RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.86 34.7923 0.993376
2 to 25 15.76 10.2947 0.109200
3 to 26 16.01 12.0093 0.200428
4 to 27 15.72 19.7483 0.712696
5 to 28 15.74 16.0574 0.480230
6 to 29 15.83 15.4719 0.438468
7 to 30 15.70 15.0243 0.406270
8 to 31 15.98 25.0935 0.907363
9 to 32 15.59 21.6591 0.801814
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.758792
Tough bday spacings test for dh-ranFile-2018-06-20_13:31: 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 7 42 68 91 106 91 36 35 11 8 5
(O-E)^2/E 0.5 0.8 0.4 0.5 0.7 2.1 5.0 0.9 1.0 0.3 0.2
Birthday Spacings: Sum(O-E)^2/E= 12.364, p= 0.739
RESULTS OF GCD FOR dh-ranFile-2018-06-20_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.135048
p-value, dist. of gcd's: 0.882650
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.556 0.600 0.097 0.293 0.730 0.028 0.045 0.396
Bits 8 to 15---> 0.486 0.344 0.968 0.250 0.706 0.081 0.594 0.067
Bits 16 to 23---> 0.284 0.777 0.294 0.543 0.772 0.303 0.397 0.338
Bits 24 to 31---> 0.494 0.640 0.868 0.384 0.292 0.773 0.479 0.390
KS test for the above 32 p values: 0.723
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_13:31,
p-values for 5 runs: 0.8135, 0.2210, 0.6444, 0.5648, 0.7194
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 196 211.4 1.124 1.124
r= 29 5151 5134.0 0.056 1.181
r= 30 23073 23103.0 0.039 1.220
r= 31 11580 11551.5 0.070 1.290
chi-square = 1.290 with df = 3; p-value = 0.268
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 196 211.4 1.124 1.124
r= 30 5133 5134.0 0.000 1.125
r= 31 23152 23103.0 0.104 1.228
r= 32 11519 11551.5 0.092 1.320
chi-square = 1.320 with df = 3; p-value = 0.276
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_13:31
b-rank test for bits 1 to 8, p=0.07115
b-rank test for bits 2 to 9, p=0.41445
b-rank test for bits 3 to 10, p=0.05732
b-rank test for bits 4 to 11, p=0.29450
b-rank test for bits 5 to 12, p=0.53034
b-rank test for bits 6 to 13, p=0.23904
b-rank test for bits 7 to 14, p=0.30755
b-rank test for bits 8 to 15, p=0.27577
b-rank test for bits 9 to 16, p=0.83486
b-rank test for bits 10 to 17, p=0.92527
b-rank test for bits 11 to 18, p=0.49518
b-rank test for bits 12 to 19, p=0.15624
b-rank test for bits 13 to 20, p=0.51682
b-rank test for bits 14 to 21, p=0.65633
b-rank test for bits 15 to 22, p=0.45096
b-rank test for bits 16 to 23, p=0.49408
b-rank test for bits 17 to 24, p=0.30796
b-rank test for bits 18 to 25, p=0.53054
b-rank test for bits 19 to 26, p=0.41893
b-rank test for bits 20 to 27, p=0.27632
b-rank test for bits 21 to 28, p=0.22041
b-rank test for bits 22 to 29, p=0.48343
b-rank test for bits 23 to 30, p=0.19298
b-rank test for bits 24 to 31, p=0.05534
b-rank test for bits 25 to 32, p=0.15485
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 = 0.027539
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_13:31
(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 141734 -0.41 0.341032
2 142133 0.52 0.699371
3 142161 0.59 0.721739
4 142394 1.13 0.871268
5 142227 0.74 0.771023
6 141924 0.03 0.513671
7 141565 -0.80 0.210551
8 141491 -0.98 0.164184
9 142044 0.31 0.623486
10 142179 0.63 0.735676
11 142415 1.18 0.881292
12 141791 -0.28 0.391093
13 141983 0.17 0.568331
14 141701 -0.49 0.313217
15 142480 1.33 0.908790
16 141521 -0.91 0.182121
