RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-19_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.80 13.6995 0.311751
2 to 25 15.89 8.4779 0.044767
3 to 26 15.85 11.1408 0.150846
4 to 27 15.70 13.9742 0.331069
5 to 28 16.01 30.9781 0.979905
6 to 29 15.78 20.9737 0.772531
7 to 30 15.97 14.6816 0.381600
8 to 31 15.86 11.9115 0.194534
9 to 32 15.94 19.0401 0.673763
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.679169
Tough bday spacings test for dh-ranFile-2017-01-19_20:31: 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 8 37 81 102 91 78 43 36 13 5 6
(O-E)^2/E 0.1 0.0 0.8 0.2 0.5 0.0 1.6 1.3 0.2 0.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 6.061, p= 0.190
RESULTS OF GCD FOR dh-ranFile-2017-01-19_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.492458
p-value, dist. of gcd's: 0.762921
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-19_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.839 0.966 0.687 0.736 0.575 0.801 0.165 0.230
Bits 8 to 15---> 0.251 0.494 0.179 0.624 0.268 0.417 0.421 0.224
Bits 16 to 23---> 0.481 0.168 0.499 0.208 0.655 0.123 0.613 0.607
Bits 24 to 31---> 0.960 0.125 0.785 0.573 0.850 0.547 0.321 0.265
KS test for the above 32 p values: 0.416
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-19_20:31,
p-values for 5 runs: 0.8960, 0.2877, 0.4945, 0.1077, 0.1302
Rank test for binary matrices (31x31) for dh-ranFile-2017-01-19_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 5242 5134.0 2.271 2.364
r= 30 23030 23103.0 0.231 2.595
r= 31 11521 11551.5 0.081 2.675
chi-square = 2.675 with df = 3; p-value = 0.556
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-01-19_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 238 211.4 3.342 3.342
r= 30 5111 5134.0 0.103 3.445
r= 31 23361 23103.0 2.880 6.325
r= 32 11290 11551.5 5.921 12.246
chi-square = 12.246 with df = 3; p-value = 0.993
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-01-19_20:31
b-rank test for bits 1 to 8, p=0.82310
b-rank test for bits 2 to 9, p=0.36889
b-rank test for bits 3 to 10, p=0.14032
b-rank test for bits 4 to 11, p=0.88714
b-rank test for bits 5 to 12, p=0.84352
b-rank test for bits 6 to 13, p=0.13040
b-rank test for bits 7 to 14, p=0.30193
b-rank test for bits 8 to 15, p=0.98862
b-rank test for bits 9 to 16, p=0.78608
b-rank test for bits 10 to 17, p=0.04269
b-rank test for bits 11 to 18, p=0.72722
b-rank test for bits 12 to 19, p=0.51348
b-rank test for bits 13 to 20, p=0.58555
b-rank test for bits 14 to 21, p=0.37679
b-rank test for bits 15 to 22, p=0.41515
b-rank test for bits 16 to 23, p=0.75107
b-rank test for bits 17 to 24, p=0.21541
b-rank test for bits 18 to 25, p=0.03312
b-rank test for bits 19 to 26, p=0.86962
b-rank test for bits 20 to 27, p=0.32616
b-rank test for bits 21 to 28, p=0.08361
b-rank test for bits 22 to 29, p=0.72147
b-rank test for bits 23 to 30, p=0.06707
b-rank test for bits 24 to 31, p=0.49349
b-rank test for bits 25 to 32, p=0.45423
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 = 0.933498
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-19_20:31
(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 142079 0.40 0.654104
2 142225 0.74 0.769605
3 142460 1.29 0.900885
4 142201 0.68 0.752214
5 141396 -1.20 0.115192
6 142608 1.63 0.948703
7 141977 0.16 0.562814
8 141715 -0.45 0.324899
9 141969 0.14 0.555439
10 143083 2.74 0.996949
11 141632 -0.65 0.258503
