RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_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 15.90 11.7710 0.186196
2 to 25 15.84 20.0900 0.730346
3 to 26 15.80 9.0973 0.062840
4 to 27 15.91 11.1988 0.153958
5 to 28 15.72 18.7806 0.658728
6 to 29 15.65 12.5085 0.231582
7 to 30 16.09 16.3232 0.498948
8 to 31 15.78 15.9102 0.469789
9 to 32 15.72 17.8344 0.600642
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.452771
Tough bday spacings test for dh-ranFile-2018-06-18_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 11 42 68 108 88 69 61 25 18 6 4
(O-E)^2/E 0.4 0.8 0.4 1.1 1.0 1.1 1.5 0.8 0.7 0.1 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.651, p= 0.337
RESULTS OF GCD FOR dh-ranFile-2018-06-18_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.294417
p-value, dist. of gcd's: 0.834071
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.728 0.900 0.133 0.375 0.317 0.232 0.903 0.635
Bits 8 to 15---> 0.607 0.610 0.015 0.288 0.196 0.149 0.133 0.388
Bits 16 to 23---> 0.702 0.533 0.425 0.685 0.517 0.049 0.468 0.315
Bits 24 to 31---> 0.863 0.267 0.740 0.691 0.167 0.368 0.135 0.357
KS test for the above 32 p values: 0.732
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_11:31,
p-values for 5 runs: 0.0771, 0.6388, 0.3793, 0.9153, 0.0425
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 217 211.4 0.147 0.147
r= 29 5221 5134.0 1.474 1.621
r= 30 23206 23103.0 0.459 2.080
r= 31 11356 11551.5 3.309 5.390
chi-square = 5.390 with df = 3; p-value = 0.855
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5168 5134.0 0.225 0.497
r= 31 23157 23103.0 0.126 0.623
r= 32 11456 11551.5 0.790 1.413
chi-square = 1.413 with df = 3; p-value = 0.297
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_11:31
b-rank test for bits 1 to 8, p=0.61665
b-rank test for bits 2 to 9, p=0.45162
b-rank test for bits 3 to 10, p=0.39504
b-rank test for bits 4 to 11, p=0.56791
b-rank test for bits 5 to 12, p=0.39858
b-rank test for bits 6 to 13, p=0.91099
b-rank test for bits 7 to 14, p=0.43363
b-rank test for bits 8 to 15, p=0.70711
b-rank test for bits 9 to 16, p=0.89485
b-rank test for bits 10 to 17, p=0.42637
b-rank test for bits 11 to 18, p=0.65781
b-rank test for bits 12 to 19, p=0.11073
b-rank test for bits 13 to 20, p=0.11375
b-rank test for bits 14 to 21, p=0.55568
b-rank test for bits 15 to 22, p=0.32692
b-rank test for bits 16 to 23, p=0.35749
b-rank test for bits 17 to 24, p=0.46682
b-rank test for bits 18 to 25, p=0.84352
b-rank test for bits 19 to 26, p=0.06094
b-rank test for bits 20 to 27, p=0.81233
b-rank test for bits 21 to 28, p=0.78823
b-rank test for bits 22 to 29, p=0.62243
b-rank test for bits 23 to 30, p=0.74266
b-rank test for bits 24 to 31, p=0.27017
b-rank test for bits 25 to 32, p=0.09381
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 = 0.749215
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_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 141622 -0.67 0.251005
2 142231 0.75 0.773844
3 141992 0.19 0.576581
4 141875 -0.08 0.468035
5 141310 -1.40 0.080711
6 141989 0.19 0.573834
7 142161 0.59 0.721739
8 142463 1.29 0.902102
9 141479 -1.01 0.157342
10 142689 1.82 0.965747
11 142021 0.26 0.602920
12 142523 1.43 0.924187
13 141998 0.21 0.582063
14 141510 -0.93 0.175406
15 142116 0.48 0.685407
