RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.89 10.4930 0.118326
2 to 25 15.94 12.7827 0.249391
3 to 26 15.63 17.4009 0.572456
4 to 27 15.81 24.2626 0.887526
5 to 28 15.88 13.8707 0.323767
6 to 29 15.60 22.8065 0.844343
7 to 30 15.78 13.7440 0.314868
8 to 31 15.76 24.9399 0.903937
9 to 32 15.87 17.1871 0.558238
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.888911
Tough bday spacings test for dh-ranFile-2018-06-25_10:31: 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 78 95 88 85 56 30 11 8 4
(O-E)^2/E 0.1 0.0 0.3 0.1 1.0 0.6 0.3 0.0 1.0 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 3.690, p= 0.040
RESULTS OF GCD FOR dh-ranFile-2018-06-25_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.209236
p-value, dist. of gcd's: 0.129372
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.545 0.441 0.569 0.982 0.964 0.166 0.920 0.356
Bits 8 to 15---> 0.952 0.640 0.948 0.078 0.416 0.980 0.987 0.251
Bits 16 to 23---> 0.368 0.306 0.735 0.162 0.779 0.541 0.450 0.583
Bits 24 to 31---> 0.282 0.653 0.900 0.177 0.013 0.941 0.190 0.084
KS test for the above 32 p values: 0.795
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_10:31,
p-values for 5 runs: 0.8687, 0.1998, 0.4869, 0.5077, 0.3378
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5054 5134.0 1.247 1.777
r= 30 23147 23103.0 0.084 1.860
r= 31 11577 11551.5 0.056 1.916
chi-square = 1.916 with df = 3; p-value = 0.410
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 195 211.4 1.275 1.275
r= 30 5076 5134.0 0.655 1.930
r= 31 23282 23103.0 1.386 3.317
r= 32 11447 11551.5 0.946 4.262
chi-square = 4.262 with df = 3; p-value = 0.766
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_10:31
b-rank test for bits 1 to 8, p=0.60729
b-rank test for bits 2 to 9, p=0.26548
b-rank test for bits 3 to 10, p=0.93568
b-rank test for bits 4 to 11, p=0.20765
b-rank test for bits 5 to 12, p=0.02033
b-rank test for bits 6 to 13, p=0.54579
b-rank test for bits 7 to 14, p=0.95022
b-rank test for bits 8 to 15, p=0.50025
b-rank test for bits 9 to 16, p=0.53326
b-rank test for bits 10 to 17, p=0.86434
b-rank test for bits 11 to 18, p=0.56472
b-rank test for bits 12 to 19, p=0.48327
b-rank test for bits 13 to 20, p=0.91741
b-rank test for bits 14 to 21, p=0.71961
b-rank test for bits 15 to 22, p=0.09272
b-rank test for bits 16 to 23, p=0.61483
b-rank test for bits 17 to 24, p=0.82443
b-rank test for bits 18 to 25, p=0.31099
b-rank test for bits 19 to 26, p=0.06583
b-rank test for bits 20 to 27, p=0.62586
b-rank test for bits 21 to 28, p=0.31199
b-rank test for bits 22 to 29, p=0.86586
b-rank test for bits 23 to 30, p=0.35412
b-rank test for bits 24 to 31, p=0.86052
b-rank test for bits 25 to 32, p=0.52479
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 = 0.705598
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_10:31
(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 142397 1.14 0.872735
2 142226 0.74 0.770315
3 141886 -0.05 0.478265
4 141690 -0.51 0.304167
5 141594 -0.74 0.230637
6 141815 -0.22 0.412781
7 142831 2.15 0.984358
8 142229 0.75 0.772436
9 141256 -1.53 0.063446
10 141318 -1.38 0.083545
11 142261 0.82 0.794364
12 142561 1.52 0.936070
13 141866 -0.10 0.459681
14 142479 1.33 0.908406
15 141573 -0.79 0.215987
16 141713 -0.46 0.323219
17 142933 2.39 0.991616
