RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.79 18.1335 0.619537
2 to 25 15.41 28.7230 0.962832
3 to 26 15.87 28.7214 0.962817
4 to 27 15.90 13.2360 0.279754
5 to 28 15.87 9.7731 0.087144
6 to 29 15.58 23.7661 0.874070
7 to 30 15.69 12.4759 0.229495
8 to 31 15.87 18.2703 0.628014
9 to 32 15.70 23.7775 0.874391
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.239493
Tough bday spacings test for dh-ranFile-2018-07-02_13:31: 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 31 78 103 86 90 54 27 18 3 2
(O-E)^2/E 0.1 0.9 0.3 0.3 1.4 1.8 0.1 0.3 0.7 2.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.808, p= 0.450
RESULTS OF GCD FOR dh-ranFile-2018-07-02_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.569171
p-value, dist. of gcd's: 0.358177
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.717 0.161 0.310 0.027 0.679 0.659 0.744 0.061
Bits 8 to 15---> 0.332 0.340 0.227 0.861 0.289 0.998 0.728 0.550
Bits 16 to 23---> 0.770 0.654 0.366 0.830 0.685 0.509 0.939 0.401
Bits 24 to 31---> 0.090 0.339 0.021 0.132 0.167 0.339 0.799 0.239
KS test for the above 32 p values: 0.235
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_13:31,
p-values for 5 runs: 0.9698, 0.1572, 0.0604, 0.6047, 0.5673
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 225 211.4 0.873 0.873
r= 29 5279 5134.0 4.095 4.967
r= 30 23174 23103.0 0.218 5.185
r= 31 11322 11551.5 4.561 9.746
chi-square = 9.746 with df = 3; p-value = 0.979
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5150 5134.0 0.050 0.666
r= 31 23116 23103.0 0.007 0.674
r= 32 11534 11551.5 0.027 0.700
chi-square = 0.700 with df = 3; p-value = 0.127
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_13:31
b-rank test for bits 1 to 8, p=0.20594
b-rank test for bits 2 to 9, p=0.95224
b-rank test for bits 3 to 10, p=0.44811
b-rank test for bits 4 to 11, p=0.21657
b-rank test for bits 5 to 12, p=0.08354
b-rank test for bits 6 to 13, p=0.26895
b-rank test for bits 7 to 14, p=0.66874
b-rank test for bits 8 to 15, p=0.56057
b-rank test for bits 9 to 16, p=0.75236
b-rank test for bits 10 to 17, p=0.02124
b-rank test for bits 11 to 18, p=0.69097
b-rank test for bits 12 to 19, p=0.19597
b-rank test for bits 13 to 20, p=0.27838
b-rank test for bits 14 to 21, p=0.30310
b-rank test for bits 15 to 22, p=0.83649
b-rank test for bits 16 to 23, p=0.78197
b-rank test for bits 17 to 24, p=0.95390
b-rank test for bits 18 to 25, p=0.95980
b-rank test for bits 19 to 26, p=0.95429
b-rank test for bits 20 to 27, p=0.87381
b-rank test for bits 21 to 28, p=0.14492
b-rank test for bits 22 to 29, p=0.50285
b-rank test for bits 23 to 30, p=0.19470
b-rank test for bits 24 to 31, p=0.32305
b-rank test for bits 25 to 32, p=0.76588
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 = 0.685675
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_13:31
(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 142299 0.91 0.818706
2 141802 -0.25 0.400996
3 141952 0.10 0.539707
4 140851 -2.47 0.006704
5 142358 1.05 0.852749
6 141555 -0.83 0.203871
7 142101 0.45 0.672861
8 142718 1.89 0.970582
9 141910 0.00 0.500625
10 141279 -1.47 0.070411
11 141428 -1.12 0.130379
12 141427 -1.13 0.129884
13 142881 2.27 0.988404
14 141636 -0.64 0.261535
15 141668 -0.56 0.286426
16 141600 -0.72 0.234922
17 141697 -0.50 0.309913
18 142108 0.46 0.678741
19 142304 0.92 0.821769
20 141971 0.14 0.557285
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_13:31
Bits used No. missing words z-score p-value
23 to 32 141990 0.2782 0.609560
22 to 31 141213 -2.4011 0.008172
21 to 30 142036 0.4368 0.668869
20 to 29 142360 1.5540 0.939912
19 to 28 141780 -0.4460 0.327811
18 to 27 142327 1.4402 0.925100
17 to 26 142133 0.7713 0.779728
16 to 25 141483 -1.4701 0.070767
15 to 24 141984 0.2575 0.601597
14 to 23 141808 -0.3494 0.363389
13 to 22 141920 0.0368 0.514675
12 to 21 141671 -0.8218 0.205588
11 to 20 142293 1.3230 0.907082
10 to 19 141980 0.2437 0.596264
9 to 18 142271 1.2471 0.893827
8 to 17 142010 0.3471 0.635756