16 142456 1.28 0.899246
17 142148 0.56 0.711455
18 141245 -1.55 0.060310
19 142196 0.67 0.748504
20 141760 -0.35 0.363582
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_11:31
Bits used No. missing words z-score p-value
23 to 32 142646 2.5402 0.994461
22 to 31 141986 0.2644 0.604256
21 to 30 141861 -0.1667 0.433821
20 to 29 141642 -0.9218 0.178309
19 to 28 141642 -0.9218 0.178309
18 to 27 141959 0.1713 0.567997
17 to 26 141569 -1.1736 0.120287
16 to 25 141104 -2.7770 0.002743
15 to 24 141743 -0.5736 0.283136
14 to 23 141592 -1.0942 0.136925
13 to 22 141912 0.0092 0.503673
12 to 21 141415 -1.7046 0.044136
11 to 20 141656 -0.8736 0.191181
10 to 19 141936 0.0920 0.536637
9 to 18 142190 0.9678 0.833435
8 to 17 141979 0.2402 0.594928
7 to 16 141785 -0.4287 0.334062
6 to 15 141500 -1.4115 0.079051
5 to 14 142621 2.4540 0.992937
4 to 13 142458 1.8920 0.970752
3 to 12 142754 2.9127 0.998208
2 to 11 141923 0.0471 0.518798
1 to 10 142137 0.7851 0.783793
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_11:31
Bits used No. missing words z-score p-value
28 to 32 141877 -0.1096 0.456366
27 to 31 141905 -0.0147 0.494145
26 to 30 142295 1.3074 0.904454
25 to 29 141760 -0.5062 0.306357
24 to 28 142598 2.3345 0.990215
23 to 27 141450 -1.5571 0.059729
22 to 26 141984 0.2531 0.599912
21 to 25 142614 2.3887 0.991546
20 to 24 141814 -0.3232 0.373290
19 to 23 142351 1.4972 0.932828
18 to 22 141561 -1.1808 0.118845
17 to 21 142387 1.6192 0.947300
16 to 20 141973 0.2158 0.585440
15 to 19 141850 -0.2011 0.420303
14 to 18 142594 2.3209 0.989854
13 to 17 142099 0.6429 0.739872
12 to 16 142071 0.5480 0.708166
11 to 15 141606 -1.0282 0.151919
10 to 14 142117 0.7040 0.759273
9 to 13 142127 0.7379 0.769702
8 to 12 142397 1.6531 0.950847
7 to 11 141980 0.2396 0.594664
6 to 10 141983 0.2497 0.598602
5 to 9 141493 -1.4113 0.079080
4 to 8 141579 -1.1198 0.131407
3 to 7 141990 0.2735 0.607749
2 to 6 141919 0.0328 0.513075
1 to 5 141143 -2.5977 0.004692
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_11:31
Bits used No. missing words z-score p-value
31 to 32 141433 -1.4051 0.079995
30 to 31 142186 0.8161 0.792789
29 to 30 141678 -0.6824 0.247496
28 to 29 142152 0.7158 0.762955
27 to 28 142108 0.5860 0.721078
26 to 27 141789 -0.3550 0.361311
25 to 26 142580 1.9784 0.976057
24 to 25 141514 -1.1662 0.121774
23 to 24 142044 0.3973 0.654411
22 to 23 141972 0.1849 0.573333
21 to 22 141996 0.2557 0.600895
20 to 21 141767 -0.4199 0.337297
19 to 20 142052 0.4209 0.663070
18 to 19 142193 0.8368 0.798643
17 to 18 142138 0.6745 0.750017
16 to 17 141611 -0.8800 0.189422
15 to 16 142168 0.7630 0.777280
14 to 15 142188 0.8220 0.794472
13 to 14 142253 1.0138 0.844655
12 to 13 142296 1.1406 0.872986
11 to 12 141938 0.0846 0.533699
10 to 11 141816 -0.2753 0.391539
9 to 10 142281 1.0964 0.863542
8 to 9 142033 0.3648 0.642373
7 to 8 141904 -0.0157 0.493728
6 to 7 141868 -0.1219 0.451482
5 to 6 141638 -0.8004 0.211744
4 to 5 142078 0.4976 0.690600
3 to 4 141563 -1.0216 0.153480
2 to 3 142171 0.7719 0.779910
1 to 2 141365 -1.6057 0.054171
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2612.29 1.588 0.943864
Test results for specific bytes for dh-ranFile-2018-06-18_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2613.56 1.606 0.945861
2 to 9 2382.68 -1.659 0.048542
3 to 10 2553.08 0.751 0.773567