18 142241 0.77 0.780809
19 141724 -0.43 0.332502
20 141697 -0.50 0.309913
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_10:31
Bits used No. missing words z-score p-value
23 to 32 142458 1.8920 0.970752
22 to 31 142016 0.3678 0.643499
21 to 30 142220 1.0713 0.857977
20 to 29 141991 0.2816 0.610883
19 to 28 141889 -0.0701 0.472056
18 to 27 142175 0.9161 0.820194
17 to 26 141482 -1.4736 0.070301
16 to 25 141953 0.1506 0.559849
15 to 24 141744 -0.5701 0.284304
14 to 23 141940 0.1058 0.542113
13 to 22 142152 0.8368 0.798646
12 to 21 142008 0.3402 0.633163
11 to 20 141555 -1.2218 0.110886
10 to 19 141686 -0.7701 0.220619
9 to 18 141841 -0.2356 0.406864
8 to 17 141292 -2.1287 0.016639
7 to 16 142081 0.5920 0.723063
6 to 15 141944 0.1196 0.547581
5 to 14 141592 -1.0942 0.136925
4 to 13 142098 0.6506 0.742343
3 to 12 142273 1.2540 0.895085
2 to 11 142170 0.8989 0.815637
1 to 10 141748 -0.5563 0.288999
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_10:31
Bits used No. missing words z-score p-value
28 to 32 141487 -1.4316 0.076125
27 to 31 141930 0.0701 0.527930
26 to 30 141551 -1.2147 0.112244
25 to 29 142133 0.7582 0.775835
24 to 28 141640 -0.9130 0.180626
23 to 27 141741 -0.5706 0.284132
22 to 26 141890 -0.0655 0.473878
21 to 25 141989 0.2701 0.606446
20 to 24 141506 -1.3672 0.085778
19 to 23 141542 -1.2452 0.106532
18 to 22 142023 0.3853 0.650001
17 to 21 142321 1.3955 0.918566
16 to 20 142055 0.4938 0.689275
15 to 19 142281 1.2599 0.896147
14 to 18 141735 -0.5909 0.277277
13 to 17 141829 -0.2723 0.392694
12 to 16 142152 0.8226 0.794635
11 to 15 142447 1.8226 0.965819
10 to 14 141960 0.1718 0.568188
9 to 13 141679 -0.7808 0.217466
8 to 12 141699 -0.7130 0.237928
7 to 11 141822 -0.2960 0.383602
6 to 10 141627 -0.9571 0.169271
5 to 9 141722 -0.6350 0.262709
4 to 8 141914 0.0158 0.506315
3 to 7 142393 1.6396 0.949452
2 to 6 142267 1.2124 0.887328
1 to 5 141827 -0.2791 0.390090
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_10:31
Bits used No. missing words z-score p-value
31 to 32 141562 -1.0246 0.152783
30 to 31 141985 0.2232 0.588316
29 to 30 141520 -1.1485 0.125388
28 to 29 142293 1.1318 0.871134
27 to 28 141583 -0.9626 0.167868
26 to 27 141792 -0.3461 0.364632
25 to 26 142367 1.3501 0.911501
24 to 25 142112 0.5978 0.725029
23 to 24 141763 -0.4317 0.332997
22 to 23 141620 -0.8535 0.196696
21 to 22 142451 1.5978 0.944961
20 to 21 142247 0.9961 0.840394
19 to 20 141825 -0.2488 0.401773
18 to 19 141292 -1.8210 0.034301
17 to 18 141966 0.1672 0.566381
16 to 17 141539 -1.0924 0.137325
15 to 16 141481 -1.2635 0.103203
14 to 15 141882 -0.0806 0.467872
13 to 14 141257 -1.9243 0.027160
12 to 13 141045 -2.5496 0.005392
11 to 12 141875 -0.1013 0.459669
10 to 11 141894 -0.0452 0.481966
9 to 10 141819 -0.2665 0.394942
8 to 9 141528 -1.1249 0.130323
7 to 8 142212 0.8928 0.814026
6 to 7 142119 0.6185 0.731876
5 to 6 142398 1.4415 0.925279
4 to 5 142396 1.4356 0.924443
3 to 4 141891 -0.0541 0.478439
2 to 3 141746 -0.4818 0.314974
1 to 2 142195 0.8427 0.800298
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2470.24 -0.421 0.336916
Test results for specific bytes for dh-ranFile-2018-06-25_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2578.69 1.113 0.867100
2 to 9 2432.73 -0.951 0.170725
3 to 10 2534.34 0.486 0.686383