17 141659 -0.58 0.279313
18 141726 -0.43 0.334201
19 142125 0.50 0.692835
20 142152 0.57 0.714638
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_13:31
Bits used No. missing words z-score p-value
23 to 32 141518 -1.3494 0.088602
22 to 31 141790 -0.4115 0.340359
21 to 30 141987 0.2678 0.605584
20 to 29 142230 1.1058 0.865585
19 to 28 142194 0.9816 0.836857
18 to 27 142149 0.8264 0.795725
17 to 26 141947 0.1299 0.551676
16 to 25 142202 1.0092 0.843562
15 to 24 142353 1.5299 0.936979
14 to 23 141938 0.0989 0.539376
13 to 22 142267 1.2333 0.891276
12 to 21 142140 0.7954 0.786814
11 to 20 141845 -0.2218 0.412224
10 to 19 142342 1.4920 0.932146
9 to 18 142345 1.5023 0.933492
8 to 17 141946 0.1264 0.550312
7 to 16 141827 -0.2839 0.388245
6 to 15 142170 0.8989 0.815637
5 to 14 142342 1.4920 0.932146
4 to 13 142072 0.5609 0.712578
3 to 12 142077 0.5782 0.718426
2 to 11 141834 -0.2598 0.397525
1 to 10 142288 1.3058 0.904183
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_13:31
Bits used No. missing words z-score p-value
28 to 32 141941 0.1074 0.542747
27 to 31 141953 0.1480 0.558842
26 to 30 141726 -0.6215 0.267149
25 to 29 141997 0.2972 0.616838
24 to 28 141881 -0.0960 0.461747
23 to 27 141847 -0.2113 0.416331
22 to 26 141499 -1.3909 0.082120
21 to 25 141471 -1.4859 0.068658
20 to 24 142278 1.2497 0.894301
19 to 23 141953 0.1480 0.558842
18 to 22 142073 0.5548 0.710489
17 to 21 142287 1.2802 0.899769
16 to 20 141925 0.0531 0.521181
15 to 19 141726 -0.6215 0.267149
14 to 18 142085 0.5955 0.724243
13 to 17 141690 -0.7435 0.228592
12 to 16 142771 2.9209 0.998255
11 to 15 141639 -0.9164 0.179736
10 to 14 142076 0.5650 0.713957
9 to 13 141946 0.1243 0.549463
8 to 12 141605 -1.0316 0.151123
7 to 11 142180 0.9175 0.820566
6 to 10 141695 -0.7265 0.233753
5 to 9 142324 1.4057 0.920088
4 to 8 141839 -0.2384 0.405783
3 to 7 141616 -0.9943 0.160029
2 to 6 141935 0.0870 0.534671
1 to 5 141778 -0.4452 0.328093
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_13:31
Bits used No. missing words z-score p-value
31 to 32 141167 -2.1898 0.014271
30 to 31 142252 1.0108 0.843950
29 to 30 141907 -0.0069 0.497258
28 to 29 142539 1.8574 0.968375
27 to 28 142197 0.8486 0.801944
26 to 27 141910 0.0020 0.500789
25 to 26 141751 -0.4671 0.320232
24 to 25 141306 -1.7797 0.037560
23 to 24 141581 -0.9685 0.166391
22 to 23 141978 0.2026 0.580263
21 to 22 142170 0.7689 0.779035
20 to 21 141334 -1.6971 0.044835
19 to 20 141552 -1.0541 0.145925
18 to 19 142563 1.9282 0.973087
17 to 18 142057 0.4356 0.668438
16 to 17 141708 -0.5939 0.276292
15 to 16 141982 0.2144 0.584869
14 to 15 142424 1.5182 0.935518
13 to 14 142030 0.3560 0.639064
12 to 13 141896 -0.0393 0.484317
11 to 12 142081 0.5064 0.693713
10 to 11 141571 -0.9980 0.159134
9 to 10 142287 1.1141 0.867376
8 to 9 141716 -0.5703 0.284239
7 to 8 141252 -1.9390 0.026249
6 to 7 142394 1.4297 0.923599
5 to 6 141616 -0.8653 0.193443
4 to 5 142072 0.4799 0.684334
3 to 4 141829 -0.2370 0.406343
2 to 3 142042 0.3914 0.652233
1 to 2 141729 -0.5319 0.297381
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2521.56 0.305 0.619786
Test results for specific bytes for dh-ranFile-2018-06-20_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2485.95 -0.199 0.421228
2 to 9 2541.91 0.593 0.723323
3 to 10 2496.40 -0.051 0.479706
