RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-08-26_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.74 23.1859 0.856704
2 to 25 15.70 20.2728 0.739485
3 to 26 15.92 13.9680 0.330631
4 to 27 15.70 13.6055 0.305195
5 to 28 15.37 38.6096 0.997975
6 to 29 15.86 22.2075 0.823128
7 to 30 15.70 18.1610 0.621250
8 to 31 15.88 22.8888 0.847094
9 to 32 15.68 16.7966 0.531775
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.094539
Tough bday spacings test for dh-ranFile-2018-08-26_01:31: 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 6 38 79 104 91 78 59 24 12 6 3
(O-E)^2/E 1.1 0.1 0.4 0.4 0.5 0.0 0.9 1.1 0.6 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 5.384, p= 0.136
RESULTS OF GCD FOR dh-ranFile-2018-08-26_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.837904
p-value, dist. of gcd's: 0.781986
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-08-26_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.654 0.922 0.463 0.640 0.931 0.236 0.088 0.528
Bits 8 to 15---> 0.793 0.939 0.314 0.403 0.025 0.692 0.460 0.480
Bits 16 to 23---> 0.388 0.622 0.986 0.282 0.594 0.487 0.630 0.528
Bits 24 to 31---> 0.822 0.923 0.044 0.941 0.494 0.207 0.771 0.078
KS test for the above 32 p values: 0.407
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-08-26_01:31,
p-values for 5 runs: 0.3907, 0.9009, 0.4669, 0.9284, 0.8125
Rank test for binary matrices (31x31) for dh-ranFile-2018-08-26_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 181 211.4 4.376 4.376
r= 29 5070 5134.0 0.798 5.175
r= 30 23128 23103.0 0.027 5.201
r= 31 11621 11551.5 0.418 5.619
chi-square = 5.619 with df = 3; p-value = 0.868
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-08-26_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 195 211.4 1.275 1.275
r= 30 5149 5134.0 0.044 1.319
r= 31 23093 23103.0 0.004 1.323
r= 32 11563 11551.5 0.011 1.335
chi-square = 1.335 with df = 3; p-value = 0.279
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-08-26_01:31
b-rank test for bits 1 to 8, p=0.65762
b-rank test for bits 2 to 9, p=0.42714
b-rank test for bits 3 to 10, p=0.50646
b-rank test for bits 4 to 11, p=0.88580
b-rank test for bits 5 to 12, p=0.90728
b-rank test for bits 6 to 13, p=0.20746
b-rank test for bits 7 to 14, p=0.66936
b-rank test for bits 8 to 15, p=0.96802
b-rank test for bits 9 to 16, p=0.68050
b-rank test for bits 10 to 17, p=0.53093
b-rank test for bits 11 to 18, p=0.36658
b-rank test for bits 12 to 19, p=0.06212
b-rank test for bits 13 to 20, p=0.51392
b-rank test for bits 14 to 21, p=0.09372
b-rank test for bits 15 to 22, p=0.36618
b-rank test for bits 16 to 23, p=0.27639
b-rank test for bits 17 to 24, p=0.73194
b-rank test for bits 18 to 25, p=0.22040
b-rank test for bits 19 to 26, p=0.35789
b-rank test for bits 20 to 27, p=0.28490
b-rank test for bits 21 to 28, p=0.16964
b-rank test for bits 22 to 29, p=0.11817
b-rank test for bits 23 to 30, p=0.41198
b-rank test for bits 24 to 31, p=0.32305
b-rank test for bits 25 to 32, p=0.02599
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 = 0.391225
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-08-26_01:31
(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 141464 -1.04 0.149056
2 142623 1.67 0.952288
3 142322 0.96 0.832523
4 142029 0.28 0.610109
5 141260 -1.52 0.064617
6 142253 0.80 0.789003
7 141508 -0.94 0.174203
8 141531 -0.88 0.188362
9 142097 0.44 0.669481