4 to 11 2597.12 1.374 0.915206
5 to 12 2515.71 0.222 0.587928
6 to 13 2550.80 0.718 0.763749
7 to 14 2497.82 -0.031 0.487678
8 to 15 2594.19 1.332 0.908571
9 to 16 2529.67 0.420 0.662603
10 to 17 2594.50 1.336 0.909288
11 to 18 2479.00 -0.297 0.383256
12 to 19 2314.09 -2.629 0.004280
13 to 20 2535.68 0.505 0.693091
14 to 21 2474.74 -0.357 0.360438
15 to 22 2486.25 -0.194 0.422908
16 to 23 2442.73 -0.810 0.209010
17 to 24 2608.90 1.540 0.938231
18 to 25 2438.55 -0.869 0.192420
19 to 26 2498.85 -0.016 0.493503
20 to 27 2433.52 -0.940 0.173573
21 to 28 2425.83 -1.049 0.147103
22 to 29 2410.07 -1.272 0.101718
23 to 30 2466.39 -0.475 0.317295
24 to 31 2549.02 0.693 0.755903
25 to 32 2522.17 0.314 0.623086
CDPARK for dh-ranFile-2018-06-25_10:31: 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
3545 1.0046 0.842447
3563 1.8265 0.966111
3545 1.0046 0.842447
3557 1.5525 0.939730
3542 0.8676 0.807188
3506 -0.7763 0.218799
3533 0.4566 0.676028
3520 -0.1370 0.445521
3511 -0.5479 0.291865
3578 2.5114 0.993988
Square side=100, avg. no. parked=3540.00 sample std.=21.82
p-value of the KSTEST for those 10 p-values: 0.025169
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_10:31
0.2272,0.3281,0.2400,0.5890,0.6923,0.4169,0.1237,0.8643,0.2555,0.6928,
The KS test for those 10 p-values: 0.646919
The 3DSPHERES test for dh-ranFile-2018-06-25_10:31
sample no r^3 equiv. uni.
1 17.482 0.441638
2 31.580 0.650996
3 26.513 0.586777
4 63.175 0.878257
5 21.795 0.516399
6 35.355 0.692259
7 32.830 0.665233
8 51.889 0.822651
9 24.997 0.565357
10 8.175 0.238539
11 67.862 0.895866
12 0.845 0.027762
13 79.104 0.928410
14 87.917 0.946634
15 14.219 0.377466
16 52.004 0.823328
17 18.223 0.455244
18 2.433 0.077901
19 63.989 0.881514
20 4.075 0.127023
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.348750
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.3 1.8 0.6 -0.5 -0.6
-0.7 1.0 -0.7 -0.0 -0.7 0.6
-0.4 -2.1 0.2 0.9 -0.3 0.5
-1.0 1.7 -1.5 2.3 -1.5 0.3
0.2 0.8 -0.2 -0.2 -0.1 0.1
1.2 0.6 0.1 0.0 0.6 0.4
0.0 1.5 0.9 -0.7 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:35.849039
z-score=-0.671125, p-value=0.263282
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_10:31
Test no p-value
1 0.040601
2 0.997782
3 0.064854
4 0.778221
5 0.019926
6 0.059215
7 0.281420
8 0.586563
9 0.245349
10 0.710441
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.074001
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_10:31:
(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 66243 2.69 66545 0.22
3 25000.00 25195 1.52 25031 0.04
4 6666.67 6850 5.04 6748 0.99
5 1388.89 1421 0.74 1417 0.57
6 238.10 242 0.06 227 0.52
7 34.72 43 1.97 29 0.94
8 4.96 5 0.00 2 1.77
p=0.93884 p=0.46226
Number of rngs required: 688947, p-value: 0.735
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_10:31
No. of wins: Observed Expected
99109 98585.9
z-score= 2.340, pvalue=0.99035
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66754 66666.7 0.114 0.114
2 37731 37654.3 0.156 0.271
3 26770 26954.7 1.266 1.537
4 19225 19313.5 0.405 1.942
5 13968 13851.4 0.981 2.923
6 9993 9943.5 0.246 3.169
7 7155 7145.0 0.014 3.183
8 5117 5139.1 0.095 3.278
9 3571 3699.9 4.488 7.766
10 2674 2666.3 0.022 7.788
11 1940 1923.3 0.144 7.933
12 1371 1388.7 0.227 8.159
13 1021 1003.7 0.298 8.457
14 718 726.1 0.091 8.548
