RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.04 9.0054 0.059909
2 to 25 15.89 12.4240 0.226188
3 to 26 15.92 15.3947 0.432924
4 to 27 15.95 13.4070 0.291460
5 to 28 15.66 24.5205 0.894032
6 to 29 15.59 27.4382 0.948053
7 to 30 15.67 30.1684 0.974844
8 to 31 15.96 18.6006 0.648065
9 to 32 15.72 12.6278 0.239276
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.638925
Tough bday spacings test for dh-ranFile-2018-06-24_13:31: 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 10 32 86 111 88 75 53 20 16 4 5
(O-E)^2/E 0.1 0.6 2.2 1.8 1.0 0.1 0.0 3.2 0.1 1.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 10.334, p= 0.588
RESULTS OF GCD FOR dh-ranFile-2018-06-24_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.178951
p-value, dist. of gcd's: 0.121351
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.673 0.630 0.039 0.712 0.786 0.129 0.154 0.495
Bits 8 to 15---> 0.722 0.036 0.642 0.281 0.456 0.478 0.897 0.639
Bits 16 to 23---> 0.701 0.291 0.254 0.163 0.597 0.928 0.816 0.959
Bits 24 to 31---> 0.122 0.509 0.435 0.544 0.981 0.622 0.119 0.732
KS test for the above 32 p values: 0.130
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_13:31,
p-values for 5 runs: 0.3169, 0.7005, 0.6046, 0.6292, 0.7684
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 229 211.4 1.462 1.462
r= 29 5112 5134.0 0.094 1.557
r= 30 23267 23103.0 1.163 2.720
r= 31 11392 11551.5 2.203 4.923
chi-square = 4.923 with df = 3; p-value = 0.822
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 211 211.4 0.001 0.001
r= 30 5229 5134.0 1.757 1.758
r= 31 23075 23103.0 0.034 1.792
r= 32 11485 11551.5 0.383 2.175
chi-square = 2.175 with df = 3; p-value = 0.463
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_13:31
b-rank test for bits 1 to 8, p=0.85958
b-rank test for bits 2 to 9, p=0.92240
b-rank test for bits 3 to 10, p=0.90876
b-rank test for bits 4 to 11, p=0.93661
b-rank test for bits 5 to 12, p=0.43353
b-rank test for bits 6 to 13, p=0.14760
b-rank test for bits 7 to 14, p=0.14600
b-rank test for bits 8 to 15, p=0.51888
b-rank test for bits 9 to 16, p=0.25068
b-rank test for bits 10 to 17, p=0.52846
b-rank test for bits 11 to 18, p=0.83773
b-rank test for bits 12 to 19, p=0.79400
b-rank test for bits 13 to 20, p=0.59225
b-rank test for bits 14 to 21, p=0.31345
b-rank test for bits 15 to 22, p=0.70096
b-rank test for bits 16 to 23, p=0.90598
b-rank test for bits 17 to 24, p=0.84022
b-rank test for bits 18 to 25, p=0.53954
b-rank test for bits 19 to 26, p=0.72825
b-rank test for bits 20 to 27, p=0.01539
b-rank test for bits 21 to 28, p=0.15220
b-rank test for bits 22 to 29, p=0.59044
b-rank test for bits 23 to 30, p=0.12995
b-rank test for bits 24 to 31, p=0.86561
b-rank test for bits 25 to 32, p=0.64474
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 = 0.279874
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_13:31
(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 142029 0.28 0.610109
2 141922 0.03 0.511808
3 141796 -0.26 0.395586
4 141572 -0.79 0.215303
5 140629 -2.99 0.001388
6 142684 1.81 0.964850
7 142447 1.26 0.895485
8 141919 0.02 0.509013
9 141247 -1.55 0.060871
10 142060 0.35 0.637593
11 142367 1.07 0.857538
12 142487 1.35 0.911443
13 141857 -0.12 0.451344
14 142276 0.86 0.804196
15 142125 0.50 0.692835
16 142126 0.51 0.693655
