RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_21:31
(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 10.9230 0.139461
2 to 25 15.78 18.5116 0.642725
3 to 26 15.94 13.1265 0.272321
4 to 27 15.80 15.6215 0.449193
5 to 28 15.90 21.9422 0.813048
6 to 29 15.73 10.4314 0.115446
7 to 30 15.87 21.4646 0.793805
8 to 31 16.03 19.8419 0.717603
9 to 32 16.08 17.4506 0.575735
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.912066
Tough bday spacings test for dh-ranFile-2018-06-20_21:31: 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 13 42 67 93 117 83 33 29 11 6 6
(O-E)^2/E 1.6 0.8 0.5 0.2 3.8 0.3 7.0 0.0 1.0 0.1 0.9
Birthday Spacings: Sum(O-E)^2/E= 16.292, p= 0.908
RESULTS OF GCD FOR dh-ranFile-2018-06-20_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.140184
p-value, dist. of gcd's: 0.306911
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.940 0.359 0.336 0.090 0.371 0.213 0.873 0.999
Bits 8 to 15---> 0.533 0.539 0.316 0.670 0.029 0.603 0.798 0.421
Bits 16 to 23---> 0.550 0.290 0.800 0.497 0.576 0.573 0.539 0.753
Bits 24 to 31---> 0.950 0.266 0.520 0.189 0.079 0.500 0.704 0.271
KS test for the above 32 p values: 0.322
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_21:31,
p-values for 5 runs: 0.4389, 0.9222, 0.0940, 0.0499, 0.0897
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5124 5134.0 0.020 0.533
r= 30 23152 23103.0 0.104 0.637
r= 31 11523 11551.5 0.070 0.707
chi-square = 0.707 with df = 3; p-value = 0.128
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5196 5134.0 0.748 0.780
r= 31 23022 23103.0 0.284 1.064
r= 32 11568 11551.5 0.024 1.088
chi-square = 1.088 with df = 3; p-value = 0.220
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_21:31
b-rank test for bits 1 to 8, p=0.81725
b-rank test for bits 2 to 9, p=0.92517
b-rank test for bits 3 to 10, p=0.63365
b-rank test for bits 4 to 11, p=0.53026
b-rank test for bits 5 to 12, p=0.25473
b-rank test for bits 6 to 13, p=0.57113
b-rank test for bits 7 to 14, p=0.19504
b-rank test for bits 8 to 15, p=0.40864
b-rank test for bits 9 to 16, p=0.36666
b-rank test for bits 10 to 17, p=0.18678
b-rank test for bits 11 to 18, p=0.39058
b-rank test for bits 12 to 19, p=0.85953
b-rank test for bits 13 to 20, p=0.08270
b-rank test for bits 14 to 21, p=0.08346
b-rank test for bits 15 to 22, p=0.99506
b-rank test for bits 16 to 23, p=0.22978
b-rank test for bits 17 to 24, p=0.20765
b-rank test for bits 18 to 25, p=0.55692
b-rank test for bits 19 to 26, p=0.50013
b-rank test for bits 20 to 27, p=0.27389
b-rank test for bits 21 to 28, p=0.49633
b-rank test for bits 22 to 29, p=0.76935
b-rank test for bits 23 to 30, p=0.57060
b-rank test for bits 24 to 31, p=0.46552
b-rank test for bits 25 to 32, p=0.35512
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 = 0.556719
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_21:31
(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 142142 0.54 0.706649
2 141087 -1.92 0.027345
3 141830 -0.19 0.426477
4 141582 -0.76 0.222198
5 142300 0.91 0.819321
6 141948 0.09 0.535996
7 141760 -0.35 0.363582
8 142300 0.91 0.819321
9 142128 0.51 0.695293
10 142495 1.37 0.914405
11 140793 -2.61 0.004550
12 142008 0.23 0.591163
13 142151 0.56 0.713844
14 141759 -0.35 0.362705
15 141602 -0.72 0.236360
16 142123 0.50 0.691191