10 142635 1.70 0.955009
11 141655 -0.59 0.276180
12 142731 1.92 0.972558
13 142242 0.78 0.781499
14 142243 0.78 0.782188
15 142793 2.06 0.980522
16 141477 -1.01 0.156220
17 141303 -1.42 0.078291
18 141842 -0.16 0.437499
19 142075 0.39 0.650651
20 142420 1.19 0.883596
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-08-26_01:31
Bits used No. missing words z-score p-value
23 to 32 141570 -1.1701 0.120980
22 to 31 141798 -0.3839 0.350528
21 to 30 141570 -1.1701 0.120980
20 to 29 141614 -1.0184 0.154249
19 to 28 142009 0.3437 0.634460
18 to 27 141855 -0.1873 0.425695
17 to 26 142066 0.5402 0.705485
16 to 25 142219 1.0678 0.857201
15 to 24 141748 -0.5563 0.288999
14 to 23 141969 0.2058 0.581510
13 to 22 142028 0.4092 0.658806
12 to 21 142368 1.5816 0.943132
11 to 20 141904 -0.0184 0.492668
10 to 19 142133 0.7713 0.779728
9 to 18 141673 -0.8149 0.207556
8 to 17 141489 -1.4494 0.073611
7 to 16 141750 -0.5494 0.291361
6 to 15 141708 -0.6942 0.243765
5 to 14 141804 -0.3632 0.358225
4 to 13 141532 -1.3011 0.096606
3 to 12 142066 0.5402 0.705485
2 to 11 141980 0.2437 0.596264
1 to 10 141821 -0.3046 0.380341
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-08-26_01:31
Bits used No. missing words z-score p-value
28 to 32 141915 0.0192 0.507667
27 to 31 141979 0.2362 0.593349
26 to 30 141370 -1.8282 0.033757
25 to 29 141705 -0.6926 0.244267
24 to 28 141963 0.1819 0.572182
23 to 27 142240 1.1209 0.868838
22 to 26 142259 1.1853 0.882055
21 to 25 141916 0.0226 0.509019
20 to 24 141972 0.2124 0.584118
19 to 23 141504 -1.3740 0.084721
18 to 22 142140 0.7819 0.782873
17 to 21 141700 -0.7096 0.238978
16 to 20 141961 0.1752 0.569520
15 to 19 141721 -0.6384 0.261605
14 to 18 141877 -0.1096 0.456366
13 to 17 141649 -0.8825 0.188760
12 to 16 141638 -0.9198 0.178848
11 to 15 141687 -0.7537 0.225526
10 to 14 141854 -0.1876 0.425611
9 to 13 142095 0.6294 0.735453
8 to 12 141425 -1.6418 0.050316
7 to 11 141972 0.2124 0.584118
6 to 10 142536 2.1243 0.983178
5 to 9 142033 0.4192 0.662473
4 to 8 142133 0.7582 0.775835
3 to 7 142056 0.4972 0.690471
2 to 6 141912 0.0091 0.503611
1 to 5 142045 0.4599 0.677205
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-08-26_01:31
Bits used No. missing words z-score p-value
31 to 32 141613 -0.8741 0.191024
30 to 31 142033 0.3648 0.642373
29 to 30 142367 1.3501 0.911501
28 to 29 142162 0.7453 0.771967
27 to 28 142238 0.9695 0.833859
26 to 27 141784 -0.3697 0.355801
25 to 26 141662 -0.7296 0.232821
24 to 25 142245 0.9902 0.838956
23 to 24 141702 -0.6116 0.270404
22 to 23 141348 -1.6558 0.048877
21 to 22 141947 0.1111 0.544240
20 to 21 141771 -0.4081 0.341617
19 to 20 142080 0.5035 0.692677
18 to 19 141828 -0.2399 0.405199
17 to 18 141759 -0.4435 0.328720
16 to 17 141670 -0.7060 0.240098
15 to 16 141895 -0.0423 0.483141
14 to 15 141800 -0.3225 0.373534
13 to 14 142394 1.4297 0.923599
12 to 13 141404 -1.4906 0.068027
11 to 12 140810 -3.2429 0.000592
10 to 11 142024 0.3383 0.632416
9 to 10 142144 0.6922 0.755607
8 to 9 141440 -1.3845 0.083110
7 to 8 142508 1.7660 0.961301
6 to 7 142144 0.6922 0.755607
5 to 6 142349 1.2970 0.902678
4 to 5 141950 0.1200 0.547747
3 to 4 141901 -0.0246 0.490198
2 to 3 142350 1.2999 0.903184
1 to 2 142256 1.0226 0.846758
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-08-26_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2573.60 1.041 0.851037
