RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.90 17.7370 0.594391
2 to 25 15.90 17.1026 0.552562
3 to 26 15.68 25.6569 0.919057
4 to 27 15.47 23.6092 0.869551
5 to 28 15.68 13.0847 0.269504
6 to 29 15.76 16.6903 0.524471
7 to 30 15.76 19.5895 0.704237
8 to 31 15.33 31.7220 0.983710
9 to 32 15.60 29.2147 0.967403
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.038114
Tough bday spacings test for dh-ranFile-2018-07-11_14:31: 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 39 86 110 81 68 51 30 15 8 4
(O-E)^2/E 0.1 0.2 2.2 1.6 2.8 1.3 0.0 0.0 0.0 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.550, p= 0.425
RESULTS OF GCD FOR dh-ranFile-2018-07-11_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.858801
p-value, dist. of gcd's: 0.982512
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.726 0.518 0.188 0.788 0.313 0.127 0.072 0.428
Bits 8 to 15---> 0.456 0.944 0.241 0.119 0.184 0.691 0.509 0.857
Bits 16 to 23---> 0.369 0.052 0.854 0.839 0.752 0.279 0.966 0.155
Bits 24 to 31---> 0.648 0.071 0.216 0.633 0.252 0.739 0.156 0.206
KS test for the above 32 p values: 0.572
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_14:31,
p-values for 5 runs: 0.7854, 0.6132, 0.1986, 0.7661, 0.1241
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 181 211.4 4.376 4.376
r= 29 5244 5134.0 2.356 6.733
r= 30 23095 23103.0 0.003 6.736
r= 31 11480 11551.5 0.443 7.178
chi-square = 7.178 with df = 3; p-value = 0.934
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5118 5134.0 0.050 0.189
r= 31 23157 23103.0 0.126 0.315
r= 32 11519 11551.5 0.092 0.406
chi-square = 0.406 with df = 3; p-value = 0.061
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_14:31
b-rank test for bits 1 to 8, p=0.78048
b-rank test for bits 2 to 9, p=0.99573
b-rank test for bits 3 to 10, p=0.90829
b-rank test for bits 4 to 11, p=0.35064
b-rank test for bits 5 to 12, p=0.97451
b-rank test for bits 6 to 13, p=0.38016
b-rank test for bits 7 to 14, p=0.39654
b-rank test for bits 8 to 15, p=0.87492
b-rank test for bits 9 to 16, p=0.25122
b-rank test for bits 10 to 17, p=0.37247
b-rank test for bits 11 to 18, p=0.10651
b-rank test for bits 12 to 19, p=0.97483
b-rank test for bits 13 to 20, p=0.05194
b-rank test for bits 14 to 21, p=0.14387
b-rank test for bits 15 to 22, p=0.07110
b-rank test for bits 16 to 23, p=0.01629
b-rank test for bits 17 to 24, p=0.70795
b-rank test for bits 18 to 25, p=0.40769
b-rank test for bits 19 to 26, p=0.19032
b-rank test for bits 20 to 27, p=0.42350
b-rank test for bits 21 to 28, p=0.33313
b-rank test for bits 22 to 29, p=0.01243
b-rank test for bits 23 to 30, p=0.71449
b-rank test for bits 24 to 31, p=0.51206
b-rank test for bits 25 to 32, p=0.46080
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 = 0.341121
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_14:31
(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 142025 0.27 0.606519
2 142211 0.70 0.759544
3 141716 -0.45 0.325741
4 142109 0.47 0.679578
5 141003 -2.12 0.017105
6 141748 -0.38 0.353109
7 141188 -1.69 0.045960
8 141452 -1.07 0.142641
9 142502 1.38 0.916934
10 142152 0.57 0.714638
11 141966 0.13 0.552669
12 141838 -0.17 0.433819
13 141656 -0.59 0.276961
14 142198 0.67 0.749991
15 142376 1.09 0.862221
16 141626 -0.66 0.253990
17 142390 1.12 0.869294