17 141382 -1.23 0.108960
18 141948 0.09 0.535996
19 141736 -0.40 0.342747
20 141161 -1.75 0.040194
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_21:31
Bits used No. missing words z-score p-value
23 to 32 142284 1.2920 0.901815
22 to 31 141944 0.1196 0.547581
21 to 30 142012 0.3540 0.638344
20 to 29 141600 -1.0667 0.143064
19 to 28 141713 -0.6770 0.249203
18 to 27 141883 -0.0908 0.463829
17 to 26 142204 1.0161 0.845210
16 to 25 141532 -1.3011 0.096606
15 to 24 141841 -0.2356 0.406864
14 to 23 141384 -1.8115 0.035033
13 to 22 141980 0.2437 0.596264
12 to 21 141736 -0.5977 0.275024
11 to 20 141877 -0.1115 0.455617
10 to 19 142229 1.1023 0.864837
9 to 18 142751 2.9023 0.998148
8 to 17 141905 -0.0149 0.494044
7 to 16 142259 1.2058 0.886045
6 to 15 141939 0.1023 0.540745
5 to 14 142042 0.4575 0.676338
4 to 13 141728 -0.6253 0.265895
3 to 12 142183 0.9437 0.827336
2 to 11 141736 -0.5977 0.275024
1 to 10 141563 -1.1942 0.116192
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_21:31
Bits used No. missing words z-score p-value
28 to 32 142127 0.7379 0.769702
27 to 31 142062 0.5175 0.697605
26 to 30 142050 0.4768 0.683265
25 to 29 141713 -0.6655 0.252857
24 to 28 141832 -0.2621 0.396609
23 to 27 142080 0.5785 0.718551
22 to 26 141777 -0.4486 0.326869
21 to 25 142152 0.8226 0.794635
20 to 24 142056 0.4972 0.690471
19 to 23 141564 -1.1706 0.120878
18 to 22 142425 1.7480 0.959771
17 to 21 141645 -0.8960 0.185117
16 to 20 141361 -1.8587 0.031532
15 to 19 141860 -0.1672 0.433598
14 to 18 142120 0.7141 0.762428
13 to 17 142046 0.4633 0.678421
12 to 16 142025 0.3921 0.652509
11 to 15 142046 0.4633 0.678421
10 to 14 141901 -0.0282 0.488737
9 to 13 142024 0.3887 0.651255
8 to 12 141733 -0.5977 0.275010
7 to 11 141627 -0.9571 0.169271
6 to 10 141829 -0.2723 0.392694
5 to 9 142428 1.7582 0.960644
4 to 8 141994 0.2870 0.612950
3 to 7 141713 -0.6655 0.252857
2 to 6 142178 0.9107 0.818785
1 to 5 141821 -0.2994 0.382308
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_21:31
Bits used No. missing words z-score p-value
31 to 32 141284 -1.8446 0.032546
30 to 31 141562 -1.0246 0.152783
29 to 30 142392 1.4238 0.922749
28 to 29 142392 1.4238 0.922749
27 to 28 142222 0.9223 0.821822
26 to 27 141447 -1.3638 0.086314
25 to 26 142102 0.5683 0.715101
24 to 25 142231 0.9489 0.828659
23 to 24 140932 -2.8830 0.001970
22 to 23 142191 0.8309 0.796981
21 to 22 141538 -1.0954 0.136678
20 to 21 141865 -0.1308 0.447980
19 to 20 141969 0.1760 0.569860
18 to 19 141962 0.1554 0.561735
17 to 18 142174 0.7807 0.782522
16 to 17 141923 0.0403 0.516083
15 to 16 142404 1.4592 0.927745
14 to 15 141656 -0.7473 0.227445
13 to 14 141707 -0.5968 0.275306
12 to 13 142141 0.6834 0.752821
11 to 12 142144 0.6922 0.755607
10 to 11 142502 1.7483 0.959793
9 to 10 141853 -0.1662 0.434014
8 to 9 141789 -0.3550 0.361311
7 to 8 141466 -1.3078 0.095478
6 to 7 141219 -2.0364 0.020857
5 to 6 141887 -0.0659 0.473741
4 to 5 142155 0.7247 0.765679
3 to 4 141596 -0.9243 0.177671
2 to 3 141901 -0.0246 0.490198
1 to 2 141587 -0.9508 0.170846
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2529.55 0.418 0.661967
Test results for specific bytes for dh-ranFile-2018-06-20_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2513.54 0.191 0.575920
2 to 9 2446.53 -0.756 0.224767
3 to 10 2309.49 -2.694 0.003527
