RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_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 15.78 18.6697 0.652182
2 to 25 15.57 18.5079 0.642502
3 to 26 15.84 22.2181 0.823524
4 to 27 15.75 28.7428 0.963028
5 to 28 15.70 20.8560 0.767204
6 to 29 15.57 23.2111 0.857496
7 to 30 15.73 17.0912 0.551799
8 to 31 15.94 14.1356 0.342519
9 to 32 15.86 18.6111 0.648693
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.061530
Tough bday spacings test for dh-ranFile-2018-06-21_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 12 33 65 105 107 68 47 26 23 9 5
(O-E)^2/E 0.9 0.4 0.9 0.5 0.9 1.3 0.5 0.5 4.4 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 11.402, p= 0.673
RESULTS OF GCD FOR dh-ranFile-2018-06-21_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.634347
p-value, dist. of gcd's: 0.424509
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.756 0.923 0.728 0.807 0.768 0.938 0.059 0.291
Bits 8 to 15---> 0.528 0.904 0.398 0.177 0.125 0.893 0.721 0.017
Bits 16 to 23---> 0.990 0.467 0.549 0.249 0.323 0.171 0.681 0.001
Bits 24 to 31---> 0.621 0.232 0.610 0.501 0.934 0.663 0.859 0.551
KS test for the above 32 p values: 0.418
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_20:31,
p-values for 5 runs: 0.1069, 0.8130, 0.4630, 0.3749, 0.3822
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5218 5134.0 1.374 1.435
r= 30 23134 23103.0 0.041 1.476
r= 31 11433 11551.5 1.216 2.692
chi-square = 2.692 with df = 3; p-value = 0.558
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 254 211.4 8.576 8.576
r= 30 5157 5134.0 0.103 8.679
r= 31 23055 23103.0 0.100 8.779
r= 32 11534 11551.5 0.027 8.806
chi-square = 8.806 with df = 3; p-value = 0.968
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_20:31
b-rank test for bits 1 to 8, p=0.72377
b-rank test for bits 2 to 9, p=0.40584
b-rank test for bits 3 to 10, p=0.95000
b-rank test for bits 4 to 11, p=0.87842
b-rank test for bits 5 to 12, p=0.16457
b-rank test for bits 6 to 13, p=0.07958
b-rank test for bits 7 to 14, p=0.47927
b-rank test for bits 8 to 15, p=0.43297
b-rank test for bits 9 to 16, p=0.66597
b-rank test for bits 10 to 17, p=0.54538
b-rank test for bits 11 to 18, p=0.34156
b-rank test for bits 12 to 19, p=0.21648
b-rank test for bits 13 to 20, p=0.48898
b-rank test for bits 14 to 21, p=0.12533
b-rank test for bits 15 to 22, p=0.04969
b-rank test for bits 16 to 23, p=0.79222
b-rank test for bits 17 to 24, p=0.58014
b-rank test for bits 18 to 25, p=0.01902
b-rank test for bits 19 to 26, p=0.00320
b-rank test for bits 20 to 27, p=0.15296
b-rank test for bits 21 to 28, p=0.25055
b-rank test for bits 22 to 29, p=0.67746
b-rank test for bits 23 to 30, p=0.00338
b-rank test for bits 24 to 31, p=0.21224
b-rank test for bits 25 to 32, p=0.29595
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 = 0.046823
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_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 142051 0.33 0.629680
2 142176 0.62 0.733378
3 142086 0.41 0.660116
4 142031 0.28 0.611900
5 142190 0.66 0.744014
6 141922 0.03 0.511808
7 141990 0.19 0.574750
8 141603 -0.72 0.237081
9 141859 -0.12 0.453195
10 141958 0.11 0.545268
11 142480 1.33 0.908790
12 141897 -0.03 0.488509
13 142051 0.33 0.629680
14 141612 -0.69 0.243623
15 141278 -1.48 0.070097
16 141791 -0.28 0.391093
17 142303 0.92 0.821159
18 143023 2.60 0.995366
19 142316 0.95 0.828985
20 141716 -0.45 0.325741
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_20:31
Bits used No. missing words z-score p-value
23 to 32 141513 -1.3667 0.085867
22 to 31 141649 -0.8977 0.184676
21 to 30 142146 0.8161 0.792780
20 to 29 141497 -1.4218 0.077538
19 to 28 141236 -2.3218 0.010121
18 to 27 141842 -0.2322 0.408202
17 to 26 141635 -0.9460 0.172083
16 to 25 142032 0.4230 0.663852
15 to 24 142139 0.7920 0.785810
14 to 23 141868 -0.1425 0.443336
13 to 22 141934 0.0851 0.533897
12 to 21 141739 -0.5873 0.278486
11 to 20 141810 -0.3425 0.365981
10 to 19 142587 2.3368 0.990275
9 to 18 141884 -0.0873 0.465199