18 142036 0.30 0.616369
19 141650 -0.61 0.272287
20 141083 -1.93 0.026761
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_14:31
Bits used No. missing words z-score p-value
23 to 32 142194 0.9816 0.836857
22 to 31 142169 0.8954 0.814717
21 to 30 142548 2.2023 0.986178
20 to 29 141931 0.0747 0.529783
19 to 28 141619 -1.0011 0.158380
18 to 27 141966 0.1954 0.577466
17 to 26 142093 0.6333 0.736746
16 to 25 141505 -1.3942 0.081622
15 to 24 142013 0.3575 0.639635
14 to 23 141965 0.1920 0.576115
13 to 22 140781 -3.8908 0.000050
12 to 21 141743 -0.5736 0.283136
11 to 20 142355 1.5368 0.937828
10 to 19 141477 -1.4908 0.068008
9 to 18 142397 1.6816 0.953679
8 to 17 141634 -0.9494 0.171205
7 to 16 141817 -0.3184 0.375099
6 to 15 141828 -0.2804 0.389567
5 to 14 141765 -0.4977 0.309351
4 to 13 142408 1.7196 0.957243
3 to 12 141918 0.0299 0.511925
2 to 11 142004 0.3264 0.627957
1 to 10 141479 -1.4839 0.068918
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_14:31
Bits used No. missing words z-score p-value
28 to 32 141843 -0.2248 0.411049
27 to 31 141922 0.0429 0.517129
26 to 30 141705 -0.6926 0.244267
25 to 29 141860 -0.1672 0.433598
24 to 28 142020 0.3752 0.646227
23 to 27 142195 0.9684 0.833571
22 to 26 142426 1.7514 0.960064
21 to 25 142260 1.1887 0.882723
20 to 24 141801 -0.3672 0.356727
19 to 23 141700 -0.7096 0.238978
18 to 22 141774 -0.4587 0.323208
17 to 21 141875 -0.1164 0.453679
16 to 20 141464 -1.5096 0.065574
15 to 19 141852 -0.1943 0.422955
14 to 18 141943 0.1141 0.545435
13 to 17 142183 0.9277 0.823217
12 to 16 142291 1.2938 0.902132
11 to 15 141620 -0.9808 0.163351
10 to 14 141925 0.0531 0.521181
9 to 13 141928 0.0633 0.525232
8 to 12 142392 1.6362 0.949098
7 to 11 141963 0.1819 0.572182
6 to 10 141619 -0.9842 0.162516
5 to 9 141996 0.2938 0.615543
4 to 8 142426 1.7514 0.960064
3 to 7 141393 -1.7503 0.040036
2 to 6 141535 -1.2689 0.102236
1 to 5 142031 0.4124 0.659992
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_14:31
Bits used No. missing words z-score p-value
31 to 32 141871 -0.1131 0.454988
30 to 31 142360 1.3294 0.908144
29 to 30 141977 0.1996 0.579110
28 to 29 141890 -0.0570 0.477264
27 to 28 141888 -0.0629 0.474915
26 to 27 141848 -0.1809 0.428217
25 to 26 142523 1.8102 0.964870
24 to 25 141573 -0.9921 0.160569
23 to 24 141819 -0.2665 0.394942
22 to 23 142222 0.9223 0.821822
21 to 22 141921 0.0344 0.513731
20 to 21 142040 0.3855 0.650051
19 to 20 142461 1.6273 0.948168
18 to 19 141809 -0.2960 0.383631
17 to 18 142134 0.6627 0.746253
16 to 17 141581 -0.9685 0.166391
15 to 16 141954 0.1318 0.552417
14 to 15 142045 0.4002 0.655498
13 to 14 141938 0.0846 0.533699
12 to 13 142142 0.6863 0.753751
11 to 12 141688 -0.6529 0.256913
10 to 11 141952 0.1259 0.550083
9 to 10 141802 -0.3166 0.375771
8 to 9 141301 -1.7945 0.036368
7 to 8 142066 0.4622 0.678014
6 to 7 142091 0.5359 0.703986
5 to 6 142254 1.0167 0.845358
4 to 5 141803 -0.3137 0.376891
3 to 4 141661 -0.7325 0.231921
2 to 3 142316 1.1996 0.884856
1 to 2 142511 1.7748 0.962038
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2522.02 0.311 0.622267
Test results for specific bytes for dh-ranFile-2018-07-11_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2472.05 -0.395 0.346307
2 to 9 2594.20 1.332 0.908601
3 to 10 2537.62 0.532 0.702636
