= 29.49 for 20 degrees of freedom, p= 0.92145
SUMMARY of craptest
p-value for no. of wins: 0.380753
p-value for throws/game: 0.921446
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_08:31
No. of wins: Observed Expected
98996 98585.9
z-score= 1.834, pvalue=0.96670
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66958 66666.7 1.273 1.273
2 37491 37654.3 0.708 1.982
3 26869 26954.7 0.273 2.254
4 19186 19313.5 0.841 3.095
5 14016 13851.4 1.956 5.051
6 10029 9943.5 0.734 5.785
7 7106 7145.0 0.213 5.998
8 5161 5139.1 0.094 6.092
9 3605 3699.9 2.432 8.524
10 2648 2666.3 0.126 8.650
11 1906 1923.3 0.156 8.806
12 1374 1388.7 0.156 8.963
13 1052 1003.7 2.323 11.285
14 715 726.1 0.171 11.456
15 521 525.8 0.044 11.501
16 391 381.2 0.255 11.755
17 273 276.5 0.045 11.801
18 187 200.8 0.952 12.753
19 128 146.0 2.216 14.969
20 118 106.2 1.308 16.276
21 266 287.1 1.553 17.829
Chisq= 17.83 for 20 degrees of freedom, p= 0.40131
SUMMARY of craptest
p-value for no. of wins: 0.966702
p-value for throws/game: 0.401313
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0021,0.0042,0.0110,0.0125,0.0146,0.0178,0.0225,0.0258,0.0270,
0.0272,0.0281,0.0356,0.0380,0.0450,0.0508,0.0512,0.0554,0.0607,0.0616,
0.0650,0.0659,0.0665,0.0677,0.0729,0.0749,0.0763,0.0770,0.0833,0.0840,
0.0968,0.0968,0.1029,0.1056,0.1073,0.1104,0.1141,0.1152,0.1176,0.1194,
0.1281,0.1347,0.1357,0.1369,0.1379,0.1398,0.1468,0.1485,0.1514,0.1620,
0.1626,0.1657,0.1711,0.1771,0.1797,0.1937,0.1953,0.1974,0.2058,0.2079,
0.2091,0.2160,0.2163,0.2225,0.2292,0.2301,0.2328,0.2340,0.2340,0.2371,
0.2372,0.2438,0.2474,0.2507,0.2521,0.2545,0.2552,0.2641,0.2653,0.2704,
0.2717,0.2754,0.2789,0.2934,0.2976,0.2985,0.3018,0.3106,0.3169,0.3184,
0.3266,0.3406,0.3438,0.3507,0.3514,0.3545,0.3593,0.3618,0.3627,0.3666,
0.3678,0.3680,0.3691,0.3769,0.3797,0.3808,0.3836,0.3846,0.3859,0.3871,
0.3882,0.3889,0.3905,0.3931,0.3957,0.3979,0.4013,0.4029,0.4097,0.4136,
0.4163,0.4189,0.4203,0.4247,0.4468,0.4523,0.4524,0.4536,0.4579,0.4619,
0.4712,0.4745,0.4775,0.4827,0.4841,0.4893,0.5086,0.5095,0.5143,0.5178,
0.5215,0.5234,0.5252,0.5258,0.5291,0.5294,0.5330,0.5425,0.5481,0.5517,
0.5522,0.5637,0.5646,0.5675,0.5678,0.5683,0.5692,0.5798,0.5802,0.5969,
0.6023,0.6157,0.6183,0.6206,0.6224,0.6256,0.6283,0.6297,0.6446,0.6450,
0.6472,0.6535,0.6561,0.6596,0.6612,0.6626,0.6627,0.6676,0.6698,0.6716,
0.6735,0.6776,0.6790,0.6832,0.6923,0.6956,0.6961,0.7089,0.7146,0.7163,
0.7170,0.7206,0.7261,0.7310,0.7374,0.7377,0.7383,0.7389,0.7401,0.7429,
0.7448,0.7453,0.7457,0.7472,0.7519,0.7535,0.7537,0.7540,0.7545,0.7573,
0.7603,0.7673,0.7684,0.7684,0.7696,0.7699,0.7744,0.7807,0.7818,0.7957,
0.8074,0.8146,0.8175,0.8194,0.8211,0.8216,0.8421,0.8478,0.8492,0.8530,
0.8630,0.8642,0.8665,0.8731,0.8732,0.8743,0.8874,0.8886,0.8925,0.8990,
0.8995,0.8995,0.9000,0.9095,0.9105,0.9214,0.9228,0.9247,0.9278,0.9346,
0.9547,0.9596,0.9600,0.9614,0.9635,0.9667,0.9677,0.9681,0.9702,0.9724,
0.9749,0.9751,0.9752,0.9767,0.9818,0.9896,0.9917,0.9922,0.9923,
Overall p-value after applying KStest on 269 p-values = 0.711229
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.