15 557 525.8 1.847 10.395
16 411 381.2 2.338 12.733
17 293 276.5 0.980 13.713
18 212 200.8 0.621 14.334
19 145 146.0 0.007 14.341
20 102 106.2 0.167 14.508
21 272 287.1 0.796 15.304
Chisq= 15.30 for 20 degrees of freedom, p= 0.24121
SUMMARY of craptest
p-value for no. of wins: 0.990353
p-value for throws/game: 0.241215
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_10:31
No. of wins: Observed Expected
98418 98585.9
z-score=-0.751, pvalue=0.22640
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66556 66666.7 0.184 0.184
2 37611 37654.3 0.050 0.234
3 27300 26954.7 4.423 4.656
4 19390 19313.5 0.303 4.959
5 13759 13851.4 0.617 5.576
6 9842 9943.5 1.037 6.613
7 6930 7145.0 6.471 13.084
8 5205 5139.1 0.846 13.930
9 3795 3699.9 2.446 16.376
10 2697 2666.3 0.354 16.730
11 1843 1923.3 3.355 20.085
12 1385 1388.7 0.010 20.095
13 999 1003.7 0.022 20.117
14 764 726.1 1.974 22.091
15 537 525.8 0.237 22.328
16 385 381.2 0.039 22.367
17 286 276.5 0.324 22.690
18 200 200.8 0.003 22.694
19 155 146.0 0.557 23.251
20 80 106.2 6.470 29.721
21 281 287.1 0.130 29.851
Chisq= 29.85 for 20 degrees of freedom, p= 0.92770
SUMMARY of craptest
p-value for no. of wins: 0.226398
p-value for throws/game: 0.927696
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0043,0.0054,0.0125,0.0166,0.0199,0.0203,0.0252,0.0272,0.0278,0.0343,
0.0397,0.0406,0.0592,0.0634,0.0649,0.0658,0.0703,0.0740,0.0761,0.0779,
0.0781,0.0835,0.0838,0.0858,0.0927,0.1017,0.1032,0.1065,0.1109,0.1122,
0.1183,0.1237,0.1254,0.1270,0.1294,0.1303,0.1369,0.1373,0.1471,0.1528,
0.1619,0.1660,0.1679,0.1693,0.1707,0.1736,0.1771,0.1806,0.1902,0.1924,
0.1967,0.1998,0.2076,0.2090,0.2092,0.2160,0.2175,0.2188,0.2206,0.2264,
0.2272,0.2306,0.2379,0.2385,0.2400,0.2412,0.2453,0.2494,0.2507,0.2555,
0.2627,0.2633,0.2655,0.2773,0.2814,0.2823,0.2841,0.2843,0.2890,0.2919,
0.3042,0.3063,0.3099,0.3110,0.3120,0.3149,0.3150,0.3173,0.3232,0.3238,
0.3281,0.3325,0.3330,0.3369,0.3378,0.3487,0.3541,0.3561,0.3604,0.3646,
0.3677,0.3775,0.3833,0.3836,0.3901,0.3927,0.3949,0.4018,0.4069,0.4101,
0.4128,0.4162,0.4169,0.4229,0.4414,0.4416,0.4455,0.4505,0.4552,0.4597,
0.4597,0.4623,0.4679,0.4721,0.4739,0.4783,0.4784,0.4820,0.4833,0.4869,
0.4877,0.4935,0.5002,0.5063,0.5077,0.5164,0.5248,0.5279,0.5333,0.5407,
0.5421,0.5448,0.5458,0.5476,0.5582,0.5598,0.5647,0.5654,0.5664,0.5682,
0.5687,0.5725,0.5829,0.5866,0.5868,0.5879,0.5883,0.5890,0.6064,0.6073,
0.6109,0.6148,0.6231,0.6259,0.6332,0.6397,0.6435,0.6469,0.6500,0.6510,
0.6527,0.6626,0.6652,0.6760,0.6864,0.6893,0.6923,0.6923,0.6928,0.6931,
0.7056,0.7104,0.7196,0.7231,0.7250,0.7319,0.7348,0.7349,0.7423,0.7559,
0.7637,0.7655,0.7703,0.7724,0.7758,0.7782,0.7792,0.7808,0.7944,0.7946,
0.7947,0.7986,0.8003,0.8072,0.8140,0.8156,0.8202,0.8227,0.8233,0.8244,
0.8404,0.8424,0.8424,0.8443,0.8580,0.8605,0.8643,0.8643,0.8659,0.8671,
0.8687,0.8711,0.8727,0.8783,0.8815,0.8873,0.8875,0.8889,0.8951,0.8959,
0.8961,0.8997,0.9039,0.9084,0.9086,0.9093,0.9115,0.9152,0.9174,0.9186,
0.9203,0.9244,0.9253,0.9277,0.9284,0.9357,0.9361,0.9382,0.9388,0.9397,
0.9415,0.9450,0.9466,0.9476,0.9495,0.9502,0.9521,0.9636,0.9658,0.9661,
0.9708,0.9796,0.9819,0.9844,0.9867,0.9904,0.9916,0.9940,0.9978,
Overall p-value after applying KStest on 269 p-values = 0.284120
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.