RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.84 23.6319 0.870214
2 to 25 15.88 11.9775 0.198504
3 to 26 15.69 20.4835 0.749751
4 to 27 16.01 16.5730 0.516363
5 to 28 15.66 19.8165 0.716276
6 to 29 15.91 19.0755 0.675787
7 to 30 15.72 19.5391 0.701522
8 to 31 15.58 34.1473 0.991964
9 to 32 16.01 16.4649 0.508849
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.133925
Tough bday spacings test for dh-ranFile-2018-06-22_17:31: 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 38 71 96 100 82 47 31 15 9 1
(O-E)^2/E 0.1 0.1 0.1 0.0 0.1 0.2 0.5 0.1 0.0 0.9 2.3
Birthday Spacings: Sum(O-E)^2/E= 4.194, p= 0.062
RESULTS OF GCD FOR dh-ranFile-2018-06-22_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.666103
p-value, dist. of gcd's: 0.585759
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.797 0.428 0.807 0.134 0.398 0.767 0.378 0.239
Bits 8 to 15---> 0.419 0.894 0.956 0.687 0.029 0.324 0.177 0.283
Bits 16 to 23---> 0.986 0.916 0.727 0.368 0.729 0.525 0.914 0.825
Bits 24 to 31---> 0.265 0.825 0.839 0.391 0.664 0.363 0.045 0.444
KS test for the above 32 p values: 0.493
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_17:31,
p-values for 5 runs: 0.0992, 0.3105, 0.2699, 0.6015, 0.8316
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 210 211.4 0.010 0.010
r= 29 5086 5134.0 0.449 0.458
r= 30 23164 23103.0 0.161 0.619
r= 31 11540 11551.5 0.011 0.631
chi-square = 0.631 with df = 3; p-value = 0.111
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 240 211.4 3.864 3.864
r= 30 5156 5134.0 0.094 3.958
r= 31 23198 23103.0 0.390 4.348
r= 32 11406 11551.5 1.833 6.182
chi-square = 6.182 with df = 3; p-value = 0.897
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_17:31
b-rank test for bits 1 to 8, p=0.71183
b-rank test for bits 2 to 9, p=0.84132
b-rank test for bits 3 to 10, p=0.34994
b-rank test for bits 4 to 11, p=0.71163
b-rank test for bits 5 to 12, p=0.99219
b-rank test for bits 6 to 13, p=0.70870
b-rank test for bits 7 to 14, p=0.30345
b-rank test for bits 8 to 15, p=0.16822
b-rank test for bits 9 to 16, p=0.63960
b-rank test for bits 10 to 17, p=0.54832
b-rank test for bits 11 to 18, p=0.20308
b-rank test for bits 12 to 19, p=0.41534
b-rank test for bits 13 to 20, p=0.30659
b-rank test for bits 14 to 21, p=0.52829
b-rank test for bits 15 to 22, p=0.08153
b-rank test for bits 16 to 23, p=0.58230
b-rank test for bits 17 to 24, p=0.47139
b-rank test for bits 18 to 25, p=0.05912
b-rank test for bits 19 to 26, p=0.69798
b-rank test for bits 20 to 27, p=0.63383
b-rank test for bits 21 to 28, p=0.92381
b-rank test for bits 22 to 29, p=0.11155
b-rank test for bits 23 to 30, p=0.46385
b-rank test for bits 24 to 31, p=0.74828
b-rank test for bits 25 to 32, p=0.75331
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 = 0.808367
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_17:31
(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 142111 0.47 0.681248
2 141770 -0.33 0.372387
3 141497 -0.96 0.167676
4 142412 1.17 0.879895
5 141464 -1.04 0.149056
6 141932 0.05 0.521121
7 142744 1.95 0.974422
8 141372 -1.26 0.104659
9 141596 -0.73 0.232060
10 141979 0.16 0.564654
11 142215 0.71 0.762443
12 142116 0.48 0.685407
13 142406 1.16 0.877066
14 141888 -0.05 0.480126
15 141636 -0.64 0.261535
16 141722 -0.44 0.330807
