RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.81 21.2266 0.783680
2 to 25 15.87 21.5165 0.795966
3 to 26 15.83 14.1152 0.341067
4 to 27 15.60 22.2918 0.826243
5 to 28 15.76 11.4250 0.166363
6 to 29 15.86 18.9369 0.667835
7 to 30 15.78 12.7826 0.249384
8 to 31 15.81 21.6891 0.803028
9 to 32 15.74 13.4300 0.293042
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.573429
Tough bday spacings test for dh-ranFile-2018-06-16_19:31: 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 11 38 73 99 86 71 63 29 18 9 3
(O-E)^2/E 0.4 0.1 0.0 0.0 1.4 0.7 2.3 0.0 0.7 0.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 6.583, p= 0.236
RESULTS OF GCD FOR dh-ranFile-2018-06-16_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.119869
p-value, dist. of gcd's: 0.050760
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.026 0.038 0.170 0.874 0.338 0.055 0.294 0.078
Bits 8 to 15---> 0.719 0.875 0.652 0.532 0.778 0.060 0.693 0.838
Bits 16 to 23---> 0.992 0.019 0.607 0.857 0.577 0.957 0.311 0.026
Bits 24 to 31---> 0.867 0.315 0.581 0.603 0.543 0.410 0.498 0.886
KS test for the above 32 p values: 0.554
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_19:31,
p-values for 5 runs: 0.5370, 0.9880, 0.4237, 0.5932, 0.1971
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 203 211.4 0.335 0.335
r= 29 4989 5134.0 4.096 4.431
r= 30 23404 23103.0 3.920 8.351
r= 31 11404 11551.5 1.884 10.235
chi-square = 10.235 with df = 3; p-value = 0.983
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 222 211.4 0.530 0.530
r= 30 5139 5134.0 0.005 0.535
r= 31 23095 23103.0 0.003 0.537
r= 32 11544 11551.5 0.005 0.542
chi-square = 0.542 with df = 3; p-value = 0.090
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_19:31
b-rank test for bits 1 to 8, p=0.59149
b-rank test for bits 2 to 9, p=0.35056
b-rank test for bits 3 to 10, p=0.40357
b-rank test for bits 4 to 11, p=0.32941
b-rank test for bits 5 to 12, p=0.16433
b-rank test for bits 6 to 13, p=0.52696
b-rank test for bits 7 to 14, p=0.26204
b-rank test for bits 8 to 15, p=0.01908
b-rank test for bits 9 to 16, p=0.15957
b-rank test for bits 10 to 17, p=0.04580
b-rank test for bits 11 to 18, p=0.10489
b-rank test for bits 12 to 19, p=0.31851
b-rank test for bits 13 to 20, p=0.21564
b-rank test for bits 14 to 21, p=0.89913
b-rank test for bits 15 to 22, p=0.57613
b-rank test for bits 16 to 23, p=0.18595
b-rank test for bits 17 to 24, p=0.40399
b-rank test for bits 18 to 25, p=0.44247
b-rank test for bits 19 to 26, p=0.54752
b-rank test for bits 20 to 27, p=0.69687
b-rank test for bits 21 to 28, p=0.07958
b-rank test for bits 22 to 29, p=0.71530
b-rank test for bits 23 to 30, p=0.92867
b-rank test for bits 24 to 31, p=0.01776
b-rank test for bits 25 to 32, p=0.55225
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 = 0.066760
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_19:31
(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 142272 0.85 0.801603
2 142132 0.52 0.698558
3 142324 0.97 0.833691
4 142484 1.34 0.910313
5 141890 -0.05 0.481989
6 141397 -1.20 0.115647
7 142051 0.33 0.629680
8 142519 1.42 0.922844
9 141936 0.06 0.524843
10 141146 -1.78 0.037254
11 141873 -0.08 0.466177
12 142109 0.47 0.679578
13 142645 1.72 0.957180
14 141287 -1.45 0.072967
15 141360 -1.28 0.099662
16 141918 0.02 0.508081