4 to 11 2492.71 -0.103 0.458956
5 to 12 2556.70 0.802 0.788672
6 to 13 2484.98 -0.212 0.415896
7 to 14 2453.60 -0.656 0.255853
8 to 15 2536.22 0.512 0.695768
9 to 16 2664.34 2.324 0.989940
10 to 17 2506.95 0.098 0.539172
11 to 18 2587.55 1.238 0.892171
12 to 19 2524.95 0.353 0.637892
13 to 20 2576.60 1.083 0.860663
14 to 21 2567.43 0.954 0.829857
15 to 22 2484.21 -0.223 0.411648
16 to 23 2506.19 0.088 0.534889
17 to 24 2672.56 2.440 0.992665
18 to 25 2509.83 0.139 0.555290
19 to 26 2515.17 0.215 0.584933
20 to 27 2521.07 0.298 0.617120
21 to 28 2554.91 0.777 0.781288
22 to 29 2497.80 -0.031 0.487577
23 to 30 2420.41 -1.126 0.130185
24 to 31 2455.28 -0.632 0.263554
25 to 32 2606.07 1.500 0.933202
CDPARK for dh-ranFile-2018-06-18_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
3508 -0.6849 0.246694
3503 -0.9132 0.180558
3493 -1.3699 0.085365
3505 -0.8219 0.205562
3521 -0.0913 0.463617
3519 -0.1826 0.427537
3549 1.1872 0.882429
3551 1.2785 0.899470
3519 -0.1826 0.427537
3545 1.0046 0.842447
Square side=100, avg. no. parked=3521.30 sample std.=19.49
p-value of the KSTEST for those 10 p-values: 0.778285
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_11:31
0.1940,0.5398,0.8067,0.3997,0.7639,0.3270,0.5539,0.8979,0.0333,0.9091,
The KS test for those 10 p-values: 0.938559
The 3DSPHERES test for dh-ranFile-2018-06-18_11:31
sample no r^3 equiv. uni.
1 45.619 0.781424
2 56.883 0.849847
3 49.636 0.808820
4 1.289 0.042060
5 0.279 0.009254
6 36.634 0.705106
7 9.859 0.280099
8 12.343 0.337293
9 20.877 0.501382
10 66.836 0.892243
11 20.277 0.491305
12 69.798 0.902372
13 10.864 0.303801
14 2.975 0.094395
15 11.982 0.329275
16 32.948 0.666556
17 56.976 0.850310
18 19.258 0.473728
19 59.655 0.863097
20 14.139 0.375810
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.725600
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.8 -0.4 -0.5 -2.4 0.8
-0.8 0.6 0.9 1.3 -0.7 -0.2
-0.9 -1.5 1.0 1.2 -0.3 -0.8
-0.8 -1.2 0.3 0.6 -0.9 2.7
-0.6 0.5 2.1 0.5 -1.0 -1.2
0.2 0.8 1.2 0.3 0.3 -0.3
1.2 0.2 0.1 1.5 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:45.819059
z-score=0.416693, p-value=0.683312
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_11:31
Test no p-value
1 0.569993
2 0.061026
3 0.132347
4 0.006916
5 0.390557
6 0.057057
7 0.022363
8 0.454631
9 0.130039
10 0.091181
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000352
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_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 66474 0.56 66734 0.07
3 25000.00 25268 2.87 24804 1.54
4 6666.67 6531 2.76 6748 0.99
5 1388.89 1457 3.34 1413 0.42
6 238.10 228 0.43 260 2.02
7 34.72 41 1.14 34 0.01
8 4.96 0 4.96 6 0.22
p=0.98654 p=0.48952
Number of rngs required: 689715, p-value: 0.937
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_11:31
No. of wins: Observed Expected
98730 98585.9
z-score= 0.645, pvalue=0.74043
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66147 66666.7 4.051 4.051
2 38003 37654.3 3.229 7.280
3 26799 26954.7 0.900 8.179
4 19496 19313.5 1.725 9.905
5 13815 13851.4 0.096 10.000
6 10049 9943.5 1.118 11.119
7 7109 7145.0 0.182 11.300
8 5163 5139.1 0.111 11.412
9 3667 3699.9 0.292 11.704
10 2759 2666.3 3.223 14.927
11 1956 1923.3 0.555 15.482
12 1397 1388.7 0.049 15.531
13 1031 1003.7 0.742 16.273
