RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.83 9.3545 0.071520
2 to 25 16.02 18.1701 0.621814
3 to 26 15.59 22.8530 0.845903
4 to 27 15.76 20.1940 0.735574
5 to 28 15.80 19.9841 0.724957
6 to 29 15.95 9.5957 0.080298
7 to 30 16.11 24.4656 0.892674
8 to 31 15.85 24.2496 0.887189
9 to 32 15.86 11.3027 0.159595
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.393467
Tough bday spacings test for dh-ranFile-2018-07-10_15:31: 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 14 39 79 76 92 75 67 32 16 9 1
(O-E)^2/E 2.6 0.2 0.4 4.8 0.3 0.1 4.3 0.2 0.1 0.9 2.3
Birthday Spacings: Sum(O-E)^2/E= 16.118, p= 0.904
RESULTS OF GCD FOR dh-ranFile-2018-07-10_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.216812
p-value, dist. of gcd's: 0.475787
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.483 0.104 0.436 0.138 0.784 0.834 0.398 0.367
Bits 8 to 15---> 0.412 0.295 0.848 0.129 0.910 0.675 0.245 0.664
Bits 16 to 23---> 0.030 0.606 0.543 0.963 0.357 0.624 0.184 0.609
Bits 24 to 31---> 0.829 0.957 0.308 0.477 0.426 0.260 0.540 0.352
KS test for the above 32 p values: 0.186
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_15:31,
p-values for 5 runs: 0.0768, 0.2281, 0.2717, 0.3500, 0.6238
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 191 211.4 1.972 1.972
r= 29 5256 5134.0 2.899 4.870
r= 30 22920 23103.0 1.450 6.321
r= 31 11633 11551.5 0.575 6.895
chi-square = 6.895 with df = 3; p-value = 0.925
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5152 5134.0 0.063 0.335
r= 31 23001 23103.0 0.451 0.786
r= 32 11628 11551.5 0.506 1.292
chi-square = 1.292 with df = 3; p-value = 0.269
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_15:31
b-rank test for bits 1 to 8, p=0.68788
b-rank test for bits 2 to 9, p=0.69494
b-rank test for bits 3 to 10, p=0.81410
b-rank test for bits 4 to 11, p=0.19846
b-rank test for bits 5 to 12, p=0.64198
b-rank test for bits 6 to 13, p=0.38896
b-rank test for bits 7 to 14, p=0.05210
b-rank test for bits 8 to 15, p=0.81391
b-rank test for bits 9 to 16, p=0.26181
b-rank test for bits 10 to 17, p=0.73157
b-rank test for bits 11 to 18, p=0.55186
b-rank test for bits 12 to 19, p=0.41096
b-rank test for bits 13 to 20, p=0.21968
b-rank test for bits 14 to 21, p=0.05268
b-rank test for bits 15 to 22, p=0.75745
b-rank test for bits 16 to 23, p=0.55294
b-rank test for bits 17 to 24, p=0.39479
b-rank test for bits 18 to 25, p=0.02713
b-rank test for bits 19 to 26, p=0.03571
b-rank test for bits 20 to 27, p=0.42950
b-rank test for bits 21 to 28, p=0.59401
b-rank test for bits 22 to 29, p=0.59709
b-rank test for bits 23 to 30, p=0.05732
b-rank test for bits 24 to 31, p=0.34892
b-rank test for bits 25 to 32, p=0.02036
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 = 0.111532
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_15:31
(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 140881 -2.40 0.008139
2 141269 -1.50 0.067314
3 142321 0.96 0.831936
4 142054 0.34 0.632324
5 142377 1.09 0.862734
6 142028 0.28 0.609212
7 141640 -0.63 0.264584
8 142002 0.22 0.585708
9 142534 1.46 0.927788
10 142158 0.58 0.719381
11 141207 -1.64 0.050403
12 141962 0.12 0.548971
13 142814 2.11 0.982730
14 141997 0.20 0.581150
15 141078 -1.94 0.026047
16 142354 1.04 0.850586
17 141406 -1.18 0.119797