4 to 11 2548.56 0.687 0.753890
5 to 12 2623.01 1.740 0.959039
6 to 13 2536.75 0.520 0.698377
7 to 14 2482.82 -0.243 0.404000
8 to 15 2532.33 0.457 0.676259
9 to 16 2411.86 -1.246 0.106296
10 to 17 2508.26 0.117 0.546472
11 to 18 2608.77 1.538 0.938000
12 to 19 2511.81 0.167 0.566301
13 to 20 2428.65 -1.009 0.156494
14 to 21 2609.18 1.544 0.938704
15 to 22 2440.78 -0.837 0.201168
16 to 23 2423.22 -1.086 0.138769
17 to 24 2556.99 0.806 0.789866
18 to 25 2480.26 -0.279 0.390067
19 to 26 2605.48 1.492 0.932114
20 to 27 2394.62 -1.490 0.068082
21 to 28 2552.34 0.740 0.770426
22 to 29 2363.33 -1.933 0.026629
23 to 30 2594.56 1.337 0.909441
24 to 31 2455.94 -0.623 0.266613
25 to 32 2525.74 0.364 0.642059
CDPARK for dh-ranFile-2018-06-20_21:31: 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
3507 -0.7306 0.232514
3516 -0.3196 0.374623
3539 0.7306 0.767486
3534 0.5023 0.692266
3508 -0.6849 0.246694
3516 -0.3196 0.374623
3544 0.9589 0.831196
3530 0.3196 0.625377
3527 0.1826 0.572463
3525 0.0913 0.536383
Square side=100, avg. no. parked=3524.60 sample std.=12.00
p-value of the KSTEST for those 10 p-values: 0.573688
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_21:31
0.6622,0.7450,0.6051,0.3055,0.1159,0.6082,0.8580,0.9058,0.3314,0.1866,
The KS test for those 10 p-values: 0.941556
The 3DSPHERES test for dh-ranFile-2018-06-20_21:31
sample no r^3 equiv. uni.
1 92.583 0.954321
2 63.957 0.881387
3 4.017 0.125321
4 56.352 0.847168
5 6.170 0.185896
6 29.114 0.621094
7 16.534 0.423701
8 14.269 0.378500
9 1.759 0.056938
10 39.420 0.731254
11 34.198 0.680161
12 1.090 0.035685
13 1.858 0.060052
14 5.873 0.177804
15 125.895 0.984952
16 51.151 0.818232
17 1.835 0.059319
18 57.320 0.852020
19 13.725 0.367143
20 7.991 0.233843
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.437144
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 0.1 1.9 2.4 -0.7
0.3 -1.8 -0.8 -0.6 0.1 -2.9
1.0 0.8 0.6 -1.0 0.1 0.2
1.0 -0.2 -0.5 -0.4 -0.1 0.6
0.6 2.3 -1.0 0.5 0.8 -0.2
-1.6 -0.5 -0.4 -0.3 -0.5 0.1
0.7 0.2 -0.4 1.0 0.9 1.0
-0.1
Chi-square with 42 degrees of freedom:42.829796
z-score=0.090538, p-value=0.564603
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_21:31
Test no p-value
1 0.024377
2 0.029186
3 0.008438
4 0.231738
5 0.602261
6 0.461436
7 0.069631
8 0.200926
9 0.486429
10 0.128097
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001809
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_21:31:
(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 66700 0.02 66576 0.12
3 25000.00 24983 0.01 25111 0.49
4 6666.67 6641 0.10 6562 1.64
5 1388.89 1375 0.14 1468 4.51
6 238.10 252 0.81 241 0.04
7 34.72 39 0.53 37 0.15
8 4.96 9 3.29 4 0.19
p=0.44282 p=0.69159
Number of rngs required: 688348, p-value: 0.475
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_21:31
No. of wins: Observed Expected
98855 98585.9
z-score= 1.204, pvalue=0.88566
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66483 66666.7 0.506 0.506
2 37685 37654.3 0.025 0.531
3 27052 26954.7 0.351 0.882
4 19353 19313.5 0.081 0.963
5 13934 13851.4 0.492 1.455
6 10131 9943.5 3.534 4.989
7 7130 7145.0 0.032 5.021
8 5055 5139.1 1.375 6.396
9 3682 3699.9 0.086 6.482
10 2666 2666.3 0.000 6.482
11 1977 1923.3 1.498 7.980
12 1290 1388.7 7.021 15.001
13 913 1003.7 8.199 23.199