17 141636 -0.64 0.261535
18 141799 -0.26 0.398288
19 141630 -0.65 0.256994
20 141599 -0.73 0.234205
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-22_17:31
Bits used No. missing words z-score p-value
23 to 32 141865 -0.1529 0.439254
22 to 31 141336 -1.9770 0.024021
21 to 30 142074 0.5678 0.714924
20 to 29 141877 -0.1115 0.455617
19 to 28 141966 0.1954 0.577466
18 to 27 142179 0.9299 0.823788
17 to 26 141809 -0.3460 0.364684
16 to 25 142271 1.2471 0.893827
15 to 24 142175 0.9161 0.820194
14 to 23 141364 -1.8804 0.030024
13 to 22 141413 -1.7115 0.043496
12 to 21 141521 -1.3391 0.090274
11 to 20 142100 0.6575 0.744565
10 to 19 141875 -0.1184 0.452884
9 to 18 142071 0.5575 0.711401
8 to 17 141724 -0.6391 0.261389
7 to 16 142201 1.0058 0.842734
6 to 15 141968 0.2023 0.580163
5 to 14 142264 1.2230 0.889335
4 to 13 142130 0.7609 0.776651
3 to 12 141914 0.0161 0.506424
2 to 11 141941 0.1092 0.543481
1 to 10 141721 -0.6494 0.258036
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-22_17:31
Bits used No. missing words z-score p-value
28 to 32 141578 -1.1232 0.130686
27 to 31 141682 -0.7706 0.220469
26 to 30 141592 -1.0757 0.141032
25 to 29 141995 0.2904 0.614248
24 to 28 141357 -1.8723 0.030582
23 to 27 141291 -2.0960 0.018040
22 to 26 141916 0.0226 0.509019
21 to 25 141483 -1.4452 0.074203
20 to 24 141866 -0.1469 0.441613
19 to 23 141510 -1.3537 0.087922
18 to 22 141484 -1.4418 0.074680
17 to 21 141855 -0.1842 0.426940
16 to 20 141411 -1.6893 0.045585
15 to 19 141419 -1.6621 0.048243
14 to 18 142661 2.5480 0.994583
13 to 17 141830 -0.2689 0.393998
12 to 16 142028 0.4023 0.656258
11 to 15 141942 0.1107 0.544091
10 to 14 141858 -0.1740 0.430933
9 to 13 141816 -0.3164 0.375860
8 to 12 142290 1.2904 0.901545
7 to 11 142026 0.3955 0.653760
6 to 10 142229 1.0836 0.860735
5 to 9 142001 0.3107 0.622003
4 to 8 141907 -0.0079 0.496849
3 to 7 141500 -1.3876 0.082636
2 to 6 141641 -0.9096 0.181519
1 to 5 142064 0.5243 0.699967
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-22_17:31
Bits used No. missing words z-score p-value
31 to 32 141466 -1.3078 0.095478
30 to 31 141860 -0.1455 0.442152
29 to 30 141997 0.2586 0.602033
28 to 29 142350 1.2999 0.903184
27 to 28 142363 1.3383 0.909594
26 to 27 141977 0.1996 0.579110
25 to 26 142148 0.7040 0.759297
24 to 25 141870 -0.1160 0.453819
23 to 24 141463 -1.3166 0.093985
22 to 23 142435 1.5506 0.939507
21 to 22 142026 0.3442 0.634637
20 to 21 142276 1.0816 0.860290
19 to 20 142464 1.6362 0.949101
18 to 19 142363 1.3383 0.909594
17 to 18 141819 -0.2665 0.394942
16 to 17 141966 0.1672 0.566381
15 to 16 140810 -3.2429 0.000592
14 to 15 141988 0.2321 0.591756
13 to 14 141920 0.0315 0.512555
12 to 13 142483 1.6922 0.954700
11 to 12 141356 -1.6322 0.051314
10 to 11 141175 -2.1662 0.015149
9 to 10 141740 -0.4995 0.308714
8 to 9 141830 -0.2340 0.407488
7 to 8 142349 1.2970 0.902678
6 to 7 141289 -1.8299 0.033634
5 to 6 142485 1.6981 0.955259
4 to 5 141679 -0.6794 0.248430
3 to 4 141600 -0.9125 0.180759
2 to 3 141674 -0.6942 0.243782
1 to 2 142400 1.4474 0.926108
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2425.29 -1.057 0.145352
Test results for specific bytes for dh-ranFile-2018-06-22_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2460.36 -0.561 0.287523
2 to 9 2492.85 -0.101 0.459722
3 to 10 2498.13 -0.026 0.489456