17 141863 -0.11 0.456900
18 141722 -0.44 0.330807
19 141883 -0.06 0.475473
20 142057 0.35 0.634962
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_13:31
Bits used No. missing words z-score p-value
23 to 32 142051 0.4885 0.687408
22 to 31 141591 -1.0977 0.136170
21 to 30 141642 -0.9218 0.178309
20 to 29 141826 -0.2873 0.386924
19 to 28 142037 0.4402 0.670119
18 to 27 141913 0.0127 0.505049
17 to 26 141873 -0.1253 0.450153
16 to 25 142088 0.6161 0.731087
15 to 24 142192 0.9747 0.835151
14 to 23 142317 1.4058 0.920102
13 to 22 142340 1.4851 0.931237
12 to 21 141041 -2.9942 0.001376
11 to 20 141644 -0.9149 0.180114
10 to 19 141379 -1.8287 0.033720
9 to 18 141637 -0.9391 0.173848
8 to 17 142467 1.9230 0.972760
7 to 16 142538 2.1678 0.984914
6 to 15 141382 -1.8184 0.034503
5 to 14 141940 0.1058 0.542113
4 to 13 142063 0.5299 0.701908
3 to 12 142334 1.4644 0.928455
2 to 11 142216 1.0575 0.854854
1 to 10 141975 0.2264 0.589574
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_13:31
Bits used No. missing words z-score p-value
28 to 32 141891 -0.0621 0.475227
27 to 31 141764 -0.4926 0.311132
26 to 30 141595 -1.0655 0.143319
25 to 29 141921 0.0396 0.515778
24 to 28 141611 -1.0113 0.155939
23 to 27 142405 1.6802 0.953544
22 to 26 141773 -0.4621 0.321992
21 to 25 142052 0.4836 0.685675
20 to 24 141412 -1.6859 0.045911
19 to 23 142354 1.5074 0.934140
18 to 22 141928 0.0633 0.525232
17 to 21 142678 2.6057 0.995415
16 to 20 142080 0.5785 0.718551
15 to 19 142314 1.3718 0.914931
14 to 18 141705 -0.6926 0.244267
13 to 17 142062 0.5175 0.697605
12 to 16 141922 0.0429 0.517129
11 to 15 141806 -0.3503 0.363068
10 to 14 141975 0.2226 0.588081
9 to 13 141906 -0.0113 0.495497
8 to 12 142444 1.8124 0.965041
7 to 11 142578 2.2667 0.988295
6 to 10 141704 -0.6960 0.243204
5 to 9 141236 -2.2825 0.011231
4 to 8 142550 2.1718 0.985063
3 to 7 141967 0.1955 0.577496
2 to 6 142019 0.3718 0.644965
1 to 5 142070 0.5446 0.707001
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_13:31
Bits used No. missing words z-score p-value
31 to 32 141797 -0.3314 0.370187
30 to 31 141269 -1.8889 0.029454
29 to 30 142224 0.9282 0.823356
28 to 29 142039 0.3825 0.648958
27 to 28 142226 0.9341 0.824882
26 to 27 141694 -0.6352 0.262652
25 to 26 142181 0.8014 0.788546
24 to 25 141483 -1.2576 0.104266
23 to 24 141771 -0.4081 0.341617
22 to 23 142137 0.6716 0.749079
21 to 22 142165 0.7542 0.774632
20 to 21 141979 0.2055 0.581416
19 to 20 142274 1.0757 0.858974
18 to 19 141517 -1.1573 0.123572
17 to 18 141493 -1.2281 0.109702
16 to 17 141692 -0.6411 0.260732
15 to 16 141833 -0.2252 0.410927
14 to 15 142545 1.8751 0.969613
13 to 14 141747 -0.4788 0.316023
12 to 13 142457 1.6155 0.946904
11 to 12 141738 -0.5054 0.306640
10 to 11 141887 -0.0659 0.473741
9 to 10 141208 -2.0688 0.019281
8 to 9 142105 0.5772 0.718097
7 to 8 142122 0.6273 0.734784
6 to 7 141382 -1.5555 0.059908
5 to 6 142305 1.1672 0.878429
4 to 5 141709 -0.5909 0.277279
3 to 4 141752 -0.4641 0.321288
2 to 3 142207 0.8781 0.810051
1 to 2 142374 1.3707 0.914767
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2532.10 0.454 0.675064
Test results for specific bytes for dh-ranFile-2018-06-24_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2550.38 0.713 0.761925
2 to 9 2399.73 -1.418 0.078081
3 to 10 2442.05 -0.820 0.206241