14 749 726.1 0.720 23.919
15 516 525.8 0.184 24.103
16 344 381.2 3.621 27.724
17 257 276.5 1.381 29.105
18 215 200.8 1.000 30.105
19 149 146.0 0.062 30.167
20 121 106.2 2.058 32.225
21 298 287.1 0.413 32.638
Chisq= 32.64 for 20 degrees of freedom, p= 0.96304
SUMMARY of craptest
p-value for no. of wins: 0.885658
p-value for throws/game: 0.963039
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_21:31
No. of wins: Observed Expected
98693 98585.9
z-score= 0.479, pvalue=0.68410
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66821 66666.7 0.357 0.357
2 37836 37654.3 0.877 1.234
3 27038 26954.7 0.257 1.491
4 19053 19313.5 3.513 5.004
5 13679 13851.4 2.146 7.150
6 9945 9943.5 0.000 7.150
7 7119 7145.0 0.095 7.245
8 5104 5139.1 0.239 7.484
9 3749 3699.9 0.653 8.137
10 2700 2666.3 0.426 8.563
11 1968 1923.3 1.038 9.600
12 1358 1388.7 0.680 10.281
13 988 1003.7 0.246 10.527
14 699 726.1 1.014 11.541
15 535 525.8 0.160 11.701
16 393 381.2 0.368 12.069
17 267 276.5 0.329 12.398
18 191 200.8 0.481 12.880
19 164 146.0 2.223 15.103
20 100 106.2 0.364 15.467
21 293 287.1 0.121 15.587
Chisq= 15.59 for 20 degrees of freedom, p= 0.25812
SUMMARY of craptest
p-value for no. of wins: 0.684101
p-value for throws/game: 0.258120
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0020,0.0035,0.0046,0.0084,0.0209,0.0244,0.0266,0.0273,0.0292,
0.0294,0.0315,0.0325,0.0350,0.0357,0.0402,0.0499,0.0569,0.0593,0.0601,
0.0681,0.0696,0.0789,0.0827,0.0835,0.0863,0.0897,0.0903,0.0940,0.0955,
0.0966,0.1063,0.1090,0.1154,0.1159,0.1162,0.1209,0.1253,0.1281,0.1285,
0.1367,0.1388,0.1395,0.1402,0.1431,0.1528,0.1565,0.1693,0.1708,0.1777,
0.1778,0.1851,0.1859,0.1866,0.1868,0.1892,0.1950,0.2009,0.2012,0.2076,
0.2126,0.2200,0.2222,0.2248,0.2274,0.2298,0.2317,0.2325,0.2338,0.2364,
0.2467,0.2492,0.2529,0.2529,0.2547,0.2581,0.2659,0.2663,0.2666,0.2712,
0.2723,0.2739,0.2750,0.2750,0.2750,0.2753,0.2904,0.3055,0.3069,0.3160,
0.3221,0.3269,0.3314,0.3362,0.3427,0.3551,0.3589,0.3613,0.3627,0.3636,
0.3667,0.3671,0.3706,0.3746,0.3746,0.3785,0.3823,0.3901,0.3906,0.3927,
0.3966,0.4040,0.4069,0.4086,0.4206,0.4237,0.4265,0.4336,0.4340,0.4371,
0.4389,0.4428,0.4480,0.4492,0.4556,0.4614,0.4638,0.4655,0.4737,0.4748,
0.4864,0.4887,0.4902,0.4940,0.4963,0.4966,0.4996,0.5001,0.5161,0.5204,
0.5303,0.5326,0.5360,0.5360,0.5364,0.5393,0.5394,0.5407,0.5465,0.5476,
0.5502,0.5567,0.5569,0.5617,0.5646,0.5663,0.5699,0.5706,0.5711,0.5725,
0.5734,0.5737,0.5757,0.5758,0.5759,0.5912,0.5963,0.6023,0.6033,0.6051,
0.6082,0.6130,0.6211,0.6254,0.6336,0.6383,0.6421,0.6427,0.6513,0.6525,
0.6620,0.6622,0.6696,0.6763,0.6763,0.6784,0.6784,0.6802,0.6833,0.6841,
0.6905,0.6912,0.6916,0.6923,0.6953,0.6976,0.6984,0.7035,0.7066,0.7138,
0.7151,0.7176,0.7186,0.7313,0.7450,0.7527,0.7528,0.7539,0.7556,0.7624,
0.7657,0.7675,0.7693,0.7697,0.7704,0.7825,0.7899,0.7938,0.7946,0.7970,
0.7981,0.7996,0.8130,0.8173,0.8182,0.8188,0.8193,0.8193,0.8218,0.8273,
0.8287,0.8312,0.8452,0.8472,0.8520,0.8580,0.8595,0.8648,0.8727,0.8814,
0.8857,0.8860,0.9018,0.9058,0.9084,0.9094,0.9121,0.9144,0.9222,0.9227,
0.9227,0.9252,0.9277,0.9321,0.9380,0.9387,0.9398,0.9416,0.9504,0.9543,
0.9590,0.9598,0.9598,0.9606,0.9630,0.9850,0.9951,0.9981,0.9992,
Overall p-value after applying KStest on 269 p-values = 0.726724
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.