18 141407 -1.17 0.120264
19 142140 0.54 0.705039
20 141505 -0.94 0.172407
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_15:31
Bits used No. missing words z-score p-value
23 to 32 141973 0.2196 0.586890
22 to 31 142139 0.7920 0.785810
21 to 30 142003 0.3230 0.626652
20 to 29 142113 0.7023 0.758757
19 to 28 141901 -0.0287 0.488542
18 to 27 141797 -0.3873 0.349251
17 to 26 142191 0.9713 0.834295
16 to 25 142532 2.1471 0.984109
15 to 24 142132 0.7678 0.778705
14 to 23 142460 1.8989 0.971209
13 to 22 141582 -1.1287 0.129507
12 to 21 141730 -0.6184 0.268163
11 to 20 141627 -0.9736 0.165140
10 to 19 142148 0.8230 0.794746
9 to 18 141736 -0.5977 0.275024
8 to 17 141841 -0.2356 0.406864
7 to 16 141585 -1.1184 0.131703
6 to 15 141782 -0.4391 0.330306
5 to 14 141652 -0.8873 0.187447
4 to 13 142199 0.9989 0.841069
3 to 12 141683 -0.7804 0.217564
2 to 11 142022 0.3885 0.651183
1 to 10 142077 0.5782 0.718426
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_15:31
Bits used No. missing words z-score p-value
28 to 32 141704 -0.6960 0.243204
27 to 31 142273 1.2328 0.891171
26 to 30 141602 -1.0418 0.148753
25 to 29 141623 -0.9706 0.165871
24 to 28 141985 0.2565 0.601221
23 to 27 141659 -0.8486 0.198059
22 to 26 142083 0.5887 0.721973
21 to 25 142037 0.4328 0.667413
20 to 24 142527 2.0938 0.981861
19 to 23 141503 -1.3774 0.084196
18 to 22 141865 -0.1503 0.440275
17 to 21 142260 1.1887 0.882723
16 to 20 141749 -0.5435 0.293396
15 to 19 141832 -0.2621 0.396609
14 to 18 142211 1.0226 0.846754
13 to 17 141809 -0.3401 0.366890
12 to 16 142349 1.4904 0.931941
11 to 15 141952 0.1446 0.557504
10 to 14 141938 0.0972 0.538711
9 to 13 142110 0.6802 0.751823
8 to 12 141531 -1.2825 0.099838
7 to 11 141829 -0.2723 0.392694
6 to 10 141683 -0.7672 0.221475
5 to 9 141570 -1.1503 0.125016
4 to 8 142421 1.7345 0.958583
3 to 7 142328 1.4192 0.922083
2 to 6 141913 0.0124 0.504963
1 to 5 142230 1.0870 0.861485
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_15:31
Bits used No. missing words z-score p-value
31 to 32 142264 1.0462 0.852271
30 to 31 141764 -0.4287 0.334070
29 to 30 142402 1.4533 0.926930
28 to 29 142205 0.8722 0.808446
27 to 28 141355 -1.6352 0.051004
26 to 27 141735 -0.5142 0.303539
25 to 26 141600 -0.9125 0.180759
24 to 25 142470 1.6539 0.950925
23 to 24 141736 -0.5113 0.304571
22 to 23 142270 1.0639 0.856318
21 to 22 141602 -0.9066 0.182315
20 to 21 142315 1.1967 0.884282
19 to 20 141356 -1.6322 0.051314
18 to 19 141934 0.0728 0.529007
17 to 18 142292 1.1288 0.870513
16 to 17 142123 0.6303 0.735749
15 to 16 142109 0.5890 0.722068
14 to 15 141784 -0.3697 0.355801
13 to 14 141566 -1.0128 0.155584
12 to 13 142180 0.7984 0.787691
11 to 12 141820 -0.2635 0.396079
10 to 11 141674 -0.6942 0.243782
9 to 10 141296 -1.8092 0.035207
8 to 9 141678 -0.6824 0.247496
7 to 8 142075 0.4887 0.687474
6 to 7 142042 0.3914 0.652233
5 to 6 141898 -0.0334 0.486669
4 to 5 142193 0.8368 0.798643
3 to 4 141740 -0.4995 0.308714
2 to 3 142345 1.2852 0.900632
1 to 2 142056 0.4327 0.667367
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2456.93 -0.609 0.271239
Test results for specific bytes for dh-ranFile-2018-07-10_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2475.08 -0.352 0.362241
2 to 9 2557.29 0.810 0.791086
3 to 10 2435.20 -0.916 0.179723
4 to 11 2552.86 0.748 0.772628