4 to 11 2474.09 -0.366 0.357037
5 to 12 2511.46 0.162 0.564378
6 to 13 2585.07 1.203 0.885535
7 to 14 2422.73 -1.093 0.137253
8 to 15 2450.57 -0.699 0.242249
9 to 16 2510.92 0.154 0.561384
10 to 17 2458.71 -0.584 0.279637
11 to 18 2411.81 -1.247 0.106173
12 to 19 2522.73 0.322 0.626090
13 to 20 2566.09 0.935 0.825029
14 to 21 2519.29 0.273 0.607518
15 to 22 2400.17 -1.412 0.079010
16 to 23 2464.94 -0.496 0.310032
17 to 24 2408.64 -1.292 0.098179
18 to 25 2565.88 0.932 0.824236
19 to 26 2590.01 1.273 0.898482
20 to 27 2438.21 -0.874 0.191116
21 to 28 2533.38 0.472 0.681554
22 to 29 2538.40 0.543 0.706437
23 to 30 2417.93 -1.161 0.122892
24 to 31 2456.23 -0.619 0.267944
25 to 32 2476.80 -0.328 0.371443
CDPARK for dh-ranFile-2018-06-22_17:31: 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
3539 0.7306 0.767486
3508 -0.6849 0.246694
3511 -0.5479 0.291865
3549 1.1872 0.882429
3544 0.9589 0.831196
3545 1.0046 0.842447
3537 0.6393 0.738676
3515 -0.3653 0.357445
3543 0.9132 0.819442
3499 -1.0959 0.136563
Square side=100, avg. no. parked=3529.00 sample std.=17.61
p-value of the KSTEST for those 10 p-values: 0.316693
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_17:31
0.2291,0.7291,0.1764,0.3147,0.3491,0.8393,0.3663,0.2356,0.7802,0.9397,
The KS test for those 10 p-values: 0.759199
The 3DSPHERES test for dh-ranFile-2018-06-22_17:31
sample no r^3 equiv. uni.
1 13.789 0.368493
2 13.440 0.361092
3 4.761 0.146742
4 25.569 0.573563
5 35.755 0.696336
6 5.346 0.163218
7 7.276 0.215365
8 11.847 0.326245
9 1.785 0.057764
10 10.614 0.297991
11 18.303 0.456709
12 38.227 0.720358
13 1.728 0.055964
14 72.634 0.911179
15 104.631 0.969429
16 113.729 0.977427
17 7.279 0.215445
18 21.958 0.519029
19 9.222 0.264647
20 4.717 0.145482
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.279762
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 0.3 -0.1 -1.8 -1.2
0.1 1.4 -0.2 0.5 0.8 1.3
-0.4 -0.3 -0.5 0.3 -0.7 0.7
0.3 -0.4 -1.4 0.2 -0.6 0.2
1.5 0.2 0.1 0.7 -1.2 -0.3
0.1 -2.0 1.2 0.3 -0.9 -0.7
-0.5 -1.0 0.1 -1.3 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:28.530527
z-score=-1.469640, p-value=0.055932
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-22_17:31
Test no p-value
1 0.668374
2 0.240584
3 0.660537
4 0.033337
5 0.180164
6 0.818966
7 0.568520
8 0.516290
9 0.673743
10 0.909654
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.876753
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_17:31:
(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 66946 1.17 66629 0.02
3 25000.00 24670 4.36 25018 0.01
4 6666.67 6657 0.01 6715 0.35
5 1388.89 1418 0.61 1341 1.65
6 238.10 261 2.20 248 0.41
7 34.72 41 1.14 39 0.53
8 4.96 6 0.22 9 3.29
p=0.86250 p=0.60596
Number of rngs required: 688941, p-value: 0.733
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_17:31
No. of wins: Observed Expected
97964 98585.9
z-score=-2.781, pvalue=0.00271
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66484 66666.7 0.501 0.501
2 37953 37654.3 2.369 2.870
3 26971 26954.7 0.010 2.879
4 19294 19313.5 0.020 2.899
5 13766 13851.4 0.527 3.426
6 9986 9943.5 0.181 3.607
7 7090 7145.0 0.424 4.031
8 5094 5139.1 0.395 4.426
9 3689 3699.9 0.032 4.458
10 2739 2666.3 1.982 6.441
11 1902 1923.3 0.237 6.677
12 1436 1388.7 1.608 8.285
13 1019 1003.7 0.233 8.518
