RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.85 9.0022 0.059807
2 to 25 15.54 20.3576 0.743653
3 to 26 15.78 25.0852 0.907182
4 to 27 15.95 18.1124 0.618219
5 to 28 15.86 15.1778 0.417321
6 to 29 15.79 26.6067 0.935907
7 to 30 15.78 13.7214 0.313286
8 to 31 15.65 15.3104 0.426863
9 to 32 16.16 30.2477 0.975387
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.438574
Tough bday spacings test for dh-ranFile-2018-07-02_05:31: 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 40 77 103 89 79 44 28 13 12 3
(O-E)^2/E 0.9 0.3 0.2 0.3 0.8 0.0 1.3 0.1 0.2 4.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 8.718, p= 0.441
RESULTS OF GCD FOR dh-ranFile-2018-07-02_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.894826
p-value, dist. of gcd's: 0.152707
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.134 0.836 0.663 0.334 0.845 0.456 0.810 0.037
Bits 8 to 15---> 0.037 0.789 0.560 0.494 0.856 0.160 0.158 0.813
Bits 16 to 23---> 0.078 0.017 0.095 0.919 0.608 0.092 0.492 0.019
Bits 24 to 31---> 0.766 0.106 0.199 0.443 0.897 0.182 0.177 0.100
KS test for the above 32 p values: 0.962
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_05:31,
p-values for 5 runs: 0.6965, 0.5994, 0.5906, 0.1978, 0.1325
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 5261 5134.0 3.141 3.233
r= 30 23092 23103.0 0.005 3.239
r= 31 11440 11551.5 1.077 4.315
chi-square = 4.315 with df = 3; p-value = 0.771
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5151 5134.0 0.056 0.084
r= 31 23002 23103.0 0.442 0.526
r= 32 11638 11551.5 0.647 1.173
chi-square = 1.173 with df = 3; p-value = 0.241
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_05:31
b-rank test for bits 1 to 8, p=0.12151
b-rank test for bits 2 to 9, p=0.29215
b-rank test for bits 3 to 10, p=0.71194
b-rank test for bits 4 to 11, p=0.06434
b-rank test for bits 5 to 12, p=0.33950
b-rank test for bits 6 to 13, p=0.06314
b-rank test for bits 7 to 14, p=0.35781
b-rank test for bits 8 to 15, p=0.32921
b-rank test for bits 9 to 16, p=0.90790
b-rank test for bits 10 to 17, p=0.96890
b-rank test for bits 11 to 18, p=0.45121
b-rank test for bits 12 to 19, p=0.37057
b-rank test for bits 13 to 20, p=0.98792
b-rank test for bits 14 to 21, p=0.81537
b-rank test for bits 15 to 22, p=0.43099
b-rank test for bits 16 to 23, p=0.79570
b-rank test for bits 17 to 24, p=0.08724
b-rank test for bits 18 to 25, p=0.91686
b-rank test for bits 19 to 26, p=0.36684
b-rank test for bits 20 to 27, p=0.44210
b-rank test for bits 21 to 28, p=0.92129
b-rank test for bits 22 to 29, p=0.53285
b-rank test for bits 23 to 30, p=0.46706
b-rank test for bits 24 to 31, p=0.39841
b-rank test for bits 25 to 32, p=0.14771
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 = 0.619829
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_05:31
(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 141633 -0.65 0.259259
2 142021 0.26 0.602920
3 142365 1.06 0.856483
4 142170 0.61 0.728752
5 142158 0.58 0.719381
6 142062 0.36 0.639344
7 141942 0.08 0.530422
8 142120 0.49 0.688718
9 142905 2.33 0.990000
10 142008 0.23 0.591163
11 142470 1.31 0.904898
12 142163 0.59 0.723305
13 142123 0.50 0.691191
14 141736 -0.40 0.342747
15 142095 0.43 0.667786
16 141961 0.12 0.548045
17 142339 1.00 0.842287
18 141947 0.09 0.535067