4 to 11 2529.88 0.423 0.663704
5 to 12 2495.20 -0.068 0.472954
6 to 13 2352.55 -2.085 0.018521
7 to 14 2422.95 -1.090 0.137935
8 to 15 2515.89 0.225 0.588911
9 to 16 2542.90 0.607 0.727994
10 to 17 2466.73 -0.471 0.318994
11 to 18 2420.34 -1.127 0.129951
12 to 19 2565.43 0.925 0.822588
13 to 20 2537.12 0.525 0.700212
14 to 21 2411.14 -1.257 0.104442
15 to 22 2433.38 -0.942 0.173057
16 to 23 2551.44 0.728 0.766553
17 to 24 2607.55 1.521 0.935872
18 to 25 2501.88 0.027 0.510618
19 to 26 2499.46 -0.008 0.496968
20 to 27 2407.20 -1.312 0.094690
21 to 28 2401.12 -1.398 0.081000
22 to 29 2488.70 -0.160 0.436512
23 to 30 2566.51 0.941 0.826529
24 to 31 2554.00 0.764 0.777452
25 to 32 2481.63 -0.260 0.397513
CDPARK for dh-ranFile-2018-06-24_13:31: 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
3549 1.1872 0.882429
3522 -0.0457 0.481790
3520 -0.1370 0.445521
3486 -1.6895 0.045562
3497 -1.1872 0.117571
3492 -1.4155 0.078457
3478 -2.0548 0.019949
3520 -0.1370 0.445521
3507 -0.7306 0.232514
3531 0.3653 0.642555
Square side=100, avg. no. parked=3510.20 sample std.=20.99
p-value of the KSTEST for those 10 p-values: 0.101917
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_13:31
0.7760,0.8651,0.0092,0.2135,0.8286,0.0638,0.0041,0.0693,0.0810,0.4904,
The KS test for those 10 p-values: 0.014763
The 3DSPHERES test for dh-ranFile-2018-06-24_13:31
sample no r^3 equiv. uni.
1 6.783 0.202370
2 52.440 0.825881
3 13.463 0.361592
4 47.726 0.796252
5 95.055 0.957933
6 30.186 0.634392
7 6.801 0.202828
8 24.832 0.562962
9 25.625 0.574361
10 89.910 0.950063
11 5.856 0.177329
12 21.969 0.519194
13 30.512 0.638350
14 13.926 0.371368
15 56.411 0.847466
16 13.921 0.371262
17 19.936 0.485483
18 20.766 0.499521
19 6.969 0.207286
20 17.623 0.444244
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.552720
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 -0.6 -0.8 -1.0 -0.8
0.3 1.7 -0.5 -0.2 0.4 -0.3
-0.3 -1.0 1.7 -0.4 -0.6 0.7
-0.2 1.2 -1.6 0.2 -0.2 -0.5
0.1 0.5 -0.3 -0.4 1.8 -1.4
-0.0 0.2 1.2 0.1 -0.2 -0.1
0.3 1.5 0.5 1.5 0.9 1.0
0.8
Chi-square with 42 degrees of freedom:30.890785
z-score=-1.212115, p-value=0.102986
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_13:31
Test no p-value
1 0.193577
2 0.555523
3 0.181619
4 0.044987
5 0.005945
6 0.977222
7 0.006862
8 0.867999
9 0.603479
10 0.405783
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.080836
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_13:31:
(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 66671 0.00 66565 0.16
3 25000.00 25044 0.08 25185 1.37
4 6666.67 6529 2.84 6556 1.84
5 1388.89 1472 4.97 1387 0.00
6 238.10 243 0.10 269 4.01
7 34.72 39 0.53 31 0.40
8 4.96 1 3.16 6 0.22
p=0.93060 p=0.76130
Number of rngs required: 687925, p-value: 0.291
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_13:31
No. of wins: Observed Expected
98336 98585.9
z-score=-1.118, pvalue=0.13189
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66976 66666.7 1.435 1.435
2 37804 37654.3 0.595 2.030
3 26951 26954.7 0.001 2.031
4 19073 19313.5 2.994 5.025
5 13853 13851.4 0.000 5.025
6 9866 9943.5 0.605 5.630
7 7032 7145.0 1.788 7.417
8 5111 5139.1 0.153 7.571
9 3800 3699.9 2.710 10.281
10 2712 2666.3 0.783 11.064
11 1871 1923.3 1.424 12.488
12 1381 1388.7 0.043 12.531
13 950 1003.7 2.875 15.406
