RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.69 13.3116 0.284908
2 to 25 16.23 11.2944 0.159145
3 to 26 16.26 28.7974 0.963559
4 to 27 15.85 14.7513 0.386612
5 to 28 16.12 11.5772 0.174963
6 to 29 16.10 20.5735 0.754052
7 to 30 15.70 26.1096 0.927514
8 to 31 15.78 12.9664 0.261569
9 to 32 15.49 17.4194 0.573677
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.839346
Tough bday spacings test for dh-ranFile-2018-07-09_20:31: 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 9 32 70 93 117 78 50 28 13 5 5
(O-E)^2/E 0.0 0.6 0.1 0.2 3.8 0.0 0.1 0.1 0.2 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 5.816, p= 0.169
RESULTS OF GCD FOR dh-ranFile-2018-07-09_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.609229
p-value, dist. of gcd's: 0.983874
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.006 0.210 0.531 0.247 0.335 0.484 0.634 0.729
Bits 8 to 15---> 0.354 0.743 0.043 0.493 0.091 0.224 0.872 0.967
Bits 16 to 23---> 0.296 0.023 0.978 0.904 0.555 0.806 0.263 0.085
Bits 24 to 31---> 0.879 0.464 0.217 0.190 0.895 0.217 0.819 0.237
KS test for the above 32 p values: 0.453
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_20:31,
p-values for 5 runs: 0.8475, 0.6402, 0.9453, 0.7531, 0.2494
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5194 5134.0 0.701 0.702
r= 30 23017 23103.0 0.320 1.022
r= 31 11578 11551.5 0.061 1.083
chi-square = 1.083 with df = 3; p-value = 0.219
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5102 5134.0 0.200 0.471
r= 31 23023 23103.0 0.277 0.749
r= 32 11656 11551.5 0.945 1.694
chi-square = 1.694 with df = 3; p-value = 0.362
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_20:31
b-rank test for bits 1 to 8, p=0.84149
b-rank test for bits 2 to 9, p=0.84099
b-rank test for bits 3 to 10, p=0.14309
b-rank test for bits 4 to 11, p=0.09843
b-rank test for bits 5 to 12, p=0.40737
b-rank test for bits 6 to 13, p=0.14490
b-rank test for bits 7 to 14, p=0.90669
b-rank test for bits 8 to 15, p=0.69038
b-rank test for bits 9 to 16, p=0.42995
b-rank test for bits 10 to 17, p=0.62214
b-rank test for bits 11 to 18, p=0.61441
b-rank test for bits 12 to 19, p=0.83872
b-rank test for bits 13 to 20, p=0.66564
b-rank test for bits 14 to 21, p=0.74013
b-rank test for bits 15 to 22, p=0.68089
b-rank test for bits 16 to 23, p=0.71791
b-rank test for bits 17 to 24, p=0.18360
b-rank test for bits 18 to 25, p=0.69155
b-rank test for bits 19 to 26, p=0.68563
b-rank test for bits 20 to 27, p=0.60171
b-rank test for bits 21 to 28, p=0.26333
b-rank test for bits 22 to 29, p=0.58054
b-rank test for bits 23 to 30, p=0.68089
b-rank test for bits 24 to 31, p=0.97662
b-rank test for bits 25 to 32, p=0.27702
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 = 0.179356
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_20:31
(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 142573 1.55 0.939505
2 142510 1.40 0.919756
3 141327 -1.36 0.086823
4 142097 0.44 0.669481
5 141846 -0.15 0.441184
6 142041 0.31 0.620822
7 142232 0.75 0.774546
8 142182 0.64 0.737963
9 142141 0.54 0.705844
10 141570 -0.79 0.213939
11 141505 -0.94 0.172407
12 142008 0.23 0.591163
13 141835 -0.17 0.431063
14 141708 -0.47 0.319036
15 142407 1.16 0.877541
16 141734 -0.41 0.341032
17 141661 -0.58 0.280886
18 141513 -0.93 0.177222