17 142106 0.46 0.677066
18 142215 0.71 0.762443
19 141377 -1.24 0.106794
20 142472 1.31 0.905686
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_19:31
Bits used No. missing words z-score p-value
23 to 32 141720 -0.6529 0.256923
22 to 31 141455 -1.5667 0.058598
21 to 30 142008 0.3402 0.633163
20 to 29 141890 -0.0667 0.473428
19 to 28 142200 1.0023 0.841903
18 to 27 142087 0.6127 0.729948
17 to 26 141522 -1.3356 0.090837
16 to 25 141748 -0.5563 0.288999
15 to 24 142065 0.5368 0.704295
14 to 23 142107 0.6816 0.752261
13 to 22 141833 -0.2632 0.396196
12 to 21 141885 -0.0839 0.466569
11 to 20 141532 -1.3011 0.096606
10 to 19 142001 0.3161 0.624038
9 to 18 141691 -0.7529 0.225766
8 to 17 142158 0.8575 0.804411
7 to 16 141471 -1.5115 0.065333
6 to 15 141938 0.0989 0.539376
5 to 14 142621 2.4540 0.992937
4 to 13 141803 -0.3667 0.356938
3 to 12 142122 0.7333 0.768326
2 to 11 142131 0.7644 0.777679
1 to 10 141626 -0.9770 0.164285
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_19:31
Bits used No. missing words z-score p-value
28 to 32 142108 0.6735 0.749672
27 to 31 142018 0.3684 0.643702
26 to 30 141575 -1.1333 0.128540
25 to 29 142181 0.9209 0.821453
24 to 28 142170 0.8836 0.811551
23 to 27 141959 0.1684 0.566855
22 to 26 142215 1.0362 0.849938
21 to 25 142389 1.6260 0.948025
20 to 24 141940 0.1040 0.541402
19 to 23 142014 0.3548 0.638635
18 to 22 141863 -0.1571 0.437602
17 to 21 142176 0.9040 0.816993
16 to 20 142343 1.4701 0.929228
15 to 19 142066 0.5311 0.702320
14 to 18 141834 -0.2554 0.399224
13 to 17 142251 1.1582 0.876610
12 to 16 141948 0.1311 0.552146
11 to 15 141905 -0.0147 0.494145
10 to 14 141851 -0.1977 0.421629
9 to 13 142286 1.2768 0.899172
8 to 12 142168 0.8768 0.809715
7 to 11 141692 -0.7367 0.230649
6 to 10 142131 0.7514 0.773801
5 to 9 141876 -0.1130 0.455022
4 to 8 141674 -0.7977 0.212514
3 to 7 142023 0.3853 0.650001
2 to 6 142083 0.5887 0.721973
1 to 5 142100 0.6463 0.740970
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_19:31
Bits used No. missing words z-score p-value
31 to 32 141574 -0.9892 0.161289
30 to 31 141456 -1.3373 0.090569
29 to 30 141363 -1.6116 0.053525
28 to 29 141568 -1.0069 0.156998
27 to 28 142187 0.8191 0.793631
26 to 27 141606 -0.8948 0.185453
25 to 26 142065 0.4592 0.676956
24 to 25 142426 1.5241 0.936258
23 to 24 141924 0.0433 0.517259
22 to 23 142364 1.3412 0.910074
21 to 22 141841 -0.2016 0.420129
20 to 21 141827 -0.2429 0.404056
19 to 20 141823 -0.2547 0.399493
18 to 19 141321 -1.7355 0.041327
17 to 18 142144 0.6922 0.755607
16 to 17 141574 -0.9892 0.161289
15 to 16 141563 -1.0216 0.153480
14 to 15 142387 1.4091 0.920591
13 to 14 141997 0.2586 0.602033
12 to 13 141806 -0.3048 0.380256
11 to 12 142196 0.8456 0.801122
10 to 11 141975 0.1937 0.576801
9 to 10 142099 0.5595 0.712089
8 to 9 141508 -1.1839 0.118233
7 to 8 141784 -0.3697 0.355801
6 to 7 141577 -0.9803 0.163463
5 to 6 142031 0.3589 0.640168
4 to 5 141260 -1.9154 0.027719
3 to 4 141859 -0.1485 0.440988
2 to 3 142423 1.5153 0.935146
1 to 2 142186 0.8161 0.792789
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2415.36 -1.197 0.115644
Test results for specific bytes for dh-ranFile-2018-06-16_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2514.49 0.205 0.581194
2 to 9 2499.70 -0.004 0.498283
3 to 10 2597.05 1.372 0.915041