Test results for specific bytes for dh-ranFile-2018-08-26_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2532.15 0.455 0.675302
2 to 9 2443.69 -0.796 0.212900
3 to 10 2378.00 -1.725 0.042227
4 to 11 2511.06 0.156 0.562159
5 to 12 2476.80 -0.328 0.371422
6 to 13 2572.75 1.029 0.848213
7 to 14 2537.19 0.526 0.700550
8 to 15 2563.92 0.904 0.816988
9 to 16 2500.07 0.001 0.500381
10 to 17 2407.62 -1.306 0.095710
11 to 18 2441.51 -0.827 0.204075
12 to 19 2513.57 0.192 0.576076
13 to 20 2409.49 -1.280 0.100283
14 to 21 2518.81 0.266 0.604877
15 to 22 2499.19 -0.012 0.495412
16 to 23 2490.26 -0.138 0.445239
17 to 24 2484.57 -0.218 0.413626
18 to 25 2473.42 -0.376 0.353480
19 to 26 2331.19 -2.387 0.008484
20 to 27 2566.58 0.942 0.826798
21 to 28 2387.10 -1.597 0.055173
22 to 29 2575.81 1.072 0.858159
23 to 30 2414.15 -1.214 0.112346
24 to 31 2581.36 1.151 0.875038
25 to 32 2612.76 1.595 0.944605
CDPARK for dh-ranFile-2018-08-26_01:31: 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
3555 1.4612 0.928018
3546 1.0502 0.853193
3548 1.1416 0.873180
3502 -0.9589 0.168804
3538 0.6849 0.753306
3509 -0.6393 0.261324
3523 0.0000 0.500000
3545 1.0046 0.842447
3472 -2.3288 0.009936
3534 0.5023 0.692266
Square side=100, avg. no. parked=3527.20 sample std.=24.64
p-value of the KSTEST for those 10 p-values: 0.353287
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-08-26_01:31
0.8788,0.1941,0.7817,0.2178,0.1917,0.7321,0.0072,0.4335,0.9854,0.5065,
The KS test for those 10 p-values: 0.832594
The 3DSPHERES test for dh-ranFile-2018-08-26_01:31
sample no r^3 equiv. uni.
1 16.205 0.417350
2 5.886 0.178163
3 22.811 0.532502
4 88.892 0.948339
5 5.902 0.178586
6 44.228 0.771052
7 73.025 0.912328
8 18.800 0.465627
9 34.779 0.686298
10 39.872 0.735278
11 14.346 0.380094
12 4.804 0.147977
13 60.850 0.868446
14 11.949 0.328547
15 30.454 0.637640
16 29.739 0.628905
17 21.250 0.507538
18 31.333 0.648112
19 23.596 0.544572
20 21.603 0.513303
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.405871
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-08-26_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 1.5 0.2 1.0 -0.5
0.1 -0.1 0.7 -2.2 1.3 1.3
-0.9 1.2 -0.1 -0.1 -1.5 0.1
0.3 -0.6 -1.7 1.0 0.2 0.0
-1.4 1.1 1.4 0.8 1.7 0.0
-0.5 0.8 0.2 0.3 -0.6 -0.8
-0.5 -2.0 2.1 1.0 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:43.215337
z-score=0.132604, p-value=0.580821
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-08-26_01:31
Test no p-value
1 0.014443
2 0.152647
3 0.197199
4 0.008767
5 0.021952
6 0.206445
7 0.928468
8 0.583972
9 0.302203
10 0.276067
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.005810
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-08-26_01:31:
(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 66642 0.01 66734 0.07
3 25000.00 25023 0.02 25013 0.01
4 6666.67 6689 0.07 6548 2.11
5 1388.89 1379 0.07 1400 0.09
6 238.10 232 0.16 249 0.50
7 34.72 28 1.30 50 6.72
8 4.96 6 0.22 5 0.00
p=0.06706 p=0.85267
Number of rngs required: 689855, p-value: 0.956
RESULTS OF CRAPS TEST for dh-ranFile-2018-08-26_01:31
No. of wins: Observed Expected
98993 98585.9
z-score= 1.821, pvalue=0.96569
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66755 66666.7 0.117 0.117
2 37827 37654.3 0.792 0.909
3 26882 26954.7 0.196 1.105
4 19350 19313.5 0.069 1.174
5 13818 13851.4 0.081 1.255
6 9866 9943.5 0.605 1.860
7 6999 7145.0 2.984 4.844
8 5138 5139.1 0.000 4.844
9 3777 3699.9 1.608 6.452
