RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.39 29.1580 0.966903
2 to 25 15.82 21.0870 0.777578
3 to 26 15.90 19.2181 0.683843
4 to 27 15.67 18.3106 0.630498
5 to 28 15.86 7.8175 0.029705
6 to 29 15.86 9.3335 0.070786
7 to 30 15.74 22.9188 0.848087
8 to 31 15.77 14.0330 0.335236
9 to 32 15.68 8.1074 0.035804
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.411004
Tough bday spacings test for dh-ranFile-2018-06-25_11:31: 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 7 39 75 103 111 70 47 21 16 10 1
(O-E)^2/E 0.5 0.2 0.0 0.3 1.8 0.8 0.5 2.6 0.1 1.7 2.3
Birthday Spacings: Sum(O-E)^2/E= 10.866, p= 0.632
RESULTS OF GCD FOR dh-ranFile-2018-06-25_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.620655
p-value, dist. of gcd's: 0.234352
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.403 0.647 0.287 0.129 0.671 0.349 0.271 0.917
Bits 8 to 15---> 0.229 0.393 0.688 0.881 0.492 0.844 0.267 0.428
Bits 16 to 23---> 0.889 0.802 0.640 0.530 0.607 0.423 0.156 0.185
Bits 24 to 31---> 0.806 0.767 0.322 0.102 0.231 0.301 0.240 0.286
KS test for the above 32 p values: 0.614
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_11:31,
p-values for 5 runs: 0.1426, 0.6342, 0.1207, 0.3459, 0.7115
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5044 5134.0 1.578 2.430
r= 30 23204 23103.0 0.441 2.871
r= 31 11554 11551.5 0.001 2.871
chi-square = 2.871 with df = 3; p-value = 0.588
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 216 211.4 0.099 0.099
r= 30 5058 5134.0 1.125 1.225
r= 31 23166 23103.0 0.172 1.396
r= 32 11560 11551.5 0.006 1.402
chi-square = 1.402 with df = 3; p-value = 0.295
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_11:31
b-rank test for bits 1 to 8, p=0.46311
b-rank test for bits 2 to 9, p=0.56649
b-rank test for bits 3 to 10, p=0.91643
b-rank test for bits 4 to 11, p=0.57913
b-rank test for bits 5 to 12, p=0.27955
b-rank test for bits 6 to 13, p=0.60241
b-rank test for bits 7 to 14, p=0.53746
b-rank test for bits 8 to 15, p=0.72548
b-rank test for bits 9 to 16, p=0.62393
b-rank test for bits 10 to 17, p=0.16908
b-rank test for bits 11 to 18, p=0.33806
b-rank test for bits 12 to 19, p=0.03312
b-rank test for bits 13 to 20, p=0.39255
b-rank test for bits 14 to 21, p=0.00993
b-rank test for bits 15 to 22, p=0.03766
b-rank test for bits 16 to 23, p=0.21431
b-rank test for bits 17 to 24, p=0.32230
b-rank test for bits 18 to 25, p=0.91038
b-rank test for bits 19 to 26, p=0.97226
b-rank test for bits 20 to 27, p=0.50269
b-rank test for bits 21 to 28, p=0.05091
b-rank test for bits 22 to 29, p=0.58512
b-rank test for bits 23 to 30, p=0.60817
b-rank test for bits 24 to 31, p=0.67010
b-rank test for bits 25 to 32, p=0.17436
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 = 0.493531
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_11:31
(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 142227 0.74 0.771023
2 141937 0.06 0.525774
3 142876 2.26 0.988045
4 142671 1.78 0.962430
5 141826 -0.19 0.422815
6 142394 1.13 0.871268
7 141877 -0.08 0.469894
8 142465 1.30 0.902907
9 141862 -0.11 0.455973
10 141557 -0.82 0.205197
11 141803 -0.25 0.401899
12 142418 1.19 0.882678
13 142209 0.70 0.758087
14 141992 0.19 0.576581
15 141160 -1.75 0.039993
16 141925 0.04 0.514603
17 142563 1.53 0.936653