8 to 17 141635 -0.9460 0.172083
7 to 16 142002 0.3196 0.625346
6 to 15 141754 -0.5356 0.296110
5 to 14 141244 -2.2942 0.010888
4 to 13 141493 -1.4356 0.075555
3 to 12 141721 -0.6494 0.258036
2 to 11 141923 0.0471 0.518798
1 to 10 141616 -1.0115 0.155893
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_20:31
Bits used No. missing words z-score p-value
28 to 32 141499 -1.3909 0.082120
27 to 31 141620 -0.9808 0.163351
26 to 30 142115 0.6972 0.757157
25 to 29 142215 1.0362 0.849938
24 to 28 141880 -0.0994 0.460401
23 to 27 141824 -0.2893 0.386193
22 to 26 141715 -0.6587 0.255030
21 to 25 141995 0.2904 0.614248
20 to 24 141662 -0.8384 0.200901
19 to 23 141671 -0.8079 0.209575
18 to 22 142274 1.2362 0.891802
17 to 21 142211 1.0226 0.846754
16 to 20 141907 -0.0079 0.496849
15 to 19 142116 0.7006 0.758216
14 to 18 141799 -0.3740 0.354202
13 to 17 142218 1.0463 0.852298
12 to 16 142272 1.2294 0.890537
11 to 15 141676 -0.7909 0.214487
10 to 14 141075 -2.8282 0.002340
9 to 13 142014 0.3548 0.638635
8 to 12 141791 -0.4011 0.344166
7 to 11 141750 -0.5401 0.294564
6 to 10 142152 0.8226 0.794635
5 to 9 142386 1.6158 0.946935
4 to 8 141801 -0.3672 0.356727
3 to 7 142027 0.3989 0.655010
2 to 6 142146 0.8023 0.788802
1 to 5 142088 0.6057 0.727630
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_20:31
Bits used No. missing words z-score p-value
31 to 32 142107 0.5831 0.720086
30 to 31 141855 -0.1603 0.436336
29 to 30 141768 -0.4169 0.338375
28 to 29 141885 -0.0718 0.471393
27 to 28 142579 1.9754 0.975890
26 to 27 142208 0.8810 0.810850
25 to 26 141971 0.1819 0.572176
24 to 25 141882 -0.0806 0.467872
23 to 24 141621 -0.8505 0.197515
22 to 23 142669 2.2409 0.987484
21 to 22 142049 0.4120 0.659832
20 to 21 141919 0.0285 0.511378
19 to 20 142594 2.0197 0.978291
18 to 19 142031 0.3589 0.640168
17 to 18 142008 0.2911 0.614498
16 to 17 141948 0.1141 0.545409
15 to 16 142272 1.0698 0.857651
14 to 15 142173 0.7778 0.781653
13 to 14 142053 0.4238 0.664146
12 to 13 141988 0.2321 0.591756
11 to 12 142455 1.6096 0.946262
10 to 11 142410 1.4769 0.930149
9 to 10 142159 0.7365 0.769284
8 to 9 141994 0.2498 0.598615
7 to 8 141663 -0.7266 0.233724
6 to 7 141718 -0.5644 0.286243
5 to 6 142405 1.4622 0.928150
4 to 5 142463 1.6332 0.948791
3 to 4 141351 -1.6470 0.049780
2 to 3 141526 -1.1308 0.129077
1 to 2 142103 0.5713 0.716101
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2390.51 -1.548 0.060753
Test results for specific bytes for dh-ranFile-2018-06-21_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2455.03 -0.636 0.262409
2 to 9 2503.61 0.051 0.520356
3 to 10 2407.60 -1.307 0.095646
4 to 11 2368.50 -1.860 0.031463
5 to 12 2479.33 -0.292 0.385012
6 to 13 2468.01 -0.452 0.325483
7 to 14 2496.89 -0.044 0.482468
8 to 15 2509.27 0.131 0.552161
9 to 16 2579.30 1.122 0.868968
10 to 17 2464.33 -0.504 0.306997
11 to 18 2643.11 2.024 0.978512
12 to 19 2494.29 -0.081 0.467822
13 to 20 2541.81 0.591 0.722840
14 to 21 2478.60 -0.303 0.381105
15 to 22 2524.47 0.346 0.635356
16 to 23 2480.71 -0.273 0.392504
17 to 24 2517.57 0.248 0.598122
18 to 25 2463.81 -0.512 0.304371
19 to 26 2504.03 0.057 0.522723
20 to 27 2516.65 0.235 0.593064
21 to 28 2585.34 1.207 0.886261
22 to 29 2510.11 0.143 0.556822
23 to 30 2503.06 0.043 0.517273
24 to 31 2423.26 -1.085 0.138913
25 to 32 2440.35 -0.844 0.199443
CDPARK for dh-ranFile-2018-06-21_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
3520 -0.1370 0.445521
3533 0.4566 0.676028
3533 0.4566 0.676028
3545 1.0046 0.842447
3507 -0.7306 0.232514
3501 -1.0046 0.157553
3514 -0.4110 0.340551
3533 0.4566 0.676028
3542 0.8676 0.807188
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3524.60 sample std.=14.05
p-value of the KSTEST for those 10 p-values: 0.736820
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_20:31
0.2853,0.8032,0.1933,0.9702,0.0868,0.5877,0.6258,0.8465,0.2238,0.8467,
The KS test for those 10 p-values: 0.812708
The 3DSPHERES test for dh-ranFile-2018-06-21_20:31
sample no r^3 equiv. uni.