19 142154 0.57 0.716223
20 141679 -0.54 0.295235
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_20:31
Bits used No. missing words z-score p-value
23 to 32 142131 0.7644 0.777679
22 to 31 142295 1.3299 0.908224
21 to 30 142011 0.3506 0.637051
20 to 29 141910 0.0023 0.500922
19 to 28 141582 -1.1287 0.129507
18 to 27 142001 0.3161 0.624038
17 to 26 141931 0.0747 0.529783
16 to 25 142148 0.8230 0.794746
15 to 24 142214 1.0506 0.853276
14 to 23 142359 1.5506 0.939500
13 to 22 141877 -0.1115 0.455617
12 to 21 141514 -1.3632 0.086409
11 to 20 141725 -0.6356 0.262512
10 to 19 142424 1.7747 0.962028
9 to 18 141630 -0.9632 0.167722
8 to 17 142035 0.4333 0.667618
7 to 16 142270 1.2437 0.893193
6 to 15 142191 0.9713 0.834295
5 to 14 142033 0.4264 0.665109
4 to 13 141556 -1.2184 0.111540
3 to 12 141831 -0.2701 0.393540
2 to 11 142151 0.8333 0.797675
1 to 10 141579 -1.1391 0.127337
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_20:31
Bits used No. missing words z-score p-value
28 to 32 141834 -0.2554 0.399224
27 to 31 141838 -0.2418 0.404469
26 to 30 141898 -0.0384 0.484682
25 to 29 142059 0.5074 0.694048
24 to 28 142238 1.1141 0.867390
23 to 27 141682 -0.7706 0.220469
22 to 26 142091 0.6158 0.730997
21 to 25 141449 -1.5604 0.059328
20 to 24 142020 0.3752 0.646227
19 to 23 141934 0.0836 0.533324
18 to 22 141990 0.2735 0.607749
17 to 21 141665 -0.8282 0.203768
16 to 20 141842 -0.2282 0.409731
15 to 19 141921 0.0396 0.515778
14 to 18 141912 0.0091 0.503611
13 to 17 142099 0.6429 0.739872
12 to 16 142246 1.1413 0.873118
11 to 15 141773 -0.4621 0.321992
10 to 14 141610 -1.0147 0.155130
9 to 13 142214 1.0328 0.849147
8 to 12 142366 1.5480 0.939193
7 to 11 142282 1.2633 0.896757
6 to 10 141589 -1.0859 0.138770
5 to 9 141974 0.2192 0.586761
4 to 8 142392 1.6362 0.949098
3 to 7 141795 -0.3876 0.349171
2 to 6 141797 -0.3808 0.351683
1 to 5 142364 1.5413 0.938373
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_20:31
Bits used No. missing words z-score p-value
31 to 32 141951 0.1229 0.548915
30 to 31 141582 -0.9656 0.167128
29 to 30 141319 -1.7414 0.040808
28 to 29 141347 -1.6588 0.048579
27 to 28 141982 0.2144 0.584869
26 to 27 142153 0.7188 0.763865
25 to 26 142193 0.8368 0.798643
24 to 25 142118 0.6155 0.730903
23 to 24 141938 0.0846 0.533699
22 to 23 141484 -1.2547 0.104801
21 to 22 142427 1.5271 0.936626
20 to 21 141599 -0.9154 0.179984
19 to 20 141808 -0.2989 0.382505
18 to 19 141345 -1.6647 0.047987
17 to 18 142100 0.5624 0.713095
16 to 17 141576 -0.9833 0.162736
15 to 16 141743 -0.4906 0.311837
14 to 15 141871 -0.1131 0.454988
13 to 14 141682 -0.6706 0.251241
12 to 13 141570 -1.0010 0.158420
11 to 12 142201 0.8604 0.805211
10 to 11 142312 1.1878 0.882547
9 to 10 141736 -0.5113 0.304571
8 to 9 141441 -1.3815 0.083562
7 to 8 141425 -1.4287 0.076545
6 to 7 141625 -0.8387 0.200810
5 to 6 141376 -1.5732 0.057831
4 to 5 141760 -0.4405 0.329787
3 to 4 141583 -0.9626 0.167868
2 to 3 141824 -0.2517 0.400632
1 to 2 141947 0.1111 0.544240
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2433.70 -0.938 0.174221
Test results for specific bytes for dh-ranFile-2018-07-09_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2518.34 0.259 0.602350
2 to 9 2579.54 1.125 0.869671
3 to 10 2551.34 0.726 0.766100
4 to 11 2400.02 -1.414 0.078683