18 141599 -0.73 0.234205
19 141983 0.17 0.568331
20 141764 -0.34 0.367095
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_11:31
Bits used No. missing words z-score p-value
23 to 32 142077 0.5782 0.718426
22 to 31 142411 1.7299 0.958176
21 to 30 142322 1.4230 0.922632
20 to 29 141689 -0.7598 0.223699
19 to 28 141484 -1.4667 0.071235
18 to 27 141551 -1.2356 0.108300
17 to 26 142011 0.3506 0.637051
16 to 25 141366 -1.8736 0.030496
15 to 24 141066 -2.9080 0.001819
14 to 23 141793 -0.4011 0.344159
13 to 22 141515 -1.3598 0.086953
12 to 21 141574 -1.1563 0.123777
11 to 20 141722 -0.6460 0.259151
10 to 19 141801 -0.3736 0.354369
9 to 18 141898 -0.0391 0.484418
8 to 17 141830 -0.2736 0.392215
7 to 16 141921 0.0402 0.516050
6 to 15 142250 1.1747 0.879947
5 to 14 141796 -0.3908 0.347975
4 to 13 142588 2.3402 0.990364
3 to 12 141964 0.1885 0.574764
2 to 11 141794 -0.3977 0.345430
1 to 10 141505 -1.3942 0.081622
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_11:31
Bits used No. missing words z-score p-value
28 to 32 142098 0.6396 0.738770
27 to 31 141486 -1.4350 0.075641
26 to 30 141324 -1.9842 0.023618
25 to 29 142175 0.9006 0.816093
24 to 28 141460 -1.5232 0.063860
23 to 27 142324 1.4057 0.920088
22 to 26 141798 -0.3774 0.352942
21 to 25 142103 0.6565 0.744252
20 to 24 142161 0.8531 0.803203
19 to 23 142190 0.9514 0.829305
18 to 22 141278 -2.1401 0.016173
17 to 21 141462 -1.5164 0.064713
16 to 20 141809 -0.3401 0.366890
15 to 19 141769 -0.4757 0.317146
14 to 18 141881 -0.0960 0.461747
13 to 17 141533 -1.2757 0.101032
12 to 16 141764 -0.4926 0.311132
11 to 15 141570 -1.1503 0.125016
10 to 14 141888 -0.0723 0.471180
9 to 13 142006 0.3277 0.628429
8 to 12 141473 -1.4791 0.069559
7 to 11 141860 -0.1672 0.433598
6 to 10 141634 -0.9333 0.175327
5 to 9 141456 -1.5367 0.062182
4 to 8 141244 -2.2554 0.012056
3 to 7 141830 -0.2689 0.393998
2 to 6 142111 0.6836 0.752895
1 to 5 142105 0.6633 0.746427
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_11:31
Bits used No. missing words z-score p-value
31 to 32 141903 -0.0187 0.492551
30 to 31 141857 -0.1544 0.438661
29 to 30 142393 1.4268 0.923175
28 to 29 141498 -1.2134 0.112496
27 to 28 142042 0.3914 0.652233
26 to 27 141617 -0.8623 0.194253
25 to 26 141728 -0.5349 0.296361
24 to 25 141481 -1.2635 0.103203
23 to 24 141354 -1.6381 0.050696
22 to 23 141637 -0.8033 0.210891
21 to 22 141662 -0.7296 0.232821
20 to 21 141573 -0.9921 0.160569
19 to 20 142181 0.8014 0.788546
18 to 19 142135 0.6657 0.747196
17 to 18 141982 0.2144 0.584869
16 to 17 142032 0.3619 0.641271
15 to 16 141423 -1.4346 0.075700
14 to 15 141465 -1.3107 0.094978
13 to 14 142469 1.6509 0.950625
12 to 13 142079 0.5005 0.691639
11 to 12 141029 -2.5968 0.004704
10 to 11 142035 0.3707 0.644573
9 to 10 141308 -1.7738 0.038045
8 to 9 142004 0.2793 0.609978
7 to 8 142066 0.4622 0.678014
6 to 7 141692 -0.6411 0.260732
5 to 6 142109 0.5890 0.722068
4 to 5 141708 -0.5939 0.276292
3 to 4 142539 1.8574 0.968375
2 to 3 142370 1.3589 0.912912
1 to 2 142342 1.2763 0.899078
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2497.21 -0.039 0.484282
Test results for specific bytes for dh-ranFile-2018-06-25_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2470.58 -0.416 0.338699
2 to 9 2520.92 0.296 0.616333
3 to 10 2489.32 -0.151 0.439999