10 2619 2666.3 0.839 7.291
11 1962 1923.3 0.778 8.069
12 1350 1388.7 1.081 9.150
13 993 1003.7 0.114 9.264
14 744 726.1 0.439 9.703
15 530 525.8 0.033 9.736
16 382 381.2 0.002 9.738
17 276 276.5 0.001 9.739
18 197 200.8 0.073 9.812
19 144 146.0 0.027 9.839
20 100 106.2 0.364 10.203
21 291 287.1 0.053 10.255
Chisq= 10.26 for 20 degrees of freedom, p= 0.03670
SUMMARY of craptest
p-value for no. of wins: 0.965695
p-value for throws/game: 0.036700
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-08-26_01:31
No. of wins: Observed Expected
98758 98585.9
z-score= 0.770, pvalue=0.77933
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66399 66666.7 1.075 1.075
2 37524 37654.3 0.451 1.526
3 26934 26954.7 0.016 1.542
4 19377 19313.5 0.209 1.751
5 14079 13851.4 3.739 5.490
6 10057 9943.5 1.295 6.784
7 7239 7145.0 1.236 8.020
8 4994 5139.1 4.095 12.116
9 3687 3699.9 0.045 12.160
10 2749 2666.3 2.565 14.726
11 1915 1923.3 0.036 14.762
12 1412 1388.7 0.390 15.151
13 1012 1003.7 0.068 15.220
14 755 726.1 1.147 16.367
15 518 525.8 0.117 16.483
16 378 381.2 0.026 16.509
17 267 276.5 0.329 16.839
18 186 200.8 1.095 17.934
19 154 146.0 0.440 18.374
20 92 106.2 1.902 20.276
21 272 287.1 0.796 21.072
Chisq= 21.07 for 20 degrees of freedom, p= 0.60709
SUMMARY of craptest
p-value for no. of wins: 0.779325
p-value for throws/game: 0.607086
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0058,0.0072,0.0085,0.0088,0.0099,0.0144,0.0220,0.0247,0.0260,
0.0338,0.0367,0.0422,0.0444,0.0489,0.0503,0.0552,0.0621,0.0646,0.0671,
0.0680,0.0736,0.0783,0.0784,0.0831,0.0847,0.0878,0.0937,0.0945,0.0957,
0.0966,0.1003,0.1123,0.1182,0.1210,0.1210,0.1359,0.1480,0.1491,0.1526,
0.1542,0.1562,0.1688,0.1696,0.1742,0.1782,0.1786,0.1788,0.1884,0.1888,
0.1910,0.1917,0.1941,0.1972,0.2041,0.2064,0.2072,0.2075,0.2076,0.2129,
0.2178,0.2204,0.2255,0.2328,0.2365,0.2390,0.2401,0.2438,0.2443,0.2613,
0.2616,0.2704,0.2761,0.2762,0.2764,0.2790,0.2815,0.2849,0.2890,0.2914,
0.3022,0.3052,0.3141,0.3230,0.3285,0.3287,0.3306,0.3416,0.3505,0.3533,
0.3535,0.3558,0.3579,0.3582,0.3662,0.3666,0.3714,0.3735,0.3801,0.3803,
0.3882,0.3907,0.3912,0.4028,0.4052,0.4059,0.4072,0.4120,0.4136,0.4173,
0.4256,0.4257,0.4271,0.4335,0.4375,0.4452,0.4564,0.4602,0.4627,0.4656,
0.4669,0.4795,0.4831,0.4865,0.4902,0.4927,0.4944,0.4954,0.5000,0.5004,
0.5036,0.5065,0.5065,0.5075,0.5077,0.5090,0.5133,0.5139,0.5277,0.5284,
0.5309,0.5318,0.5325,0.5442,0.5446,0.5477,0.5622,0.5695,0.5722,0.5761,
0.5808,0.5815,0.5840,0.5841,0.5841,0.5933,0.5943,0.5963,0.6049,0.6071,
0.6101,0.6212,0.6217,0.6289,0.6304,0.6324,0.6345,0.6376,0.6397,0.6424,
0.6481,0.6507,0.6537,0.6576,0.6588,0.6625,0.6694,0.6695,0.6753,0.6772,
0.6805,0.6863,0.6905,0.6918,0.6923,0.6927,0.7005,0.7055,0.7055,0.7319,
0.7321,0.7353,0.7355,0.7395,0.7533,0.7556,0.7556,0.7706,0.7711,0.7720,
0.7758,0.7793,0.7797,0.7815,0.7817,0.7820,0.7822,0.7829,0.7890,0.7927,
0.8125,0.8170,0.8221,0.8231,0.8268,0.8325,0.8326,0.8339,0.8379,0.8390,
0.8424,0.8468,0.8471,0.8482,0.8510,0.8527,0.8532,0.8567,0.8572,0.8582,
0.8683,0.8684,0.8688,0.8732,0.8750,0.8788,0.8821,0.8836,0.8858,0.9009,
0.9027,0.9032,0.9073,0.9115,0.9123,0.9219,0.9230,0.9236,0.9280,0.9284,
0.9285,0.9309,0.9393,0.9408,0.9431,0.9446,0.9483,0.9523,0.9550,0.9557,
0.9613,0.9657,0.9680,0.9726,0.9805,0.9832,0.9854,0.9863,0.9980,
Overall p-value after applying KStest on 269 p-values = 0.897281
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.