19 142441 1.24 0.892922
20 141586 -0.76 0.224991
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_05:31
Bits used No. missing words z-score p-value
23 to 32 141833 -0.2632 0.396196
22 to 31 141963 0.1851 0.573413
21 to 30 142650 2.5540 0.994676
20 to 29 142179 0.9299 0.823788
19 to 28 141966 0.1954 0.577466
18 to 27 141880 -0.1011 0.459721
17 to 26 141753 -0.5391 0.294920
16 to 25 141976 0.2299 0.590914
15 to 24 141823 -0.2977 0.382970
14 to 23 142166 0.8851 0.811940
13 to 22 141972 0.2161 0.585547
12 to 21 141987 0.2678 0.605584
11 to 20 141870 -0.1356 0.446061
10 to 19 141789 -0.4149 0.339096
9 to 18 142228 1.0989 0.864086
8 to 17 141542 -1.2667 0.102639
7 to 16 141958 0.1678 0.566641
6 to 15 142031 0.4196 0.662594
5 to 14 142132 0.7678 0.778705
4 to 13 141526 -1.3218 0.093113
3 to 12 141660 -0.8598 0.194961
2 to 11 142044 0.4644 0.678812
1 to 10 142317 1.4058 0.920102
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_05:31
Bits used No. missing words z-score p-value
28 to 32 141974 0.2192 0.586761
27 to 31 142073 0.5548 0.710489
26 to 30 142301 1.3277 0.907861
25 to 29 142174 0.8972 0.815190
24 to 28 141723 -0.6316 0.263815
23 to 27 141573 -1.1401 0.127122
22 to 26 141966 0.1921 0.576169
21 to 25 141856 -0.1808 0.428270
20 to 24 142083 0.5887 0.721973
19 to 23 142049 0.4735 0.682057
18 to 22 141737 -0.5842 0.279553
17 to 21 141777 -0.4486 0.326869
16 to 20 141652 -0.8723 0.191521
15 to 19 141535 -1.2689 0.102236
14 to 18 142250 1.1548 0.875917
13 to 17 142181 0.9209 0.821453
12 to 16 141515 -1.3367 0.090658
11 to 15 141686 -0.7571 0.224510
10 to 14 141897 -0.0418 0.483330
9 to 13 141967 0.1955 0.577496
8 to 12 142114 0.6938 0.756095
7 to 11 141890 -0.0655 0.473878
6 to 10 142029 0.4057 0.657504
5 to 9 141879 -0.1028 0.459056
4 to 8 141598 -1.0554 0.145631
3 to 7 142150 0.8158 0.792702
2 to 6 141622 -0.9740 0.165028
1 to 5 141898 -0.0384 0.484682
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_05:31
Bits used No. missing words z-score p-value
31 to 32 141459 -1.3284 0.092022
30 to 31 142122 0.6273 0.734784
29 to 30 141693 -0.6381 0.261691
28 to 29 142193 0.8368 0.798643
27 to 28 142318 1.2055 0.885998
26 to 27 141652 -0.7591 0.223901
25 to 26 141904 -0.0157 0.493728
24 to 25 141715 -0.5732 0.283240
23 to 24 141248 -1.9508 0.025539
22 to 23 142254 1.0167 0.845358
21 to 22 142279 1.0905 0.862247
20 to 21 141949 0.1170 0.546578
19 to 20 142144 0.6922 0.755607
18 to 19 142236 0.9636 0.832384
17 to 18 141624 -0.8417 0.199983
16 to 17 142554 1.9017 0.971394
15 to 16 141756 -0.4523 0.325526
14 to 15 141942 0.0964 0.538387
13 to 14 142022 0.3324 0.630191
12 to 13 141796 -0.3343 0.369074
11 to 12 141885 -0.0718 0.471393
10 to 11 141828 -0.2399 0.405199
9 to 10 141620 -0.8535 0.196696
8 to 9 142001 0.2704 0.606579
7 to 8 141720 -0.5585 0.288253
6 to 7 141575 -0.9862 0.162012
5 to 6 141832 -0.2281 0.409780
4 to 5 141851 -0.1721 0.431693
3 to 4 141676 -0.6883 0.245635
2 to 3 142123 0.6303 0.735749
1 to 2 141980 0.2085 0.582568
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2590.85 1.285 0.900561
Test results for specific bytes for dh-ranFile-2018-07-02_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2525.25 0.357 0.639505
2 to 9 2523.11 0.327 0.628102
3 to 10 2374.28 -1.778 0.037710
4 to 11 2467.32 -0.462 0.321990