5 to 12 2418.80 -1.148 0.125426
6 to 13 2462.25 -0.534 0.296725
7 to 14 2451.63 -0.684 0.246963
8 to 15 2503.98 0.056 0.522448
9 to 16 2444.80 -0.781 0.217492
10 to 17 2415.69 -1.192 0.116578
11 to 18 2656.51 2.213 0.986564
12 to 19 2552.25 0.739 0.770032
13 to 20 2472.72 -0.386 0.349821
14 to 21 2592.24 1.304 0.903957
15 to 22 2625.33 1.772 0.961843
16 to 23 2490.76 -0.131 0.448035
17 to 24 2530.66 0.434 0.667706
18 to 25 2576.87 1.087 0.861518
19 to 26 2502.73 0.039 0.515425
20 to 27 2469.96 -0.425 0.335493
21 to 28 2392.46 -1.521 0.064155
22 to 29 2518.83 0.266 0.604969
23 to 30 2496.80 -0.045 0.481951
24 to 31 2535.83 0.507 0.693798
25 to 32 2514.37 0.203 0.580521
CDPARK for dh-ranFile-2018-07-10_15:31: 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
3536 0.5936 0.723613
3530 0.3196 0.625377
3558 1.5982 0.944998
3566 1.9635 0.975204
3489 -1.5525 0.060270
3554 1.4155 0.921543
3493 -1.3699 0.085365
3480 -1.9635 0.024796
3589 3.0137 0.998710
3467 -2.5571 0.005278
Square side=100, avg. no. parked=3526.20 sample std.=39.43
p-value of the KSTEST for those 10 p-values: 0.019755
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_15:31
0.1403,0.4235,0.8370,0.4037,0.3896,0.5946,0.9963,0.2988,0.4197,0.5217,
The KS test for those 10 p-values: 0.483491
The 3DSPHERES test for dh-ranFile-2018-07-10_15:31
sample no r^3 equiv. uni.
1 59.635 0.863006
2 39.786 0.734518
3 23.659 0.545539
4 42.450 0.757077
5 33.348 0.670965
6 43.959 0.768993
7 29.449 0.625300
8 27.201 0.596143
9 16.391 0.420956
10 17.601 0.443839
11 10.471 0.294638
12 32.279 0.659033
13 6.545 0.196014
14 104.845 0.969646
15 26.354 0.584579
16 8.744 0.252839
17 22.197 0.522846
18 0.447 0.014793
19 27.580 0.601220
20 38.780 0.725465
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.246216
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 -0.1 0.2 -0.7 2.1
0.7 1.7 2.1 1.2 -0.7 -1.1
0.7 -0.8 -1.0 -0.2 0.7 0.8
0.9 -0.5 0.2 -2.0 -1.0 1.5
-0.2 -0.7 1.2 -1.1 -0.4 0.6
-1.3 0.6 -0.5 0.5 -0.8 -0.8
-1.6 -0.1 0.9 -0.7 0.9 1.0
0.8
Chi-square with 42 degrees of freedom:45.019446
z-score=0.329449, p-value=0.653308
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_15:31
Test no p-value
1 0.521136
2 0.086946
3 0.443563
4 0.711381
5 0.239102
6 0.707582
7 0.805155
8 0.116277
9 0.211407
10 0.121026
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.383279
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_15:31:
(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 66536 0.26 66636 0.01
3 25000.00 25115 0.53 24931 0.19
4 6666.67 6663 0.00 6740 0.81
5 1388.89 1383 0.02 1410 0.32
6 238.10 253 0.93 238 0.00
7 34.72 41 1.14 36 0.05
8 4.96 8 1.86 8 1.86
p=0.42300 p=0.22214
Number of rngs required: 688191, p-value: 0.404
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_15:31
No. of wins: Observed Expected
98702 98585.9
z-score= 0.519, pvalue=0.69828
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67086 66666.7 2.638 2.638
2 37575 37654.3 0.167 2.805
3 26676 26954.7 2.882 5.687
4 19281 19313.5 0.055 5.742
5 13945 13851.4 0.632 6.374
6 9716 9943.5 5.207 11.581
7 7230 7145.0 1.011 12.591
8 5084 5139.1 0.590 13.182
9 3759 3699.9 0.945 14.127
10 2596 2666.3 1.853 15.980
11 1942 1923.3 0.181 16.161
12 1361 1388.7 0.554 16.715
13 1023 1003.7 0.371 17.086
14 740 726.1 0.265 17.351