5 to 12 2592.78 1.312 0.905250
6 to 13 2490.96 -0.128 0.449149
7 to 14 2384.96 -1.627 0.051873
8 to 15 2482.30 -0.250 0.401181
9 to 16 2501.24 0.018 0.507017
10 to 17 2475.15 -0.351 0.362633
11 to 18 2571.75 1.015 0.844858
12 to 19 2459.70 -0.570 0.284363
13 to 20 2487.19 -0.181 0.428109
14 to 21 2589.73 1.269 0.897764
15 to 22 2507.10 0.100 0.539980
16 to 23 2517.34 0.245 0.596871
17 to 24 2548.58 0.687 0.753986
18 to 25 2524.97 0.353 0.638000
19 to 26 2569.66 0.985 0.837713
20 to 27 2385.62 -1.618 0.052874
21 to 28 2619.46 1.689 0.954436
22 to 29 2409.89 -1.274 0.101275
23 to 30 2466.67 -0.471 0.318695
24 to 31 2672.99 2.446 0.992786
25 to 32 2487.68 -0.174 0.430830
CDPARK for dh-ranFile-2018-07-09_20:31: 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
3510 -0.5936 0.276387
3565 1.9178 0.972432
3529 0.2740 0.607947
3540 0.7763 0.781201
3557 1.5525 0.939730
3521 -0.0913 0.463617
3511 -0.5479 0.291865
3547 1.0959 0.863437
3521 -0.0913 0.463617
3514 -0.4110 0.340551
Square side=100, avg. no. parked=3531.50 sample std.=18.71
p-value of the KSTEST for those 10 p-values: 0.391078
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_20:31
0.8249,0.8557,0.4472,0.8176,0.1006,0.9957,0.5598,0.8763,0.3008,0.9597,
The KS test for those 10 p-values: 0.057101
The 3DSPHERES test for dh-ranFile-2018-07-09_20:31
sample no r^3 equiv. uni.
1 5.237 0.160166
2 76.623 0.922238
3 15.606 0.405600
4 5.044 0.154762
5 35.794 0.696735
6 57.079 0.850825
7 95.942 0.959160
8 17.693 0.445550
9 45.609 0.781351
10 55.328 0.841858
11 51.409 0.819788
12 18.018 0.451526
13 18.988 0.468974
14 18.155 0.454018
15 58.856 0.859406
16 40.321 0.739212
17 60.661 0.867615
18 8.038 0.235037
19 45.729 0.782225
20 23.785 0.547443
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.075429
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.6 0.1 -0.5 -0.2 0.9
-0.1 0.1 -0.8 -1.8 -0.5 -0.8
-0.1 -0.7 3.0 0.4 -1.0 0.3
0.6 -0.0 -0.1 -1.2 -0.1 1.1
0.4 -0.1 0.7 -0.4 1.1 0.2
-0.7 0.0 -1.7 -0.8 -1.6 0.1
1.0 -0.4 -0.8 1.0 1.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:36.965576
z-score=-0.549301, p-value=0.308766
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_20:31
Test no p-value
1 0.422054
2 0.876707
3 0.000457
4 0.893910
5 0.046653
6 0.244006
7 0.130500
8 0.374125
9 0.005389
10 0.630252
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.042775
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_20:31:
(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 66892 0.76 66646 0.01
3 25000.00 24847 0.94 25087 0.30
4 6666.67 6675 0.01 6631 0.19
5 1388.89 1326 2.85 1367 0.35
6 238.10 222 1.09 238 0.00
7 34.72 33 0.09 25 2.72
8 4.96 4 0.19 5 0.00
p=0.56724 p=0.26490
Number of rngs required: 688117, p-value: 0.371
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_20:31
No. of wins: Observed Expected
98658 98585.9
z-score= 0.323, pvalue=0.62652
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66781 66666.7 0.196 0.196
2 37471 37654.3 0.893 1.089
3 27362 26954.7 6.154 7.242
4 19231 19313.5 0.352 7.594
5 13678 13851.4 2.171 9.765
6 9991 9943.5 0.226 9.992
7 7085 7145.0 0.504 10.496
8 5133 5139.1 0.007 10.503
9 3696 3699.9 0.004 10.507
10 2673 2666.3 0.017 10.524
11 1885 1923.3 0.764 11.288
12 1400 1388.7 0.091 11.379
13 974 1003.7 0.880 12.259
14 718 726.1 0.091 12.350