12 142195 0.67 0.747759
13 142243 0.78 0.782188
14 141911 0.00 0.501557
15 141731 -0.42 0.338464
16 141725 -0.43 0.333351
17 142367 1.07 0.857538
18 142252 0.80 0.788327
19 141828 -0.19 0.424645
20 141782 -0.30 0.383042
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-01-19_20:31
Bits used No. missing words z-score p-value
23 to 32 141464 -1.5356 0.062316
22 to 31 142042 0.4575 0.676338
21 to 30 141774 -0.4667 0.320373
20 to 29 141604 -1.0529 0.146202
19 to 28 142350 1.5196 0.935688
18 to 27 142035 0.4333 0.667618
17 to 26 142105 0.6747 0.750075
16 to 25 142564 2.2575 0.988011
15 to 24 141791 -0.4080 0.341624
14 to 23 142120 0.7264 0.766218
13 to 22 142131 0.7644 0.777679
12 to 21 142110 0.6920 0.755521
11 to 20 141985 0.2609 0.602927
10 to 19 141668 -0.8322 0.202656
9 to 18 142018 0.3747 0.646067
8 to 17 141867 -0.1460 0.441974
7 to 16 141453 -1.5736 0.057796
6 to 15 141917 0.0264 0.510550
5 to 14 141652 -0.8873 0.187447
4 to 13 141788 -0.4184 0.337835
3 to 12 141998 0.3058 0.620106
2 to 11 141743 -0.5736 0.283136
1 to 10 141945 0.1230 0.548947
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-01-19_20:31
Bits used No. missing words z-score p-value
28 to 32 141431 -1.6215 0.052460
27 to 31 141763 -0.4960 0.309935
26 to 30 142214 1.0328 0.849147
25 to 29 142405 1.6802 0.953544
24 to 28 142179 0.9141 0.819677
23 to 27 141902 -0.0248 0.490088
22 to 26 141854 -0.1876 0.425611
21 to 25 141554 -1.2045 0.114197
20 to 24 141878 -0.1062 0.457711
19 to 23 141651 -0.8757 0.190598
18 to 22 141488 -1.4282 0.076612
17 to 21 141917 0.0260 0.510371
16 to 20 142192 0.9582 0.831020
15 to 19 142199 0.9819 0.836933
14 to 18 141907 -0.0079 0.496849
13 to 17 141609 -1.0181 0.154323
12 to 16 141562 -1.1774 0.119520
11 to 15 141549 -1.2215 0.110956
10 to 14 142379 1.5921 0.944319
9 to 13 141948 0.1311 0.552146
8 to 12 142277 1.2463 0.893680
7 to 11 141639 -0.9164 0.179736
6 to 10 141638 -0.9198 0.178848
5 to 9 141780 -0.4384 0.330546
4 to 8 142537 2.1277 0.983319
3 to 7 141788 -0.4113 0.340431
2 to 6 142092 0.6192 0.732114
1 to 5 141972 0.2124 0.584118
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-01-19_20:31
Bits used No. missing words z-score p-value
31 to 32 141787 -0.3609 0.359104
30 to 31 142265 1.0492 0.852951
29 to 30 141500 -1.2075 0.113627
28 to 29 141909 -0.0010 0.499612
27 to 28 142313 1.1908 0.883127
26 to 27 141486 -1.2488 0.105876
25 to 26 141149 -2.2429 0.012453
24 to 25 141142 -2.2635 0.011802
23 to 24 141428 -1.4199 0.077825
22 to 23 141627 -0.8328 0.202470
21 to 22 142162 0.7453 0.771967
20 to 21 142124 0.6332 0.736713
19 to 20 141135 -2.2842 0.011181
18 to 19 141841 -0.2016 0.420129
17 to 18 141836 -0.2163 0.414372
16 to 17 141761 -0.4376 0.330856
15 to 16 141656 -0.7473 0.227445
14 to 15 142363 1.3383 0.909594
13 to 14 142042 0.3914 0.652233
12 to 13 141594 -0.9302 0.176140
11 to 12 141853 -0.1662 0.434014
10 to 11 141746 -0.4818 0.314974
9 to 10 141763 -0.4317 0.332997
8 to 9 141840 -0.2045 0.418976
7 to 8 142495 1.7276 0.957974
6 to 7 141941 0.0934 0.537216
5 to 6 142258 1.0285 0.848149
4 to 5 141668 -0.7119 0.238267
3 to 4 142128 0.6450 0.740551
2 to 3 142157 0.7306 0.767485
1 to 2 141785 -0.3668 0.356901
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-19_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2502.53 0.036 0.514298
Test results for specific bytes for dh-ranFile-2017-01-19_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2363.10 -1.936 0.026431