1 44.376 0.772178
2 5.189 0.158845
3 33.305 0.670497
4 8.991 0.258970
5 9.894 0.280921
6 114.872 0.978270
7 32.882 0.665822
8 8.578 0.248682
9 1.946 0.062805
10 90.853 0.951608
11 65.441 0.887114
12 8.446 0.245371
13 28.787 0.616942
14 34.117 0.679293
15 8.333 0.242520
16 4.934 0.151647
17 23.708 0.546273
18 0.476 0.015744
19 18.751 0.464762
20 2.441 0.078138
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.616335
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 0.6 0.3 -1.0 2.2
-0.1 0.6 -1.2 0.3 1.4 -0.3
-1.5 -0.2 -0.5 -0.0 1.1 -0.8
0.1 0.9 1.2 -1.0 0.6 -0.6
1.7 0.3 -1.5 -0.1 -0.8 -0.7
-0.6 -0.7 -0.9 0.0 -1.5 1.3
-0.9 0.5 -0.4 1.0 -1.3 1.0
-0.1
Chi-square with 42 degrees of freedom:35.676811
z-score=-0.689917, p-value=0.256502
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_20:31
Test no p-value
1 0.086414
2 0.067317
3 0.115639
4 0.593411
5 0.868132
6 0.177214
7 0.104215
8 0.649862
9 0.003926
10 0.035558
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004059
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_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 66485 0.50 66545 0.22
3 25000.00 25137 0.75 25047 0.09
4 6666.67 6661 0.00 6792 2.36
5 1388.89 1445 2.27 1361 0.56
6 238.10 223 0.96 217 1.87
7 34.72 40 0.80 32 0.21
8 4.96 8 1.86 5 0.00
p=0.69196 p=0.49517
Number of rngs required: 688031, p-value: 0.334
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_20:31
No. of wins: Observed Expected
98239 98585.9
z-score=-1.551, pvalue=0.06041
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66245 66666.7 2.667 2.667
2 37688 37654.3 0.030 2.697
3 26905 26954.7 0.092 2.789
4 19266 19313.5 0.117 2.906
5 13820 13851.4 0.071 2.977
6 10064 9943.5 1.459 4.436
7 7277 7145.0 2.438 6.874
8 5249 5139.1 2.351 9.225
9 3750 3699.9 0.679 9.905
10 2735 2666.3 1.770 11.675
11 1929 1923.3 0.017 11.691
12 1401 1388.7 0.108 11.800
13 1030 1003.7 0.688 12.488
14 755 726.1 1.147 13.635
15 475 525.8 4.915 18.550
16 369 381.2 0.387 18.937
17 299 276.5 1.824 20.761
18 193 200.8 0.305 21.067
19 171 146.0 4.287 25.353
20 109 106.2 0.073 25.426
21 270 287.1 1.020 26.446
Chisq= 26.45 for 20 degrees of freedom, p= 0.84843
SUMMARY of craptest
p-value for no. of wins: 0.060408
p-value for throws/game: 0.848426
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_20:31
No. of wins: Observed Expected
98363 98585.9
z-score=-0.997, pvalue=0.15944
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66703 66666.7 0.020 0.020
2 37734 37654.3 0.169 0.188
3 27039 26954.7 0.263 0.452
4 19246 19313.5 0.236 0.687
5 14016 13851.4 1.956 2.643
6 9731 9943.5 4.543 7.186