4 to 11 2423.96 -1.075 0.141104
5 to 12 2539.70 0.561 0.712757
6 to 13 2455.14 -0.634 0.262911
7 to 14 2407.44 -1.309 0.095278
8 to 15 2528.06 0.397 0.654278
9 to 16 2546.52 0.658 0.744680
10 to 17 2581.98 1.159 0.876854
11 to 18 2353.97 -2.065 0.019455
12 to 19 2474.59 -0.359 0.359682
13 to 20 2608.74 1.538 0.937951
14 to 21 2507.68 0.109 0.543243
15 to 22 2410.96 -1.259 0.103982
16 to 23 2496.53 -0.049 0.480435
17 to 24 2487.62 -0.175 0.430508
18 to 25 2424.19 -1.072 0.141836
19 to 26 2412.40 -1.239 0.107695
20 to 27 2661.32 2.281 0.988738
21 to 28 2549.31 0.697 0.757225
22 to 29 2431.73 -0.966 0.167146
23 to 30 2523.42 0.331 0.629748
24 to 31 2462.81 -0.526 0.299474
25 to 32 2503.39 0.048 0.519134
CDPARK for dh-ranFile-2018-06-25_11:31: 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
3538 0.6849 0.753306
3526 0.1370 0.554479
3509 -0.6393 0.261324
3484 -1.7808 0.037471
3542 0.8676 0.807188
3550 1.2329 0.891189
3501 -1.0046 0.157553
3537 0.6393 0.738676
3556 1.5068 0.934075
3531 0.3653 0.642555
Square side=100, avg. no. parked=3527.40 sample std.=21.63
p-value of the KSTEST for those 10 p-values: 0.591465
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_11:31
0.1870,0.8098,0.0114,0.8355,0.1739,0.4360,0.0737,0.9319,0.7630,0.6780,
The KS test for those 10 p-values: 0.680964
The 3DSPHERES test for dh-ranFile-2018-06-25_11:31
sample no r^3 equiv. uni.
1 33.067 0.667871
2 2.710 0.086388
3 12.823 0.347828
4 9.521 0.271939
5 7.025 0.208759
6 12.718 0.345529
7 57.461 0.852713
8 0.675 0.022237
9 26.887 0.591900
10 173.027 0.996873
11 21.183 0.506434
12 4.084 0.127272
13 49.480 0.807825
14 18.374 0.457987
15 7.029 0.208866
16 29.276 0.623139
17 79.087 0.928370
18 49.574 0.808425
19 76.290 0.921369
20 67.647 0.895115
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.830734
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 2.0 -1.6 1.1 1.0
-1.0 -2.0 0.1 0.5 0.2 0.6
-0.3 0.9 1.0 -0.7 -0.6 -0.3
-1.3 -0.5 0.2 0.5 0.0 0.5
0.4 1.0 0.6 -0.1 -0.0 -0.4
-0.1 -0.1 -2.0 0.0 0.2 -0.1
1.4 0.8 -0.8 -0.1 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:33.212979
z-score=-0.958743, p-value=0.168275
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_11:31
Test no p-value
1 0.166420
2 0.428933
3 0.551373
4 0.510601
5 0.432140
6 0.254012
7 0.137973
8 0.767469
9 0.043726
10 0.851345
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.632518
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_11:31:
(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 66704 0.02 66508 0.38
3 25000.00 24991 0.00 25215 1.85
4 6666.67 6656 0.02 6662 0.00
5 1388.89 1373 0.18 1310 4.48
6 238.10 234 0.07 270 4.28
7 34.72 38 0.31 31 0.40
8 4.96 3 0.77 3 0.77
p=0.03281 p=0.94149
Number of rngs required: 688863, p-value: 0.702
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_11:31
No. of wins: Observed Expected
98573 98585.9
z-score=-0.058, pvalue=0.47707
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66719 66666.7 0.041 0.041
2 37573 37654.3 0.176 0.217
3 27104 26954.7 0.827 1.043
4 19217 19313.5 0.482 1.525
5 13982 13851.4 1.231 2.756
6 9873 9943.5 0.500 3.257
7 7115 7145.0 0.126 3.383
8 5167 5139.1 0.152 3.535
9 3620 3699.9 1.724 5.258
10 2633 2666.3 0.416 5.674
11 1962 1923.3 0.778 6.452
12 1383 1388.7 0.024 6.476
13 993 1003.7 0.114 6.590