7 to 16 141743 -0.5736 0.283136
6 to 15 141951 0.1437 0.557127
5 to 14 142014 0.3609 0.640925
4 to 13 141316 -2.0460 0.020380
3 to 12 141447 -1.5942 0.055441
2 to 11 141643 -0.9184 0.179210
1 to 10 141957 0.1644 0.565284
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_13:31
Bits used No. missing words z-score p-value
28 to 32 141783 -0.4282 0.334239
27 to 31 142476 1.9209 0.972629
26 to 30 141700 -0.7096 0.238978
25 to 29 142071 0.5480 0.708166
24 to 28 142148 0.8091 0.790757
23 to 27 141985 0.2565 0.601221
22 to 26 141791 -0.4011 0.344166
21 to 25 141911 0.0057 0.502258
20 to 24 141941 0.1074 0.542747
19 to 23 141262 -2.1943 0.014106
18 to 22 142041 0.4463 0.672324
17 to 21 141982 0.2463 0.597290
16 to 20 141597 -1.0587 0.144858
15 to 19 142109 0.6768 0.750749
14 to 18 141592 -1.0757 0.141032
13 to 17 142392 1.6362 0.949098
12 to 16 142074 0.5582 0.711647
11 to 15 141847 -0.2113 0.416331
10 to 14 142067 0.5345 0.703493
9 to 13 142309 1.3548 0.912262
8 to 12 142026 0.3955 0.653760
7 to 11 141893 -0.0554 0.477928
6 to 10 141803 -0.3604 0.359259
5 to 9 141799 -0.3740 0.354202
4 to 8 141860 -0.1672 0.433598
3 to 7 141590 -1.0825 0.139521
2 to 6 141871 -0.1299 0.448310
1 to 5 141989 0.2701 0.606446
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_13:31
Bits used No. missing words z-score p-value
31 to 32 141700 -0.6175 0.268455
30 to 31 142371 1.3619 0.913379
29 to 30 141775 -0.3963 0.345959
28 to 29 142266 1.0521 0.853629
27 to 28 141807 -0.3019 0.381380
26 to 27 141392 -1.5260 0.063499
25 to 26 142018 0.3206 0.625728
24 to 25 141796 -0.3343 0.369074
23 to 24 141837 -0.2134 0.415522
22 to 23 142566 1.9371 0.973632
21 to 22 142682 2.2793 0.988674
20 to 21 141919 0.0285 0.511378
19 to 20 142105 0.5772 0.718097
18 to 19 141668 -0.7119 0.238267
17 to 18 141638 -0.8004 0.211744
16 to 17 142276 1.0816 0.860290
15 to 16 142371 1.3619 0.913379
14 to 15 141111 -2.3550 0.009262
13 to 14 141868 -0.1219 0.451482
12 to 13 142732 2.4268 0.992383
11 to 12 142069 0.4710 0.681181
10 to 11 142279 1.0905 0.862247
9 to 10 142119 0.6185 0.731876
8 to 9 141865 -0.1308 0.447980
7 to 8 141596 -0.9243 0.177671
6 to 7 141266 -1.8977 0.028866
5 to 6 141540 -1.0895 0.137974
4 to 5 141802 -0.3166 0.375771
3 to 4 141699 -0.6204 0.267483
2 to 3 142108 0.5860 0.721078
1 to 2 142179 0.7955 0.786835
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2457.96 -0.595 0.276054
Test results for specific bytes for dh-ranFile-2018-07-02_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2611.00 1.570 0.941769
2 to 9 2432.60 -0.953 0.170237
3 to 10 2547.25 0.668 0.748019
4 to 11 2618.64 1.678 0.953308
5 to 12 2432.41 -0.956 0.169563
6 to 13 2454.31 -0.646 0.259106
7 to 14 2576.00 1.075 0.858772
8 to 15 2532.78 0.464 0.678525
9 to 16 2566.96 0.947 0.828152
10 to 17 2503.38 0.048 0.519048
11 to 18 2366.72 -1.885 0.029726
12 to 19 2526.31 0.372 0.645063
13 to 20 2569.17 0.978 0.836015
14 to 21 2507.90 0.112 0.544453
15 to 22 2560.52 0.856 0.803975
16 to 23 2474.00 -0.368 0.356561
17 to 24 2422.09 -1.102 0.135269
18 to 25 2490.74 -0.131 0.447888
19 to 26 2429.73 -0.994 0.160162
20 to 27 2510.92 0.154 0.561377
21 to 28 2311.27 -2.669 0.003804
22 to 29 2426.17 -1.044 0.148207
23 to 30 2395.29 -1.481 0.069321
24 to 31 2478.78 -0.300 0.382047
25 to 32 2371.00 -1.824 0.034051
CDPARK for dh-ranFile-2018-07-02_13:31: 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
3511 -0.5479 0.291865
3522 -0.0457 0.481790
3513 -0.4566 0.323972
3512 -0.5023 0.307734
3479 -2.0091 0.022262
3525 0.0913 0.536383
3540 0.7763 0.781201
3523 0.0000 0.500000
3512 -0.5023 0.307734
3539 0.7306 0.767486
Square side=100, avg. no. parked=3517.60 sample std.=16.37
p-value of the KSTEST for those 10 p-values: 0.428575
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_13:31
0.5239,0.2555,0.2527,0.4171,0.0591,0.5749,0.6905,0.7620,0.3516,0.2770,
The KS test for those 10 p-values: 0.429305
The 3DSPHERES test for dh-ranFile-2018-07-02_13:31
sample no r^3 equiv. uni.