4 to 11 2471.08 -0.409 0.341290
5 to 12 2495.62 -0.062 0.475318
6 to 13 2521.24 0.300 0.618077
7 to 14 2573.11 1.034 0.849432
8 to 15 2642.59 2.017 0.978131
9 to 16 2571.61 1.013 0.844390
10 to 17 2442.95 -0.807 0.209899
11 to 18 2500.96 0.014 0.505393
12 to 19 2404.20 -1.355 0.087729
13 to 20 2517.24 0.244 0.596326
14 to 21 2486.37 -0.193 0.423553
15 to 22 2513.38 0.189 0.575030
16 to 23 2541.52 0.587 0.721466
17 to 24 2501.46 0.021 0.508232
18 to 25 2455.98 -0.623 0.266805
19 to 26 2499.83 -0.002 0.499014
20 to 27 2558.07 0.821 0.794224
21 to 28 2587.80 1.242 0.892831
22 to 29 2644.87 2.049 0.979757
23 to 30 2502.68 0.038 0.515097
24 to 31 2565.28 0.923 0.822032
25 to 32 2590.60 1.281 0.899963
CDPARK for dh-ranFile-2018-07-11_14:31: 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
3539 0.7306 0.767486
3552 1.3242 0.907282
3527 0.1826 0.572463
3539 0.7306 0.767486
3495 -1.2785 0.100530
3542 0.8676 0.807188
3514 -0.4110 0.340551
3508 -0.6849 0.246694
3526 0.1370 0.554479
3535 0.5479 0.708135
Square side=100, avg. no. parked=3527.70 sample std.=16.59
p-value of the KSTEST for those 10 p-values: 0.596322
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_14:31
0.5911,0.3892,0.1033,0.4743,0.1078,0.9825,0.0770,0.5990,0.4991,0.8348,
The KS test for those 10 p-values: 0.801158
The 3DSPHERES test for dh-ranFile-2018-07-11_14:31
sample no r^3 equiv. uni.
1 12.563 0.342143
2 44.040 0.769612
3 4.047 0.126186
4 29.341 0.623955
5 13.502 0.362419
6 19.472 0.477459
7 34.283 0.681062
8 5.044 0.154751
9 52.315 0.825149
10 45.164 0.778085
11 55.093 0.840618
12 8.321 0.242213
13 62.429 0.875189
14 55.875 0.844718
15 72.595 0.911062
16 22.486 0.527421
17 14.531 0.383904
18 21.128 0.505533
19 51.534 0.820537
20 5.838 0.176849
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.412344
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 0.6 1.1 0.6 0.1
0.9 -0.3 -0.3 1.0 -2.2 0.8
-0.7 -0.6 0.0 1.9 -1.0 1.5
-1.2 0.7 -1.2 0.1 -0.9 1.0
-0.1 1.4 0.7 -1.3 -0.5 -1.3
0.4 0.7 -0.3 0.9 -0.6 0.2
0.5 -0.1 -0.8 -1.8 2.4 1.0
-1.1
Chi-square with 42 degrees of freedom:43.442138
z-score=0.157350, p-value=0.590255
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_14:31
Test no p-value
1 0.287104
2 0.602213
3 0.031506
4 0.934949
5 0.451456
6 0.313271
7 0.769537
8 0.377542
9 0.634963
10 0.144502
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.955860
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_14:31:
(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 66580 0.11 66366 1.36
3 25000.00 25043 0.07 25258 2.66
4 6666.67 6678 0.02 6711 0.29
5 1388.89 1427 1.05 1401 0.11
6 238.10 238 0.00 227 0.52
7 34.72 24 3.31 34 0.01
8 4.96 9 3.29 2 1.77
p=0.75086 p=0.65222
Number of rngs required: 688858, p-value: 0.700
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_14:31
No. of wins: Observed Expected
98462 98585.9
z-score=-0.554, pvalue=0.28980
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66640 66666.7 0.011 0.011
2 37993 37654.3 3.046 3.057
3 26974 26954.7 0.014 3.071
4 19274 19313.5 0.081 3.151
5 13877 13851.4 0.047 3.199
6 9912 9943.5 0.100 3.299
7 6989 7145.0 3.407 6.706
8 5063 5139.1 1.126 7.832
9 3670 3699.9 0.241 8.073
10 2626 2666.3 0.609 8.682
11 2002 1923.3 3.218 11.900
12 1371 1388.7 0.227 12.126
13 966 1003.7 1.417 13.544