15 556 525.8 1.730 19.081
16 368 381.2 0.454 19.535
17 281 276.5 0.072 19.607
18 220 200.8 1.830 21.436
19 143 146.0 0.061 21.497
20 122 106.2 2.346 23.843
21 296 287.1 0.275 24.118
Chisq= 24.12 for 20 degrees of freedom, p= 0.76273
SUMMARY of craptest
p-value for no. of wins: 0.698277
p-value for throws/game: 0.762734
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_15:31
No. of wins: Observed Expected
98237 98585.9
z-score=-1.560, pvalue=0.05934
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66280 66666.7 2.243 2.243
2 37356 37654.3 2.363 4.606
3 27335 26954.7 5.365 9.971
4 19420 19313.5 0.588 10.559
5 13820 13851.4 0.071 10.630
6 9935 9943.5 0.007 10.637
7 7187 7145.0 0.247 10.884
8 5214 5139.1 1.092 11.976
9 3719 3699.9 0.099 12.075
10 2581 2666.3 2.729 14.804
11 1926 1923.3 0.004 14.808
12 1440 1388.7 1.892 16.700
13 1053 1003.7 2.420 19.120
14 767 726.1 2.299 21.419
15 515 525.8 0.223 21.642
16 401 381.2 1.034 22.676
17 303 276.5 2.532 25.208
18 228 200.8 3.676 28.883
19 157 146.0 0.831 29.715
20 88 106.2 3.124 32.838
21 275 287.1 0.511 33.350
Chisq= 33.35 for 20 degrees of freedom, p= 0.96912
SUMMARY of craptest
p-value for no. of wins: 0.059345
p-value for throws/game: 0.969124
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0053,0.0081,0.0148,0.0198,0.0204,0.0248,0.0260,0.0271,0.0296,0.0352,
0.0357,0.0504,0.0510,0.0513,0.0521,0.0527,0.0573,0.0593,0.0603,0.0642,
0.0673,0.0715,0.0768,0.0803,0.0842,0.0854,0.0869,0.0998,0.1044,0.1115,
0.1163,0.1166,0.1198,0.1203,0.1210,0.1250,0.1254,0.1286,0.1295,0.1317,
0.1382,0.1403,0.1488,0.1556,0.1596,0.1651,0.1659,0.1724,0.1797,0.1808,
0.1823,0.1843,0.1857,0.1874,0.1960,0.1981,0.1985,0.2114,0.2168,0.2175,
0.2176,0.2197,0.2215,0.2221,0.2281,0.2391,0.2432,0.2438,0.2447,0.2462,
0.2470,0.2475,0.2528,0.2601,0.2618,0.2646,0.2682,0.2690,0.2712,0.2717,
0.2750,0.2934,0.2946,0.2948,0.2967,0.2988,0.3035,0.3046,0.3080,0.3087,
0.3303,0.3341,0.3355,0.3489,0.3493,0.3498,0.3500,0.3518,0.3558,0.3570,
0.3622,0.3669,0.3670,0.3833,0.3890,0.3896,0.3927,0.3935,0.3948,0.3961,
0.3966,0.3984,0.4036,0.4037,0.4069,0.4110,0.4121,0.4197,0.4210,0.4230,
0.4235,0.4263,0.4295,0.4358,0.4403,0.4436,0.4438,0.4480,0.4758,0.4768,
0.4820,0.4827,0.4835,0.4867,0.4885,0.5050,0.5154,0.5211,0.5217,0.5224,
0.5228,0.5290,0.5387,0.5396,0.5433,0.5455,0.5490,0.5519,0.5529,0.5575,
0.5805,0.5812,0.5846,0.5857,0.5869,0.5940,0.5946,0.5961,0.5971,0.6012,
0.6012,0.6050,0.6060,0.6086,0.6092,0.6218,0.6237,0.6238,0.6253,0.6254,
0.6267,0.6323,0.6420,0.6512,0.6522,0.6533,0.6590,0.6639,0.6674,0.6674,
0.6677,0.6710,0.6755,0.6875,0.6879,0.6938,0.6949,0.6983,0.7050,0.7076,
0.7114,0.7184,0.7194,0.7220,0.7221,0.7236,0.7250,0.7255,0.7316,0.7345,
0.7356,0.7357,0.7518,0.7571,0.7574,0.7588,0.7627,0.7690,0.7700,0.7726,
0.7787,0.7837,0.7858,0.7877,0.7911,0.7947,0.7986,0.8052,0.8084,0.8139,
0.8141,0.8287,0.8319,0.8339,0.8343,0.8370,0.8411,0.8459,0.8468,0.8482,
0.8506,0.8523,0.8563,0.8615,0.8615,0.8627,0.8630,0.8705,0.8827,0.8843,
0.8872,0.8912,0.8927,0.9006,0.9037,0.9040,0.9101,0.9215,0.9221,0.9247,
0.9269,0.9278,0.9319,0.9450,0.9509,0.9565,0.9586,0.9618,0.9634,0.9691,
0.9696,0.9712,0.9752,0.9819,0.9827,0.9841,0.9866,0.9963,0.9987,
Overall p-value after applying KStest on 269 p-values = 0.997646
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.