5 to 12 2555.94 0.791 0.785558
6 to 13 2583.77 1.185 0.881941
7 to 14 2502.85 0.040 0.516048
8 to 15 2476.11 -0.338 0.367750
9 to 16 2490.13 -0.140 0.444516
10 to 17 2451.91 -0.680 0.248208
11 to 18 2555.24 0.781 0.782669
12 to 19 2644.99 2.051 0.979843
13 to 20 2500.22 0.003 0.501257
14 to 21 2459.71 -0.570 0.284410
15 to 22 2392.94 -1.514 0.064998
16 to 23 2398.41 -1.437 0.075392
17 to 24 2495.41 -0.065 0.474134
18 to 25 2633.98 1.895 0.970942
19 to 26 2449.66 -0.712 0.238265
20 to 27 2334.30 -2.343 0.009556
21 to 28 2559.04 0.835 0.798124
22 to 29 2461.71 -0.542 0.294059
23 to 30 2425.78 -1.050 0.146929
24 to 31 2509.63 0.136 0.554179
25 to 32 2495.00 -0.071 0.471800
CDPARK for dh-ranFile-2018-07-02_05:31: 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
3563 1.8265 0.966111
3510 -0.5936 0.276387
3511 -0.5479 0.291865
3535 0.5479 0.708135
3504 -0.8676 0.192812
3528 0.2283 0.590298
3522 -0.0457 0.481790
3511 -0.5479 0.291865
3516 -0.3196 0.374623
3530 0.3196 0.625377
Square side=100, avg. no. parked=3523.00 sample std.=16.39
p-value of the KSTEST for those 10 p-values: 0.637279
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_05:31
0.6151,0.9473,0.7169,0.8472,0.1531,0.8833,0.1308,0.7145,0.2747,0.1652,
The KS test for those 10 p-values: 0.695918
The 3DSPHERES test for dh-ranFile-2018-07-02_05:31
sample no r^3 equiv. uni.
1 6.029 0.182068
2 50.977 0.817179
3 13.413 0.360526
4 13.758 0.367831
5 17.193 0.436229
6 23.704 0.546209
7 0.415 0.013740
8 1.590 0.051632
9 2.619 0.083607
10 48.859 0.803805
11 19.839 0.483815
12 0.265 0.008789
13 8.396 0.244127
14 1.483 0.048243
15 10.341 0.291571
16 1.708 0.055339
17 22.912 0.534069
18 31.295 0.647659
19 78.810 0.927704
20 3.727 0.116838
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.020906
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 -1.8 -1.1 -0.7 -0.4
-0.6 0.2 -0.7 -1.1 0.1 -0.6
0.5 0.2 -0.4 1.1 -0.7 -0.1
0.1 0.7 -1.4 -1.6 1.5 0.5
-0.4 2.2 0.4 1.1 1.0 -1.5
-0.0 0.8 0.7 -0.8 0.2 0.6
-0.5 -0.4 -0.8 1.0 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:32.339569
z-score=-1.054039, p-value=0.141527
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_05:31
Test no p-value
1 0.479823
2 0.423886
3 0.172648
4 0.081194
5 0.000001
6 0.905364
7 0.172340
8 0.568774
9 0.193871
10 0.015770
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.010454
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_05:31:
(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 66608 0.05 66636 0.01
3 25000.00 25161 1.04 24990 0.00
4 6666.67 6612 0.45 6732 0.64
5 1388.89 1344 1.45 1370 0.26
6 238.10 232 0.16 240 0.02
7 34.72 36 0.05 29 0.94
8 4.96 6 0.22 2 1.77
p=0.24396 p=0.27464
Number of rngs required: 688151, p-value: 0.386
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_05:31
No. of wins: Observed Expected
98473 98585.9
z-score=-0.505, pvalue=0.30686
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66539 66666.7 0.244 0.244
2 37434 37654.3 1.289 1.534
3 27127 26954.7 1.101 2.635
4 19319 19313.5 0.002 2.636
5 14030 13851.4 2.302 4.939
6 9881 9943.5 0.393 5.332
7 7084 7145.0 0.521 5.853
8 5125 5139.1 0.039 5.892
9 3685 3699.9 0.060 5.951
10 2675 2666.3 0.028 5.980
11 1919 1923.3 0.010 5.990
12 1388 1388.7 0.000 5.990
13 1024 1003.7 0.410 6.400
14 792 726.1 5.973 12.373