2 to 9 2571.27 1.008 0.843260
3 to 10 2587.54 1.238 0.892151
4 to 11 2527.15 0.384 0.649510
5 to 12 2370.14 -1.836 0.033147
6 to 13 2425.19 -1.058 0.145019
7 to 14 2461.32 -0.547 0.292196
8 to 15 2447.33 -0.745 0.228184
9 to 16 2569.44 0.982 0.836967
10 to 17 2422.88 -1.091 0.137710
11 to 18 2448.59 -0.727 0.233603
12 to 19 2426.18 -1.044 0.148253
13 to 20 2534.50 0.488 0.687186
14 to 21 2430.88 -0.977 0.164171
15 to 22 2438.26 -0.873 0.191310
16 to 23 2483.92 -0.227 0.410039
17 to 24 2450.44 -0.701 0.241688
18 to 25 2444.86 -0.780 0.217766
19 to 26 2447.38 -0.744 0.228408
20 to 27 2454.35 -0.646 0.259292
21 to 28 2600.23 1.417 0.921830
22 to 29 2487.35 -0.179 0.428993
23 to 30 2610.06 1.557 0.940210
24 to 31 2460.28 -0.562 0.287144
25 to 32 2606.58 1.507 0.934124
CDPARK for dh-ranFile-2017-01-19_20:31: 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
3482 -1.8721 0.030593
3516 -0.3196 0.374623
3539 0.7306 0.767486
3539 0.7306 0.767486
3522 -0.0457 0.481790
3519 -0.1826 0.427537
3506 -0.7763 0.218799
3505 -0.8219 0.205562
3540 0.7763 0.781201
3504 -0.8676 0.192812
Square side=100, avg. no. parked=3517.20 sample std.=17.85
p-value of the KSTEST for those 10 p-values: 0.586282
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-19_20:31
0.1019,0.8595,0.3106,0.4454,0.0652,0.6163,0.2005,0.1879,0.2450,0.4832,
The KS test for those 10 p-values: 0.174471
The 3DSPHERES test for dh-ranFile-2017-01-19_20:31
sample no r^3 equiv. uni.
1 9.767 0.277880
2 35.967 0.698475
3 79.027 0.928227
4 15.133 0.396158
5 15.137 0.396236
6 20.398 0.493357
7 51.690 0.821468
8 82.316 0.935679
9 4.551 0.140755
10 3.355 0.105808
11 22.719 0.531069
12 0.428 0.014151
13 12.324 0.336877
14 14.997 0.393404
15 17.388 0.439883
16 15.523 0.403949
17 48.175 0.799275
18 7.641 0.224856
19 0.655 0.021584
20 13.294 0.357969
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.424633
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-19_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.3 -1.6 -0.5 0.0 -0.1
-0.4 -0.9 -0.5 -0.3 -0.3 1.8
0.0 1.4 0.7 -0.4 -0.5 1.6
-1.6 -2.1 1.6 -0.4 -0.4 -0.3
-0.9 0.4 -0.9 1.8 -0.1 0.5
1.7 -1.1 1.2 -0.6 -1.5 -0.7
1.2 -0.1 -2.0 -0.7 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:46.251706
z-score=0.463899, p-value=0.698934
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-01-19_20:31
Test no p-value
1 0.243029
2 0.035406
3 0.811735
4 0.876440
5 0.065032
6 0.050100
7 0.167889
8 0.032708
9 0.798807
10 0.479650
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.048118
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-19_20:31:
(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 66524 0.31 66951 1.21
3 25000.00 25109 0.48 24925 0.23
4 6666.67 6701 0.18 6506 3.87
5 1388.89 1435 1.53 1358 0.69
6 238.10 189 10.12 218 1.70
7 34.72 37 0.15 30 0.64
8 4.96 4 0.19 11 7.36
p=0.95612 p=0.98448
Number of rngs required: 689555, p-value: 0.910
RESULTS OF CRAPS TEST for dh-ranFile-2017-01-19_20:31
No. of wins: Observed Expected
98341 98585.9
z-score=-1.095, pvalue=0.13673
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66696 66666.7 0.013 0.013
2 37597 37654.3 0.087 0.100
3 26896 26954.7 0.128 0.228
4 19268 19313.5 0.107 0.335
5 13992 13851.4 1.427 1.762
6 10030 9943.5 0.752 2.514
7 6992 7145.0 3.277 5.791
8 5178 5139.1 0.295 6.086
9 3722 3699.9 0.132 6.218
10 2602 2666.3 1.551 7.769