4 to 11 2436.60 -0.897 0.184966
5 to 12 2516.82 0.238 0.593994
6 to 13 2392.21 -1.524 0.063712
7 to 14 2485.88 -0.200 0.420848
8 to 15 2557.75 0.817 0.792966
9 to 16 2487.89 -0.171 0.432007
10 to 17 2540.80 0.577 0.718029
11 to 18 2559.27 0.838 0.799048
12 to 19 2502.13 0.030 0.512005
13 to 20 2433.42 -0.942 0.173220
14 to 21 2359.14 -1.992 0.023182
15 to 22 2548.78 0.690 0.754836
16 to 23 2606.77 1.510 0.934478
17 to 24 2491.76 -0.117 0.453616
18 to 25 2510.72 0.152 0.560254
19 to 26 2534.31 0.485 0.686262
20 to 27 2469.91 -0.426 0.335219
21 to 28 2501.44 0.020 0.508132
22 to 29 2418.64 -1.151 0.124949
23 to 30 2451.81 -0.682 0.247767
24 to 31 2368.93 -1.854 0.031897
25 to 32 2407.40 -1.310 0.095175
CDPARK for dh-ranFile-2018-06-16_19:31: 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
3526 0.1370 0.554479
3507 -0.7306 0.232514
3510 -0.5936 0.276387
3527 0.1826 0.572463
3508 -0.6849 0.246694
3514 -0.4110 0.340551
3516 -0.3196 0.374623
3542 0.8676 0.807188
3551 1.2785 0.899470
3537 0.6393 0.738676
Square side=100, avg. no. parked=3523.80 sample std.=14.63
p-value of the KSTEST for those 10 p-values: 0.762851
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_19:31
0.1512,0.9970,0.2784,0.1761,0.6318,0.5875,0.7195,0.3866,0.3478,0.3081,
The KS test for those 10 p-values: 0.546435
The 3DSPHERES test for dh-ranFile-2018-06-16_19:31
sample no r^3 equiv. uni.
1 0.147 0.004873
2 142.201 0.991262
3 70.184 0.903621
4 75.405 0.919016
5 10.836 0.303160
6 12.461 0.339896
7 12.963 0.350849
8 23.017 0.535702
9 2.622 0.083695
10 59.920 0.864304
11 45.642 0.781596
12 32.297 0.659238
13 83.540 0.938250
14 9.056 0.260569
15 9.232 0.264890
16 132.509 0.987929
17 12.296 0.336261
18 30.865 0.642574
19 3.009 0.095428
20 83.249 0.937648
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.183113
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.5 1.8 0.6 -0.8 2.4
-1.4 -0.4 0.5 0.2 -0.0 -0.7
-0.1 0.2 0.3 0.1 -0.1 0.5
-0.2 -1.8 -0.5 -0.3 1.5 -0.1
1.2 -0.4 0.4 -0.3 1.1 0.2
0.9 -0.7 0.1 -1.3 0.1 0.6
0.7 0.2 1.7 0.4 -0.6 -1.0
0.8
Chi-square with 42 degrees of freedom:33.842225
z-score=-0.890086, p-value=0.189102
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_19:31
Test no p-value
1 0.224658
2 0.098051
3 0.129605
4 0.339727
5 0.001353
6 0.018503
7 0.820592
8 0.199132
9 0.839873
10 0.216109
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.011798
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_19:31:
(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 66624 0.03 66650 0.00
3 25000.00 25075 0.23 24974 0.03
4 6666.67 6708 0.26 6738 0.76
5 1388.89 1334 2.17 1367 0.35
6 238.10 223 0.96 233 0.11
7 34.72 33 0.09 29 0.94
8 4.96 2 1.77 8 1.86
p=0.51691 p=0.33063
Number of rngs required: 687614, p-value: 0.181
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_19:31
No. of wins: Observed Expected
98367 98585.9
z-score=-0.979, pvalue=0.16382
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66537 66666.7 0.252 0.252
2 37694 37654.3 0.042 0.294
3 26969 26954.7 0.008 0.302
4 19181 19313.5 0.908 1.210
5 13894 13851.4 0.131 1.341
6 9874 9943.5 0.486 1.827
7 7277 7145.0 2.438 4.265
8 5126 5139.1 0.033 4.298
9 3808 3699.9 3.160 7.459
10 2719 2666.3 1.042 8.500
11 1891 1923.3 0.543 9.044
12 1389 1388.7 0.000 9.044
13 977 1003.7 0.711 9.755