4 to 11 2454.94 -0.637 0.261962
5 to 12 2613.54 1.606 0.945835
6 to 13 2480.90 -0.270 0.393547
7 to 14 2467.20 -0.464 0.321372
8 to 15 2452.55 -0.671 0.251118
9 to 16 2581.57 1.154 0.875656
10 to 17 2534.13 0.483 0.685328
11 to 18 2576.49 1.082 0.860325
12 to 19 2585.85 1.214 0.887654
13 to 20 2492.04 -0.113 0.455181
14 to 21 2549.77 0.704 0.759244
15 to 22 2564.50 0.912 0.819168
16 to 23 2601.80 1.440 0.925020
17 to 24 2478.69 -0.301 0.381587
18 to 25 2461.73 -0.541 0.294177
19 to 26 2567.25 0.951 0.829221
20 to 27 2286.53 -3.019 0.001268
21 to 28 2563.54 0.899 0.815565
22 to 29 2566.87 0.946 0.827851
23 to 30 2484.44 -0.220 0.412904
24 to 31 2513.56 0.192 0.576060
25 to 32 2500.40 0.006 0.502229
CDPARK for dh-ranFile-2018-06-20_13:31: 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
3491 -1.4612 0.071982
3497 -1.1872 0.117571
3520 -0.1370 0.445521
3561 1.7352 0.958644
3524 0.0457 0.518210
3527 0.1826 0.572463
3525 0.0913 0.536383
3522 -0.0457 0.481790
3515 -0.3653 0.357445
3538 0.6849 0.753306
Square side=100, avg. no. parked=3522.00 sample std.=18.58
p-value of the KSTEST for those 10 p-values: 0.807562
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_13:31
0.7633,0.0487,0.9779,0.7962,0.8372,0.5566,0.4091,0.2857,0.1921,0.5203,
The KS test for those 10 p-values: 0.977660
The 3DSPHERES test for dh-ranFile-2018-06-20_13:31
sample no r^3 equiv. uni.
1 14.201 0.377108
2 15.590 0.405279
3 96.528 0.959949
4 6.646 0.198724
5 41.964 0.753103
6 7.438 0.219584
7 18.064 0.452355
8 72.789 0.911637
9 12.231 0.334811
10 18.494 0.460155
11 6.438 0.193127
12 27.257 0.596902
13 64.465 0.883381
14 3.438 0.108288
15 10.687 0.299691
16 22.379 0.525732
17 35.633 0.695097
18 32.988 0.666994
19 8.780 0.253725
20 25.811 0.576994
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.780385
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.2 0.6 0.9 0.2 -0.4
-0.6 1.1 1.3 -0.2 2.4 -0.9
-1.3 -0.1 0.8 0.1 1.4 -0.9
1.3 0.1 -1.2 -1.1 0.6 -0.7
-0.7 -0.4 0.7 -0.0 -1.4 0.1
1.1 -1.1 -1.7 -0.5 -0.8 0.8
-1.4 -1.0 3.0 -0.7 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:50.239195
z-score=0.898970, p-value=0.820643
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_13:31
Test no p-value
1 0.026261
2 0.393650
3 0.370630
4 0.289576
5 0.632091
6 0.605472
7 0.016266
8 0.842895
9 0.094568
10 0.007903
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.035790
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_13:31:
(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 66769 0.16 66918 0.95
3 25000.00 25059 0.14 24722 3.09
4 6666.67 6544 2.26 6713 0.32
5 1388.89 1360 0.60 1364 0.45
6 238.10 229 0.35 243 0.10
7 34.72 32 0.21 32 0.21
8 4.96 6 0.22 7 0.84
p=0.31426 p=0.57232
Number of rngs required: 687125, p-value: 0.068
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_13:31
No. of wins: Observed Expected
98415 98585.9
z-score=-0.764, pvalue=0.22238
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66539 66666.7 0.244 0.244
2 38015 37654.3 3.455 3.699
3 26704 26954.7 2.332 6.032
4 19209 19313.5 0.565 6.597
5 13889 13851.4 0.102 6.699
6 9811 9943.5 1.767 8.465
7 7231 7145.0 1.035 9.500
8 5207 5139.1 0.898 10.398
9 3621 3699.9 1.681 12.079
10 2767 2666.3 3.803 15.882
11 1923 1923.3 0.000 15.882
12 1376 1388.7 0.117 15.999
13 1033 1003.7 0.854 16.854
14 731 726.1 0.033 16.886