11 1979 1923.3 1.611 9.380
12 1383 1388.7 0.024 9.404
13 1032 1003.7 0.797 10.201
14 721 726.1 0.036 10.237
15 517 525.8 0.148 10.386
16 374 381.2 0.134 10.520
17 247 276.5 3.155 13.675
18 206 200.8 0.133 13.809
19 163 146.0 1.983 15.792
20 100 106.2 0.364 16.155
21 305 287.1 1.114 17.270
Chisq= 17.27 for 20 degrees of freedom, p= 0.36460
SUMMARY of craptest
p-value for no. of wins: 0.136725
p-value for throws/game: 0.364603
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-19_20:31
No. of wins: Observed Expected
98550 98585.9
z-score=-0.160, pvalue=0.43629
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66836 66666.7 0.430 0.430
2 37714 37654.3 0.095 0.525
3 26913 26954.7 0.065 0.589
4 19397 19313.5 0.361 0.951
5 13764 13851.4 0.552 1.502
6 9970 9943.5 0.070 1.573
7 7082 7145.0 0.556 2.129
8 5106 5139.1 0.213 2.342
9 3623 3699.9 1.597 3.938
10 2632 2666.3 0.441 4.380
11 1928 1923.3 0.011 4.391
12 1416 1388.7 0.535 4.926
13 1000 1003.7 0.014 4.940
14 715 726.1 0.171 5.111
15 523 525.8 0.015 5.126
16 374 381.2 0.134 5.260
17 266 276.5 0.402 5.662
18 196 200.8 0.116 5.778
19 132 146.0 1.340 7.118
20 104 106.2 0.046 7.164
21 309 287.1 1.668 8.832
Chisq= 8.83 for 20 degrees of freedom, p= 0.01523
SUMMARY of craptest
p-value for no. of wins: 0.436291
p-value for throws/game: 0.015228
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0112,0.0118,0.0125,0.0142,0.0152,0.0216,0.0264,0.0306,0.0327,0.0331,
0.0331,0.0354,0.0427,0.0448,0.0481,0.0501,0.0525,0.0578,0.0623,0.0650,
0.0652,0.0671,0.0766,0.0778,0.0836,0.1019,0.1058,0.1059,0.1077,0.1110,
0.1136,0.1142,0.1152,0.1195,0.1234,0.1255,0.1302,0.1304,0.1367,0.1377,
0.1403,0.1408,0.1450,0.1462,0.1483,0.1508,0.1543,0.1642,0.1651,0.1679,
0.1683,0.1745,0.1761,0.1787,0.1788,0.1797,0.1874,0.1879,0.1899,0.1906,
0.1913,0.1928,0.1945,0.2005,0.2025,0.2027,0.2056,0.2082,0.2154,0.2178,
0.2188,0.2242,0.2249,0.2274,0.2282,0.2284,0.2304,0.2336,0.2383,0.2417,
0.2430,0.2450,0.2507,0.2585,0.2593,0.2648,0.2681,0.2779,0.2831,0.2871,
0.2877,0.2922,0.3019,0.3099,0.3106,0.3118,0.3150,0.3204,0.3209,0.3249,
0.3262,0.3305,0.3309,0.3311,0.3330,0.3334,0.3369,0.3378,0.3385,0.3404,
0.3416,0.3569,0.3580,0.3591,0.3646,0.3689,0.3746,0.3768,0.3816,0.3830,
0.3934,0.3962,0.3962,0.4039,0.4100,0.4144,0.4151,0.4158,0.4171,0.4190,
0.4201,0.4208,0.4246,0.4246,0.4256,0.4275,0.4290,0.4340,0.4363,0.4399,
0.4420,0.4454,0.4542,0.4577,0.4796,0.4807,0.4818,0.4832,0.4901,0.4925,
0.4934,0.4935,0.4941,0.4945,0.4968,0.4989,0.4996,0.5016,0.5104,0.5106,
0.5135,0.5143,0.5311,0.5372,0.5474,0.5489,0.5521,0.5554,0.5556,0.5628,
0.5728,0.5748,0.5841,0.5855,0.5863,0.6029,0.6066,0.6125,0.6163,0.6201,
0.6240,0.6461,0.6495,0.6522,0.6541,0.6553,0.6676,0.6738,0.6763,0.6792,
0.6872,0.6873,0.6985,0.6989,0.7215,0.7272,0.7321,0.7357,0.7367,0.7406,
0.7478,0.7501,0.7511,0.7522,0.7555,0.7629,0.7662,0.7675,0.7675,0.7675,
0.7696,0.7720,0.7725,0.7777,0.7812,0.7822,0.7852,0.7861,0.7883,0.7988,
0.7993,0.8006,0.8117,0.8197,0.8215,0.8231,0.8310,0.8369,0.8370,0.8392,
0.8433,0.8435,0.8481,0.8491,0.8503,0.8530,0.8575,0.8595,0.8696,0.8764,
0.8831,0.8871,0.8922,0.8937,0.8960,0.9009,0.9096,0.9102,0.9218,0.9282,
0.9335,0.9341,0.9357,0.9357,0.9402,0.9443,0.9487,0.9535,0.9561,0.9580,
0.9598,0.9657,0.9799,0.9833,0.9845,0.9880,0.9886,0.9934,0.9969,
Overall p-value after applying KStest on 269 p-values = 0.081434
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.