14 705 726.1 0.615 14.159
15 517 525.8 0.148 14.308
16 392 381.2 0.309 14.616
17 305 276.5 2.929 17.545
18 206 200.8 0.133 17.679
19 147 146.0 0.007 17.686
20 96 106.2 0.982 18.668
21 275 287.1 0.511 19.179
Chisq= 19.18 for 20 degrees of freedom, p= 0.48979
SUMMARY of craptest
p-value for no. of wins: 0.289800
p-value for throws/game: 0.489791
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_14:31
No. of wins: Observed Expected
98557 98585.9
z-score=-0.129, pvalue=0.44865
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66667 66666.7 0.000 0.000
2 37788 37654.3 0.475 0.475
3 26855 26954.7 0.369 0.844
4 19406 19313.5 0.443 1.287
5 13730 13851.4 1.064 2.351
6 9955 9943.5 0.013 2.365
7 7169 7145.0 0.080 2.445
8 5224 5139.1 1.404 3.848
9 3688 3699.9 0.038 3.887
10 2657 2666.3 0.032 3.919
11 1825 1923.3 5.027 8.946
12 1374 1388.7 0.156 9.102
13 1033 1003.7 0.854 9.957
14 714 726.1 0.203 10.160
15 522 525.8 0.028 10.188
16 410 381.2 2.184 12.371
17 249 276.5 2.743 15.114
18 228 200.8 3.676 18.790
19 139 146.0 0.334 19.124
20 91 106.2 2.180 21.304
21 276 287.1 0.430 21.734
Chisq= 21.73 for 20 degrees of freedom, p= 0.64487
SUMMARY of craptest
p-value for no. of wins: 0.448650
p-value for throws/game: 0.644869
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0124,0.0163,0.0171,0.0268,0.0315,0.0364,0.0381,0.0400,0.0460,
0.0519,0.0519,0.0611,0.0656,0.0680,0.0689,0.0705,0.0711,0.0716,0.0770,
0.0816,0.0877,0.1005,0.1022,0.1033,0.1065,0.1078,0.1187,0.1241,0.1262,
0.1270,0.1426,0.1439,0.1445,0.1546,0.1548,0.1561,0.1584,0.1606,0.1625,
0.1634,0.1664,0.1712,0.1768,0.1844,0.1877,0.1903,0.1986,0.2063,0.2099,
0.2159,0.2319,0.2390,0.2406,0.2422,0.2443,0.2467,0.2512,0.2517,0.2540,
0.2569,0.2668,0.2695,0.2723,0.2770,0.2792,0.2831,0.2871,0.2898,0.3094,
0.3133,0.3134,0.3232,0.3257,0.3331,0.3406,0.3411,0.3413,0.3421,0.3463,
0.3506,0.3531,0.3567,0.3624,0.3686,0.3725,0.3751,0.3758,0.3769,0.3775,
0.3802,0.3836,0.3839,0.3892,0.3896,0.3949,0.3965,0.4077,0.4110,0.4123,
0.4230,0.4235,0.4236,0.4248,0.4280,0.4282,0.4336,0.4338,0.4487,0.4515,
0.4537,0.4550,0.4561,0.4608,0.4743,0.4749,0.4753,0.4773,0.4775,0.4898,
0.4990,0.4991,0.5054,0.5055,0.5082,0.5087,0.5119,0.5121,0.5137,0.5151,
0.5171,0.5175,0.5212,0.5245,0.5252,0.5274,0.5298,0.5337,0.5454,0.5501,
0.5524,0.5526,0.5527,0.5545,0.5715,0.5722,0.5725,0.5750,0.5761,0.5775,
0.5791,0.5903,0.5911,0.5944,0.5963,0.5963,0.5990,0.6022,0.6065,0.6132,
0.6155,0.6164,0.6181,0.6223,0.6240,0.6280,0.6331,0.6350,0.6396,0.6449,
0.6462,0.6476,0.6501,0.6522,0.6555,0.6600,0.6780,0.6796,0.6811,0.6909,
0.7000,0.7026,0.7040,0.7042,0.7079,0.7081,0.7145,0.7146,0.7215,0.7261,
0.7367,0.7388,0.7463,0.7500,0.7509,0.7521,0.7538,0.7595,0.7661,0.7675,
0.7675,0.7695,0.7696,0.7781,0.7805,0.7854,0.7883,0.7942,0.8012,0.8072,
0.8147,0.8205,0.8218,0.8220,0.8232,0.8251,0.8336,0.8348,0.8369,0.8395,
0.8406,0.8444,0.8447,0.8454,0.8494,0.8536,0.8566,0.8588,0.8622,0.8693,
0.8696,0.8749,0.8752,0.8827,0.8849,0.8928,0.9000,0.9021,0.9073,0.9081,
0.9083,0.9086,0.9111,0.9169,0.9191,0.9336,0.9349,0.9378,0.9439,0.9482,
0.9491,0.9537,0.9559,0.9572,0.9601,0.9601,0.9620,0.9649,0.9661,0.9674,
0.9745,0.9748,0.9781,0.9798,0.9825,0.9825,0.9837,0.9862,0.9957,
Overall p-value after applying KStest on 269 p-values = 0.259887
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.