15 544 525.8 0.627 12.978
16 331 381.2 6.599 19.576
17 277 276.5 0.001 19.577
18 201 200.8 0.000 19.577
19 151 146.0 0.172 19.750
20 113 106.2 0.433 20.183
21 305 287.1 1.114 21.297
Chisq= 21.30 for 20 degrees of freedom, p= 0.62018
SUMMARY of craptest
p-value for no. of wins: 0.626523
p-value for throws/game: 0.620179
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_20:31
No. of wins: Observed Expected
98325 98585.9
z-score=-1.167, pvalue=0.12166
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66625 66666.7 0.026 0.026
2 37703 37654.3 0.063 0.089
3 27024 26954.7 0.178 0.267
4 19091 19313.5 2.562 2.829
5 13929 13851.4 0.435 3.264
6 9952 9943.5 0.007 3.271
7 7121 7145.0 0.081 3.352
8 5255 5139.1 2.615 5.967
9 3677 3699.9 0.141 6.108
10 2628 2666.3 0.550 6.658
11 2014 1923.3 4.274 10.933
12 1368 1388.7 0.310 11.243
13 996 1003.7 0.059 11.302
14 715 726.1 0.171 11.473
15 527 525.8 0.003 11.475
16 379 381.2 0.012 11.488
17 278 276.5 0.008 11.495
18 189 200.8 0.697 12.192
19 143 146.0 0.061 12.253
20 97 106.2 0.800 13.053
21 289 287.1 0.012 13.065
Chisq= 13.07 for 20 degrees of freedom, p= 0.12542
SUMMARY of craptest
p-value for no. of wins: 0.121663
p-value for throws/game: 0.125423
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0054,0.0062,0.0234,0.0408,0.0428,0.0432,0.0467,0.0480,0.0486,
0.0519,0.0529,0.0571,0.0578,0.0593,0.0754,0.0765,0.0787,0.0836,0.0851,
0.0864,0.0868,0.0910,0.0984,0.1006,0.1013,0.1048,0.1115,0.1217,0.1254,
0.1273,0.1295,0.1305,0.1388,0.1431,0.1449,0.1548,0.1551,0.1584,0.1591,
0.1602,0.1627,0.1671,0.1677,0.1679,0.1695,0.1724,0.1742,0.1750,0.1772,
0.1794,0.1800,0.1836,0.1899,0.2008,0.2038,0.2103,0.2139,0.2165,0.2168,
0.2188,0.2205,0.2238,0.2350,0.2368,0.2440,0.2469,0.2494,0.2512,0.2616,
0.2625,0.2630,0.2633,0.2649,0.2764,0.2770,0.2809,0.2844,0.2849,0.2919,
0.2952,0.2957,0.3008,0.3046,0.3088,0.3118,0.3187,0.3190,0.3220,0.3298,
0.3354,0.3406,0.3410,0.3492,0.3517,0.3537,0.3617,0.3626,0.3710,0.3741,
0.3825,0.3866,0.3911,0.3935,0.3992,0.4006,0.4012,0.4045,0.4056,0.4074,
0.4097,0.4221,0.4281,0.4300,0.4308,0.4311,0.4412,0.4455,0.4472,0.4491,
0.4515,0.4527,0.4540,0.4550,0.4556,0.4636,0.4636,0.4644,0.4690,0.4839,
0.4847,0.4929,0.5009,0.5036,0.5070,0.5158,0.5298,0.5311,0.5333,0.5337,
0.5400,0.5442,0.5474,0.5489,0.5554,0.5598,0.5672,0.5737,0.5805,0.5849,
0.5868,0.5912,0.5969,0.6017,0.6024,0.6077,0.6079,0.6092,0.6144,0.6202,
0.6208,0.6221,0.6240,0.6265,0.6303,0.6340,0.6371,0.6380,0.6402,0.6462,
0.6651,0.6656,0.6676,0.6695,0.6809,0.6809,0.6856,0.6904,0.6915,0.6940,
0.6967,0.7058,0.7131,0.7162,0.7179,0.7295,0.7309,0.7310,0.7380,0.7392,
0.7399,0.7401,0.7431,0.7531,0.7540,0.7541,0.7639,0.7661,0.7745,0.7777,
0.7812,0.7814,0.7822,0.7947,0.7977,0.7986,0.8052,0.8060,0.8176,0.8192,
0.8198,0.8249,0.8343,0.8377,0.8387,0.8393,0.8410,0.8415,0.8419,0.8449,
0.8475,0.8491,0.8508,0.8533,0.8557,0.8594,0.8634,0.8674,0.8676,0.8697,
0.8725,0.8731,0.8763,0.8767,0.8775,0.8789,0.8825,0.8932,0.8939,0.8953,
0.8968,0.8978,0.9045,0.9053,0.9067,0.9082,0.9198,0.9222,0.9275,0.9366,
0.9384,0.9392,0.9395,0.9395,0.9397,0.9453,0.9491,0.9544,0.9592,0.9597,
0.9620,0.9636,0.9674,0.9724,0.9766,0.9782,0.9839,0.9928,0.9957,
Overall p-value after applying KStest on 269 p-values = 0.629626
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.