14 745 726.1 0.490 10.245
15 521 525.8 0.044 10.289
16 390 381.2 0.205 10.495
17 277 276.5 0.001 10.495
18 211 200.8 0.515 11.010
19 147 146.0 0.007 11.018
20 100 106.2 0.364 11.381
21 273 287.1 0.694 12.075
Chisq= 12.08 for 20 degrees of freedom, p= 0.08653
SUMMARY of craptest
p-value for no. of wins: 0.163824
p-value for throws/game: 0.086531
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_19:31
No. of wins: Observed Expected
99064 98585.9
z-score= 2.139, pvalue=0.98376
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66613 66666.7 0.043 0.043
2 37814 37654.3 0.677 0.720
3 26901 26954.7 0.107 0.827
4 19316 19313.5 0.000 0.828
5 13925 13851.4 0.391 1.219
6 9880 9943.5 0.406 1.625
7 7183 7145.0 0.202 1.827
8 5137 5139.1 0.001 1.827
9 3665 3699.9 0.329 2.156
10 2588 2666.3 2.299 4.455
11 1892 1923.3 0.510 4.965
12 1400 1388.7 0.091 5.057
13 995 1003.7 0.076 5.132
14 694 726.1 1.423 6.555
15 551 525.8 1.204 7.759
16 402 381.2 1.140 8.900
17 258 276.5 1.243 10.143
18 185 200.8 1.248 11.390
19 167 146.0 3.025 14.416
20 117 106.2 1.095 15.511
21 317 287.1 3.111 18.622
Chisq= 18.62 for 20 degrees of freedom, p= 0.45348
SUMMARY of craptest
p-value for no. of wins: 0.983763
p-value for throws/game: 0.453478
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0049,0.0118,0.0178,0.0185,0.0189,0.0191,0.0232,0.0260,0.0261,
0.0277,0.0319,0.0373,0.0384,0.0413,0.0458,0.0508,0.0535,0.0546,0.0586,
0.0604,0.0637,0.0653,0.0668,0.0730,0.0780,0.0796,0.0837,0.0865,0.0905,
0.0906,0.0908,0.0952,0.0954,0.0966,0.0981,0.0997,0.1049,0.1068,0.1156,
0.1156,0.1182,0.1199,0.1249,0.1285,0.1296,0.1512,0.1535,0.1570,0.1596,
0.1613,0.1613,0.1635,0.1638,0.1643,0.1643,0.1664,0.1697,0.1732,0.1761,
0.1806,0.1831,0.1850,0.1855,0.1860,0.1891,0.1971,0.1991,0.2125,0.2156,
0.2161,0.2247,0.2258,0.2306,0.2325,0.2359,0.2467,0.2478,0.2494,0.2569,
0.2606,0.2620,0.2649,0.2764,0.2784,0.2890,0.2930,0.2943,0.3032,0.3081,
0.3110,0.3153,0.3185,0.3294,0.3306,0.3352,0.3363,0.3380,0.3397,0.3399,
0.3406,0.3411,0.3478,0.3506,0.3508,0.3558,0.3569,0.3746,0.3803,0.3866,
0.3962,0.3992,0.3995,0.4036,0.4040,0.4041,0.4095,0.4201,0.4208,0.4216,
0.4237,0.4320,0.4376,0.4410,0.4425,0.4535,0.4536,0.4550,0.4662,0.4666,
0.4734,0.4820,0.4941,0.4978,0.4983,0.5081,0.5081,0.5120,0.5169,0.5173,
0.5248,0.5270,0.5316,0.5357,0.5370,0.5394,0.5414,0.5428,0.5464,0.5475,
0.5521,0.5522,0.5540,0.5545,0.5603,0.5669,0.5725,0.5734,0.5761,0.5768,
0.5770,0.5808,0.5812,0.5875,0.5915,0.5932,0.5940,0.6020,0.6030,0.6074,
0.6240,0.6297,0.6318,0.6332,0.6386,0.6402,0.6426,0.6437,0.6500,0.6521,
0.6592,0.6678,0.6770,0.6771,0.6796,0.6863,0.6931,0.6969,0.6986,0.7023,
0.7043,0.7121,0.7153,0.7180,0.7187,0.7195,0.7220,0.7299,0.7387,0.7410,
0.7497,0.7523,0.7548,0.7556,0.7624,0.7629,0.7683,0.7738,0.7777,0.7778,
0.7816,0.7837,0.7928,0.7930,0.7936,0.7960,0.7990,0.8011,0.8016,0.8030,
0.8044,0.8072,0.8097,0.8116,0.8170,0.8206,0.8215,0.8262,0.8337,0.8378,
0.8399,0.8419,0.8499,0.8571,0.8643,0.8674,0.8736,0.8755,0.8766,0.8860,
0.8991,0.8992,0.8995,0.9036,0.9057,0.9101,0.9103,0.9150,0.9190,0.9206,
0.9228,0.9287,0.9292,0.9345,0.9351,0.9363,0.9376,0.9383,0.9480,0.9566,
0.9572,0.9833,0.9838,0.9879,0.9880,0.9913,0.9918,0.9929,0.9970,
Overall p-value after applying KStest on 269 p-values = 0.418650
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.