14 698 726.1 1.091 16.496
15 521 525.8 0.044 16.541
16 359 381.2 1.287 17.828
17 281 276.5 0.072 17.900
18 198 200.8 0.040 17.940
19 143 146.0 0.061 18.001
20 111 106.2 0.216 18.217
21 309 287.1 1.668 19.885
Chisq= 19.88 for 20 degrees of freedom, p= 0.53485
SUMMARY of craptest
p-value for no. of wins: 0.131887
p-value for throws/game: 0.534847
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_13:31
No. of wins: Observed Expected
98380 98585.9
z-score=-0.921, pvalue=0.17860
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66496 66666.7 0.437 0.437
2 37686 37654.3 0.027 0.464
3 26800 26954.7 0.888 1.352
4 19278 19313.5 0.065 1.417
5 13907 13851.4 0.223 1.640
6 9940 9943.5 0.001 1.641
7 7198 7145.0 0.393 2.034
8 5217 5139.1 1.182 3.216
9 3731 3699.9 0.262 3.478
10 2666 2666.3 0.000 3.478
11 1908 1923.3 0.122 3.600
12 1472 1388.7 4.992 8.592
13 1020 1003.7 0.264 8.856
14 726 726.1 0.000 8.856
15 502 525.8 1.080 9.936
16 406 381.2 1.620 11.556
17 311 276.5 4.294 15.851
18 206 200.8 0.133 15.984
19 143 146.0 0.061 16.045
20 99 106.2 0.490 16.535
21 288 287.1 0.003 16.538
Chisq= 16.54 for 20 degrees of freedom, p= 0.31723
SUMMARY of craptest
p-value for no. of wins: 0.178598
p-value for throws/game: 0.317234
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0014,0.0041,0.0059,0.0069,0.0092,0.0112,0.0148,0.0154,0.0185,
0.0193,0.0199,0.0295,0.0337,0.0345,0.0364,0.0392,0.0450,0.0456,0.0459,
0.0599,0.0599,0.0609,0.0638,0.0693,0.0781,0.0785,0.0808,0.0810,0.0810,
0.0947,0.1019,0.1030,0.1043,0.1044,0.1097,0.1176,0.1191,0.1214,0.1217,
0.1236,0.1293,0.1299,0.1300,0.1300,0.1319,0.1362,0.1379,0.1433,0.1460,
0.1476,0.1522,0.1537,0.1559,0.1629,0.1731,0.1738,0.1773,0.1783,0.1786,
0.1790,0.1801,0.1816,0.1936,0.2024,0.2028,0.2062,0.2073,0.2135,0.2153,
0.2262,0.2325,0.2393,0.2432,0.2443,0.2507,0.2543,0.2607,0.2627,0.2773,
0.2799,0.2814,0.2908,0.2913,0.2915,0.3066,0.3111,0.3135,0.3160,0.3169,
0.3172,0.3190,0.3213,0.3220,0.3308,0.3416,0.3616,0.3631,0.3702,0.3713,
0.3714,0.3869,0.3956,0.3975,0.4058,0.4109,0.4329,0.4335,0.4348,0.4365,
0.4442,0.4455,0.4455,0.4502,0.4513,0.4565,0.4569,0.4632,0.4730,0.4737,
0.4752,0.4755,0.4777,0.4818,0.4855,0.4904,0.4949,0.4955,0.4970,0.4995,
0.5050,0.5086,0.5090,0.5106,0.5118,0.5158,0.5171,0.5189,0.5192,0.5252,
0.5285,0.5348,0.5395,0.5421,0.5444,0.5527,0.5555,0.5630,0.5744,0.5775,
0.5814,0.5881,0.5883,0.5889,0.5896,0.5904,0.5923,0.5971,0.6035,0.6046,
0.6101,0.6220,0.6292,0.6298,0.6344,0.6350,0.6376,0.6383,0.6389,0.6389,
0.6421,0.6426,0.6447,0.6450,0.6481,0.6490,0.6637,0.6701,0.6729,0.6751,
0.6857,0.6874,0.6928,0.6937,0.6976,0.7002,0.7005,0.7010,0.7011,0.7019,
0.7070,0.7123,0.7181,0.7186,0.7217,0.7280,0.7282,0.7311,0.7323,0.7348,
0.7491,0.7613,0.7619,0.7666,0.7684,0.7746,0.7760,0.7775,0.7864,0.7885,
0.7940,0.7963,0.8042,0.8101,0.8158,0.8225,0.8226,0.8234,0.8249,0.8259,
0.8265,0.8286,0.8352,0.8377,0.8402,0.8475,0.8549,0.8575,0.8590,0.8596,
0.8651,0.8656,0.8680,0.8784,0.8824,0.8940,0.8955,0.8975,0.9060,0.9088,
0.9114,0.9148,0.9149,0.9201,0.9224,0.9282,0.9285,0.9306,0.9312,0.9341,
0.9359,0.9366,0.9469,0.9481,0.9501,0.9535,0.9579,0.9585,0.9649,0.9650,
0.9696,0.9728,0.9748,0.9772,0.9811,0.9849,0.9851,0.9883,0.9954,
Overall p-value after applying KStest on 269 p-values = 0.411059
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.