14 733 726.1 0.065 6.655
15 523 525.8 0.015 6.670
16 384 381.2 0.021 6.691
17 265 276.5 0.482 7.173
18 211 200.8 0.515 7.688
19 162 146.0 1.757 9.445
20 108 106.2 0.030 9.475
21 273 287.1 0.694 10.169
Chisq= 10.17 for 20 degrees of freedom, p= 0.03499
SUMMARY of craptest
p-value for no. of wins: 0.477069
p-value for throws/game: 0.034991
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_11:31
No. of wins: Observed Expected
98335 98585.9
z-score=-1.122, pvalue=0.13093
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66590 66666.7 0.088 0.088
2 37581 37654.3 0.143 0.231
3 26905 26954.7 0.092 0.323
4 19287 19313.5 0.036 0.359
5 13695 13851.4 1.766 2.125
6 9936 9943.5 0.006 2.131
7 7208 7145.0 0.555 2.686
8 5175 5139.1 0.251 2.937
9 3798 3699.9 2.603 5.540
10 2756 2666.3 3.018 8.558
11 1982 1923.3 1.790 10.348
12 1372 1388.7 0.202 10.550
13 1030 1003.7 0.688 11.238
14 744 726.1 0.439 11.677
15 574 525.8 4.412 16.089
16 375 381.2 0.099 16.188
17 300 276.5 1.990 18.178
18 198 200.8 0.040 18.218
19 137 146.0 0.553 18.771
20 102 106.2 0.167 18.938
21 255 287.1 3.592 22.530
Chisq= 22.53 for 20 degrees of freedom, p= 0.68757
SUMMARY of craptest
p-value for no. of wins: 0.130934
p-value for throws/game: 0.687567
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0047,0.0099,0.0114,0.0121,0.0162,0.0195,0.0222,0.0236,0.0297,
0.0305,0.0328,0.0331,0.0350,0.0358,0.0375,0.0377,0.0380,0.0400,0.0437,
0.0507,0.0509,0.0622,0.0639,0.0647,0.0696,0.0708,0.0712,0.0737,0.0756,
0.0757,0.0816,0.0864,0.0870,0.0950,0.0953,0.1010,0.1024,0.1032,0.1040,
0.1077,0.1083,0.1125,0.1207,0.1238,0.1250,0.1273,0.1288,0.1309,0.1380,
0.1411,0.1418,0.1426,0.1558,0.1576,0.1606,0.1664,0.1671,0.1683,0.1691,
0.1739,0.1744,0.1753,0.1851,0.1870,0.1943,0.2052,0.2088,0.2089,0.2109,
0.2143,0.2237,0.2291,0.2315,0.2328,0.2342,0.2344,0.2405,0.2540,0.2592,
0.2607,0.2613,0.2629,0.2670,0.2713,0.2719,0.2763,0.2795,0.2857,0.2866,
0.2950,0.2964,0.2995,0.3011,0.3111,0.3171,0.3216,0.3223,0.3352,0.3381,
0.3387,0.3442,0.3454,0.3455,0.3459,0.3478,0.3480,0.3487,0.3529,0.3544,
0.3597,0.3669,0.3671,0.3922,0.3926,0.3929,0.3940,0.4019,0.4034,0.4110,
0.4228,0.4233,0.4278,0.4289,0.4305,0.4321,0.4336,0.4360,0.4387,0.4400,
0.4560,0.4580,0.4617,0.4631,0.4699,0.4712,0.4771,0.4804,0.4843,0.4844,
0.4922,0.4926,0.4935,0.5027,0.5064,0.5106,0.5146,0.5160,0.5191,0.5258,
0.5302,0.5375,0.5432,0.5514,0.5545,0.5665,0.5683,0.5748,0.5766,0.5791,
0.5849,0.5851,0.5881,0.5915,0.5919,0.6024,0.6074,0.6082,0.6100,0.6137,
0.6163,0.6207,0.6231,0.6239,0.6284,0.6297,0.6305,0.6320,0.6325,0.6342,
0.6371,0.6398,0.6413,0.6426,0.6446,0.6469,0.6522,0.6543,0.6679,0.6701,
0.6706,0.6780,0.6780,0.6810,0.6838,0.6876,0.6881,0.6916,0.7020,0.7115,
0.7128,0.7184,0.7221,0.7255,0.7387,0.7388,0.7443,0.7447,0.7464,0.7472,
0.7529,0.7533,0.7572,0.7581,0.7630,0.7674,0.7675,0.7710,0.7776,0.7885,
0.8016,0.8032,0.8056,0.8072,0.8078,0.8084,0.8098,0.8161,0.8293,0.8307,
0.8355,0.8441,0.8481,0.8513,0.8527,0.8713,0.8769,0.8799,0.8809,0.8827,
0.8893,0.8912,0.8951,0.8991,0.9029,0.9104,0.9129,0.9164,0.9166,0.9201,
0.9214,0.9226,0.9232,0.9284,0.9319,0.9341,0.9367,0.9380,0.9415,0.9506,
0.9582,0.9624,0.9669,0.9684,0.9723,0.9880,0.9887,0.9904,0.9969,
Overall p-value after applying KStest on 269 p-values = 0.116396
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.