14 683 726.1 2.563 11.081
15 516 525.8 0.184 11.265
16 375 381.2 0.099 11.364
17 274 276.5 0.023 11.388
18 210 200.8 0.419 11.806
19 137 146.0 0.553 12.359
20 88 106.2 3.124 15.483
21 294 287.1 0.165 15.648
Chisq= 15.65 for 20 degrees of freedom, p= 0.26181
SUMMARY of craptest
p-value for no. of wins: 0.002707
p-value for throws/game: 0.261809
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_17:31
No. of wins: Observed Expected
98278 98585.9
z-score=-1.377, pvalue=0.08427
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66521 66666.7 0.318 0.318
2 37673 37654.3 0.009 0.328
3 26960 26954.7 0.001 0.329
4 19209 19313.5 0.565 0.894
5 13943 13851.4 0.605 1.499
6 9862 9943.5 0.669 2.168
7 7269 7145.0 2.151 4.319
8 5201 5139.1 0.746 5.065
9 3760 3699.9 0.977 6.043
10 2665 2666.3 0.001 6.043
11 1987 1923.3 2.108 8.151
12 1364 1388.7 0.441 8.592
13 1043 1003.7 1.538 10.129
14 708 726.1 0.453 10.582
15 546 525.8 0.773 11.356
16 358 381.2 1.406 12.762
17 247 276.5 3.155 15.917
18 182 200.8 1.765 17.683
19 153 146.0 0.337 18.020
20 107 106.2 0.006 18.026
21 242 287.1 7.089 25.114
Chisq= 25.11 for 20 degrees of freedom, p= 0.80291
SUMMARY of craptest
p-value for no. of wins: 0.084268
p-value for throws/game: 0.802910
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0027,0.0151,0.0180,0.0240,0.0292,0.0300,0.0306,0.0333,0.0336,
0.0435,0.0446,0.0456,0.0482,0.0513,0.0559,0.0560,0.0578,0.0591,0.0618,
0.0742,0.0747,0.0790,0.0815,0.0826,0.0843,0.0879,0.0903,0.0940,0.0955,
0.0982,0.0992,0.1047,0.1062,0.1107,0.1115,0.1229,0.1307,0.1339,0.1339,
0.1366,0.1373,0.1410,0.1454,0.1455,0.1467,0.1491,0.1632,0.1677,0.1682,
0.1764,0.1767,0.1802,0.1808,0.1815,0.1911,0.1985,0.2031,0.2154,0.2154,
0.2205,0.2291,0.2321,0.2342,0.2356,0.2392,0.2406,0.2422,0.2438,0.2467,
0.2484,0.2570,0.2580,0.2614,0.2615,0.2615,0.2618,0.2646,0.2647,0.2679,
0.2699,0.2796,0.2798,0.2831,0.2875,0.2919,0.2980,0.3035,0.3066,0.3087,
0.3100,0.3105,0.3147,0.3167,0.3244,0.3262,0.3308,0.3491,0.3499,0.3570,
0.3574,0.3611,0.3631,0.3647,0.3663,0.3683,0.3685,0.3714,0.3724,0.3759,
0.3777,0.3914,0.3940,0.3949,0.3983,0.3984,0.4075,0.4153,0.4190,0.4269,
0.4278,0.4309,0.4393,0.4416,0.4422,0.4437,0.4529,0.4538,0.4556,0.4567,
0.4597,0.4638,0.4714,0.4801,0.4895,0.4928,0.4968,0.5064,0.5088,0.5090,
0.5126,0.5163,0.5164,0.5190,0.5211,0.5254,0.5283,0.5435,0.5441,0.5483,
0.5614,0.5644,0.5647,0.5664,0.5685,0.5736,0.5775,0.5791,0.5802,0.5823,
0.5858,0.5918,0.6015,0.6020,0.6060,0.6075,0.6142,0.6220,0.6261,0.6338,
0.6346,0.6396,0.6538,0.6563,0.6605,0.6638,0.6661,0.6684,0.6737,0.6758,
0.6812,0.6816,0.6854,0.6869,0.6963,0.6980,0.7000,0.7015,0.7064,0.7087,
0.7114,0.7116,0.7118,0.7149,0.7163,0.7204,0.7265,0.7291,0.7295,0.7326,
0.7387,0.7446,0.7483,0.7498,0.7533,0.7592,0.7593,0.7624,0.7669,0.7675,
0.7767,0.7802,0.7975,0.8029,0.8065,0.8084,0.8190,0.8194,0.8202,0.8238,
0.8242,0.8247,0.8250,0.8251,0.8312,0.8316,0.8386,0.8393,0.8413,0.8424,
0.8427,0.8603,0.8607,0.8625,0.8702,0.8768,0.8771,0.8799,0.8824,0.8855,
0.8893,0.8937,0.8938,0.8969,0.8985,0.9015,0.9027,0.9032,0.9096,0.9096,
0.9097,0.9112,0.9137,0.9164,0.9238,0.9261,0.9395,0.9397,0.9491,0.9547,
0.9553,0.9564,0.9694,0.9744,0.9774,0.9861,0.9920,0.9922,0.9946,
Overall p-value after applying KStest on 269 p-values = 0.862829
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.