15 526 525.8 0.000 12.373
16 452 381.2 13.170 25.543
17 280 276.5 0.043 25.586
18 161 200.8 7.899 33.486
19 157 146.0 0.831 34.317
20 117 106.2 1.095 35.412
21 285 287.1 0.016 35.427
Chisq= 35.43 for 20 degrees of freedom, p= 0.98206
SUMMARY of craptest
p-value for no. of wins: 0.306860
p-value for throws/game: 0.982057
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_05:31
No. of wins: Observed Expected
98303 98585.9
z-score=-1.265, pvalue=0.10292
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66693 66666.7 0.010 0.010
2 37637 37654.3 0.008 0.018
3 26782 26954.7 1.107 1.125
4 19511 19313.5 2.020 3.146
5 14045 13851.4 2.705 5.851
6 9641 9943.5 9.205 15.056
7 7243 7145.0 1.343 16.400
8 5200 5139.1 0.722 17.122
9 3688 3699.9 0.038 17.160
10 2675 2666.3 0.028 17.189
11 1962 1923.3 0.778 17.966
12 1334 1388.7 2.158 20.124
13 974 1003.7 0.880 21.003
14 700 726.1 0.941 21.945
15 492 525.8 2.177 24.122
16 390 381.2 0.205 24.327
17 275 276.5 0.009 24.336
18 216 200.8 1.146 25.482
19 149 146.0 0.062 25.544
20 87 106.2 3.476 29.020
21 306 287.1 1.242 30.262
Chisq= 30.26 for 20 degrees of freedom, p= 0.93429
SUMMARY of craptest
p-value for no. of wins: 0.102916
p-value for throws/game: 0.934289
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0088,0.0096,0.0105,0.0137,0.0158,0.0168,0.0188,0.0209,0.0255,
0.0370,0.0370,0.0377,0.0482,0.0516,0.0553,0.0598,0.0631,0.0643,0.0650,
0.0754,0.0785,0.0812,0.0836,0.0872,0.0907,0.0920,0.0923,0.0931,0.0952,
0.1005,0.1022,0.1026,0.1029,0.1057,0.1168,0.1215,0.1271,0.1308,0.1325,
0.1335,0.1415,0.1456,0.1469,0.1477,0.1527,0.1531,0.1579,0.1596,0.1620,
0.1650,0.1652,0.1723,0.1726,0.1769,0.1817,0.1821,0.1915,0.1928,0.1939,
0.1950,0.1967,0.1978,0.1990,0.2000,0.2239,0.2245,0.2250,0.2383,0.2406,
0.2440,0.2441,0.2456,0.2482,0.2593,0.2617,0.2638,0.2746,0.2747,0.2764,
0.2796,0.2832,0.2844,0.2883,0.2916,0.2919,0.2919,0.2922,0.2941,0.2949,
0.3069,0.3133,0.3220,0.3255,0.3269,0.3292,0.3342,0.3391,0.3395,0.3427,
0.3578,0.3605,0.3668,0.3678,0.3678,0.3691,0.3706,0.3746,0.3830,0.3859,
0.3962,0.3984,0.4052,0.4098,0.4173,0.4239,0.4269,0.4283,0.4310,0.4317,
0.4362,0.4386,0.4409,0.4421,0.4427,0.4445,0.4461,0.4512,0.4565,0.4591,
0.4597,0.4671,0.4714,0.4718,0.4739,0.4741,0.4798,0.4818,0.4833,0.4838,
0.4847,0.4924,0.4937,0.4943,0.5013,0.5160,0.5304,0.5329,0.5341,0.5351,
0.5384,0.5462,0.5466,0.5480,0.5542,0.5601,0.5666,0.5688,0.5734,0.5762,
0.5775,0.5775,0.5826,0.5855,0.5868,0.5903,0.5906,0.5909,0.5912,0.5994,
0.6029,0.6056,0.6066,0.6077,0.6151,0.6182,0.6198,0.6254,0.6281,0.6302,
0.6373,0.6393,0.6395,0.6477,0.6575,0.6626,0.6632,0.6678,0.6788,0.6821,
0.6887,0.6912,0.6959,0.6965,0.7081,0.7105,0.7119,0.7145,0.7169,0.7194,
0.7220,0.7233,0.7288,0.7348,0.7357,0.7437,0.7556,0.7561,0.7662,0.7706,
0.7787,0.7827,0.7856,0.7890,0.7927,0.7957,0.7981,0.7986,0.8038,0.8102,
0.8119,0.8125,0.8152,0.8154,0.8172,0.8215,0.8238,0.8324,0.8364,0.8423,
0.8454,0.8454,0.8472,0.8564,0.8565,0.8622,0.8641,0.8759,0.8819,0.8833,
0.8860,0.8929,0.8948,0.8966,0.9006,0.9049,0.9054,0.9072,0.9079,0.9079,
0.9169,0.9191,0.9201,0.9213,0.9277,0.9343,0.9359,0.9473,0.9618,0.9661,
0.9689,0.9709,0.9714,0.9754,0.9798,0.9821,0.9879,0.9900,0.9947,
Overall p-value after applying KStest on 269 p-values = 0.602200
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.