14 718 726.1 0.091 16.364
15 513 525.8 0.313 16.677
16 360 381.2 1.174 17.851
17 286 276.5 0.324 18.175
18 192 200.8 0.388 18.563
19 137 146.0 0.553 19.116
20 113 106.2 0.433 19.549
21 290 287.1 0.029 19.578
Chisq= 19.58 for 20 degrees of freedom, p= 0.51542
SUMMARY of craptest
p-value for no. of wins: 0.740434
p-value for throws/game: 0.515417
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_11:31
No. of wins: Observed Expected
98671 98585.9
z-score= 0.381, pvalue=0.64832
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66826 66666.7 0.381 0.381
2 37481 37654.3 0.798 1.179
3 26853 26954.7 0.384 1.563
4 19167 19313.5 1.111 2.673
5 14003 13851.4 1.659 4.332
6 9927 9943.5 0.028 4.360
7 7068 7145.0 0.830 5.190
8 5199 5139.1 0.699 5.889
9 3681 3699.9 0.096 5.985
10 2697 2666.3 0.354 6.338
11 1984 1923.3 1.914 8.252
12 1361 1388.7 0.554 8.806
13 1058 1003.7 2.936 11.742
14 732 726.1 0.047 11.790
15 509 525.8 0.539 12.329
16 408 381.2 1.891 14.220
17 293 276.5 0.980 15.200
18 201 200.8 0.000 15.200
19 136 146.0 0.683 15.883
20 123 106.2 2.652 18.535
21 293 287.1 0.121 18.656
Chisq= 18.66 for 20 degrees of freedom, p= 0.45572
SUMMARY of craptest
p-value for no. of wins: 0.648325
p-value for throws/game: 0.455719
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0027,0.0047,0.0069,0.0093,0.0150,0.0224,0.0333,0.0421,0.0425,
0.0441,0.0485,0.0488,0.0542,0.0571,0.0597,0.0603,0.0609,0.0610,0.0628,
0.0771,0.0791,0.0791,0.0800,0.0807,0.0854,0.0912,0.0938,0.0944,0.1107,
0.1137,0.1188,0.1203,0.1218,0.1300,0.1302,0.1314,0.1323,0.1326,0.1330,
0.1349,0.1369,0.1489,0.1519,0.1535,0.1540,0.1573,0.1675,0.1754,0.1783,
0.1783,0.1806,0.1862,0.1894,0.1912,0.1940,0.1965,0.2056,0.2117,0.2316,
0.2317,0.2467,0.2475,0.2510,0.2559,0.2636,0.2668,0.2702,0.2801,0.2831,
0.2879,0.2944,0.2975,0.3038,0.3064,0.3153,0.3166,0.3269,0.3270,0.3293,
0.3341,0.3371,0.3373,0.3373,0.3572,0.3575,0.3613,0.3636,0.3675,0.3733,
0.3746,0.3758,0.3793,0.3881,0.3906,0.3915,0.3950,0.3986,0.3997,0.4116,
0.4159,0.4203,0.4253,0.4264,0.4275,0.4275,0.4336,0.4338,0.4515,0.4516,
0.4528,0.4546,0.4557,0.4564,0.4590,0.4636,0.4668,0.4676,0.4680,0.4698,
0.4737,0.4876,0.4895,0.4913,0.4937,0.4941,0.4989,0.5014,0.5037,0.5131,
0.5154,0.5168,0.5188,0.5325,0.5337,0.5349,0.5366,0.5392,0.5398,0.5539,
0.5553,0.5557,0.5679,0.5680,0.5700,0.5733,0.5738,0.5766,0.5821,0.5849,
0.5854,0.5947,0.5949,0.5986,0.5999,0.6006,0.6009,0.6029,0.6043,0.6070,
0.6077,0.6102,0.6167,0.6171,0.6224,0.6351,0.6379,0.6388,0.6424,0.6483,
0.6544,0.6578,0.6587,0.6631,0.6666,0.6833,0.6854,0.6854,0.6906,0.6909,
0.6958,0.7016,0.7051,0.7071,0.7082,0.7115,0.7211,0.7217,0.7256,0.7283,
0.7303,0.7323,0.7399,0.7402,0.7404,0.7427,0.7485,0.7492,0.7500,0.7593,
0.7630,0.7639,0.7697,0.7736,0.7738,0.7773,0.7783,0.7799,0.7813,0.7814,
0.7838,0.7882,0.7887,0.7928,0.7945,0.7986,0.8067,0.8088,0.8123,0.8299,
0.8334,0.8341,0.8424,0.8435,0.8447,0.8498,0.8503,0.8546,0.8607,0.8630,
0.8631,0.8635,0.8730,0.8824,0.8922,0.8922,0.8948,0.8979,0.8992,0.8995,
0.9002,0.9021,0.9024,0.9027,0.9045,0.9091,0.9110,0.9153,0.9242,0.9328,
0.9332,0.9374,0.9386,0.9439,0.9459,0.9473,0.9508,0.9657,0.9708,0.9761,
0.9865,0.9899,0.9899,0.9902,0.9915,0.9927,0.9929,0.9945,0.9982,
Overall p-value after applying KStest on 269 p-values = 0.549479
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.