15 501 525.8 1.173 18.059
16 385 381.2 0.039 18.098
17 303 276.5 2.532 20.630
18 205 200.8 0.087 20.716
19 181 146.0 8.399 29.115
20 95 106.2 1.184 30.299
21 274 287.1 0.599 30.898
Chisq= 30.90 for 20 degrees of freedom, p= 0.94345
SUMMARY of craptest
p-value for no. of wins: 0.222380
p-value for throws/game: 0.943454
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_13:31
No. of wins: Observed Expected
98691 98585.9
z-score= 0.470, pvalue=0.68091
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66522 66666.7 0.314 0.314
2 37918 37654.3 1.846 2.160
3 26621 26954.7 4.132 6.292
4 19524 19313.5 2.295 8.587
5 13929 13851.4 0.435 9.022
6 9764 9943.5 3.242 12.264
7 7121 7145.0 0.081 12.345
8 5113 5139.1 0.132 12.477
9 3782 3699.9 1.823 14.300
10 2704 2666.3 0.533 14.833
11 1949 1923.3 0.343 15.176
12 1398 1388.7 0.062 15.238
13 986 1003.7 0.313 15.550
14 710 726.1 0.359 15.909
15 562 525.8 2.487 18.396
16 397 381.2 0.659 19.055
17 266 276.5 0.402 19.457
18 219 200.8 1.644 21.101
19 148 146.0 0.028 21.129
20 96 106.2 0.982 22.111
21 271 287.1 0.904 23.016
Chisq= 23.02 for 20 degrees of freedom, p= 0.71198
SUMMARY of craptest
p-value for no. of wins: 0.680913
p-value for throws/game: 0.711978
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0013,0.0079,0.0143,0.0163,0.0262,0.0263,0.0275,0.0283,0.0358,0.0376,
0.0448,0.0448,0.0487,0.0553,0.0573,0.0673,0.0677,0.0687,0.0712,0.0720,
0.0813,0.0821,0.0886,0.0946,0.0974,0.1083,0.1092,0.1176,0.1350,0.1459,
0.1511,0.1549,0.1562,0.1591,0.1600,0.1642,0.1664,0.1797,0.1821,0.1921,
0.1930,0.1931,0.1934,0.1987,0.2004,0.2106,0.2196,0.2204,0.2210,0.2224,
0.2286,0.2338,0.2390,0.2502,0.2511,0.2537,0.2620,0.2671,0.2671,0.2685,
0.2756,0.2758,0.2763,0.2763,0.2793,0.2839,0.2842,0.2857,0.2896,0.2916,
0.2927,0.2936,0.2942,0.2945,0.2974,0.2997,0.3027,0.3075,0.3080,0.3132,
0.3143,0.3202,0.3214,0.3281,0.3342,0.3348,0.3381,0.3404,0.3410,0.3436,
0.3574,0.3706,0.3771,0.3816,0.3836,0.3882,0.3897,0.3911,0.3935,0.3936,
0.3961,0.3970,0.3975,0.4053,0.4058,0.4063,0.4063,0.4091,0.4122,0.4129,
0.4144,0.4163,0.4189,0.4212,0.4385,0.4455,0.4510,0.4524,0.4552,0.4602,
0.4617,0.4790,0.4797,0.4802,0.4818,0.4834,0.4843,0.4860,0.4939,0.4941,
0.4952,0.4973,0.5008,0.5022,0.5137,0.5168,0.5182,0.5203,0.5212,0.5257,
0.5303,0.5305,0.5347,0.5364,0.5394,0.5426,0.5427,0.5495,0.5503,0.5517,
0.5559,0.5566,0.5588,0.5588,0.5648,0.5683,0.5723,0.5725,0.5761,0.5770,
0.5803,0.5849,0.5940,0.5969,0.5997,0.6055,0.6056,0.6168,0.6198,0.6235,
0.6321,0.6391,0.6401,0.6444,0.6522,0.6563,0.6670,0.6684,0.6809,0.6843,
0.6853,0.6928,0.6937,0.6951,0.6994,0.7061,0.7105,0.7120,0.7126,0.7127,
0.7140,0.7146,0.7184,0.7194,0.7217,0.7232,0.7233,0.7242,0.7296,0.7357,
0.7386,0.7531,0.7533,0.7588,0.7592,0.7633,0.7710,0.7722,0.7734,0.7771,
0.7790,0.7804,0.7868,0.7957,0.7962,0.8018,0.8019,0.8076,0.8135,0.8156,
0.8156,0.8192,0.8206,0.8206,0.8279,0.8292,0.8349,0.8369,0.8372,0.8429,
0.8436,0.8440,0.8603,0.8656,0.8674,0.8685,0.8713,0.8757,0.8813,0.8826,
0.8834,0.8877,0.8913,0.8943,0.8998,0.9042,0.9074,0.9088,0.9116,0.9201,
0.9236,0.9250,0.9253,0.9321,0.9321,0.9335,0.9355,0.9370,0.9435,0.9458,
0.9586,0.9599,0.9684,0.9685,0.9731,0.9777,0.9779,0.9934,0.9983,
Overall p-value after applying KStest on 269 p-values = 0.563405
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.