7 7051 7145.0 1.237 8.423
8 5212 5139.1 1.035 9.458
9 3748 3699.9 0.626 10.085
10 2581 2666.3 2.729 12.813
11 1857 1923.3 2.287 15.101
12 1423 1388.7 0.845 15.946
13 1038 1003.7 1.171 17.117
14 719 726.1 0.070 17.187
15 516 525.8 0.184 17.371
16 339 381.2 4.661 22.033
17 275 276.5 0.009 22.041
18 216 200.8 1.146 23.187
19 171 146.0 4.287 27.474
20 112 106.2 0.315 27.789
21 273 287.1 0.694 28.483
Chisq= 28.48 for 20 degrees of freedom, p= 0.90154
SUMMARY of craptest
p-value for no. of wins: 0.159442
p-value for throws/game: 0.901542
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0023,0.0032,0.0034,0.0039,0.0041,0.0101,0.0109,0.0157,0.0174,
0.0190,0.0315,0.0356,0.0468,0.0497,0.0498,0.0588,0.0604,0.0608,0.0615,
0.0628,0.0673,0.0701,0.0756,0.0775,0.0781,0.0796,0.0821,0.0859,0.0864,
0.0868,0.0956,0.1042,0.1069,0.1156,0.1252,0.1253,0.1291,0.1389,0.1516,
0.1530,0.1559,0.1576,0.1588,0.1594,0.1634,0.1646,0.1707,0.1721,0.1721,
0.1771,0.1772,0.1847,0.1933,0.1975,0.1994,0.2009,0.2096,0.2122,0.2145,
0.2165,0.2238,0.2320,0.2325,0.2337,0.2371,0.2425,0.2436,0.2454,0.2487,
0.2491,0.2506,0.2550,0.2565,0.2580,0.2590,0.2624,0.2785,0.2809,0.2853,
0.2862,0.2908,0.2946,0.2959,0.2961,0.3044,0.3070,0.3228,0.3255,0.3257,
0.3341,0.3384,0.3406,0.3416,0.3425,0.3442,0.3542,0.3567,0.3660,0.3749,
0.3811,0.3822,0.3850,0.3862,0.3911,0.3925,0.3982,0.4058,0.4082,0.4097,
0.4175,0.4245,0.4330,0.4363,0.4433,0.4455,0.4532,0.4604,0.4630,0.4648,
0.4652,0.4670,0.4678,0.4679,0.4714,0.4793,0.4825,0.4885,0.4890,0.4952,
0.4968,0.5006,0.5114,0.5118,0.5173,0.5188,0.5204,0.5227,0.5277,0.5339,
0.5453,0.5454,0.5454,0.5463,0.5491,0.5508,0.5518,0.5522,0.5568,0.5585,
0.5722,0.5748,0.5801,0.5877,0.5918,0.5931,0.5934,0.5981,0.5986,0.6104,
0.6119,0.6142,0.6145,0.6163,0.6169,0.6213,0.6253,0.6258,0.6297,0.6297,
0.6343,0.6354,0.6386,0.6402,0.6425,0.6487,0.6499,0.6522,0.6550,0.6598,
0.6601,0.6629,0.6639,0.6641,0.6658,0.6660,0.6705,0.6729,0.6760,0.6760,
0.6760,0.6775,0.6793,0.6812,0.6920,0.7161,0.7201,0.7213,0.7228,0.7238,
0.7276,0.7283,0.7334,0.7368,0.7440,0.7561,0.7572,0.7582,0.7672,0.7679,
0.7693,0.7722,0.7817,0.7858,0.7888,0.7922,0.7928,0.7946,0.8032,0.8067,
0.8072,0.8108,0.8127,0.8130,0.8212,0.8235,0.8290,0.8424,0.8465,0.8467,
0.8468,0.8484,0.8499,0.8523,0.8575,0.8577,0.8588,0.8681,0.8690,0.8784,
0.8863,0.8871,0.8905,0.8918,0.8926,0.9015,0.9036,0.9088,0.9226,0.9282,
0.9301,0.9344,0.9380,0.9463,0.9469,0.9488,0.9500,0.9516,0.9630,0.9680,
0.9702,0.9759,0.9783,0.9783,0.9785,0.9875,0.9903,0.9903,0.9954,
Overall p-value after applying KStest on 269 p-values = 0.809152
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.