1 66.093 0.889538
2 13.992 0.372753
3 39.325 0.730408
4 50.980 0.817196
5 120.756 0.982140
6 204.911 0.998920
7 6.005 0.181399
8 26.909 0.592197
9 1.671 0.054187
10 3.211 0.101492
11 83.126 0.937392
12 25.206 0.568380
13 126.388 0.985197
14 43.698 0.766975
15 121.429 0.982537
16 14.251 0.378135
17 10.918 0.305072
18 2.963 0.094038
19 22.388 0.525873
20 9.254 0.265436
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.086890
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -0.3 0.1 0.9 0.5 -0.9
0.7 0.5 1.5 -0.1 0.6 0.4
-1.0 -0.1 -0.6 0.1 -0.4 -1.4
-0.8 0.8 0.7 1.2 -1.0 1.1
0.2 1.3 0.0 0.1 -0.1 -0.7
-0.1 -1.1 -1.5 0.0 -0.5 0.4
-0.2 -0.4 -0.4 0.4 -1.3 1.0
0.8
Chi-square with 42 degrees of freedom:26.689567
z-score=-1.670505, p-value=0.031685
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_13:31
Test no p-value
1 0.258491
2 0.127748
3 0.618186
4 0.198781
5 0.421392
6 0.498919
7 0.048132
8 0.001752
9 0.068489
10 0.684986
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.027752
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_13:31:
(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 66642 0.01 66732 0.06
3 25000.00 25110 0.48 24938 0.15
4 6666.67 6594 0.79 6658 0.01
5 1388.89 1379 0.07 1394 0.02
6 238.10 222 1.09 232 0.16
7 34.72 45 3.04 41 1.14
8 4.96 7 0.84 4 0.19
p=0.61237 p=0.05687
Number of rngs required: 687523, p-value: 0.154
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_13:31
No. of wins: Observed Expected
98720 98585.9
z-score= 0.600, pvalue=0.72573
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66735 66666.7 0.070 0.070
2 37622 37654.3 0.028 0.098
3 26934 26954.7 0.016 0.114
4 19147 19313.5 1.435 1.548
5 13753 13851.4 0.699 2.248
6 9993 9943.5 0.246 2.494
7 7088 7145.0 0.455 2.949
8 5236 5139.1 1.828 4.777
9 3706 3699.9 0.010 4.787
10 2667 2666.3 0.000 4.787
11 1942 1923.3 0.181 4.969
12 1470 1388.7 4.755 9.723
13 1082 1003.7 6.106 15.829
14 670 726.1 4.340 20.170
15 521 525.8 0.044 20.214
16 390 381.2 0.205 20.420
17 281 276.5 0.072 20.492
18 227 200.8 3.410 23.902
19 140 146.0 0.245 24.147
20 106 106.2 0.000 24.148
21 290 287.1 0.029 24.177
Chisq= 24.18 for 20 degrees of freedom, p= 0.76524
SUMMARY of craptest
p-value for no. of wins: 0.725733
p-value for throws/game: 0.765236
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_13:31
No. of wins: Observed Expected
98297 98585.9
z-score=-1.292, pvalue=0.09819
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66597 66666.7 0.073 0.073
2 37746 37654.3 0.223 0.296
3 26941 26954.7 0.007 0.303
4 19324 19313.5 0.006 0.309
5 13666 13851.4 2.482 2.791
6 10000 9943.5 0.321 3.111
7 7243 7145.0 1.343 4.455
8 5051 5139.1 1.509 5.964
9 3678 3699.9 0.129 6.093
10 2679 2666.3 0.061 6.154
11 1890 1923.3 0.578 6.732
12 1437 1388.7 1.677 8.409
13 1010 1003.7 0.039 8.448
14 737 726.1 0.162 8.610
15 541 525.8 0.437 9.048
16 398 381.2 0.745 9.792
17 300 276.5 1.990 11.783
18 214 200.8 0.864 12.646
19 158 146.0 0.989 13.635
20 107 106.2 0.006 13.641
21 283 287.1 0.059 13.700
Chisq= 13.70 for 20 degrees of freedom, p= 0.15463
SUMMARY of craptest
p-value for no. of wins: 0.098188
p-value for throws/game: 0.154633
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0038,0.0067,0.0082,0.0093,0.0141,0.0204,0.0206,0.0212,0.0223,
0.0268,0.0278,0.0289,0.0297,0.0317,0.0341,0.0481,0.0542,0.0554,0.0569,
0.0591,0.0604,0.0613,0.0635,0.0685,0.0693,0.0704,0.0708,0.0835,0.0869,
0.0871,0.0896,0.0940,0.0982,0.1015,0.1269,0.1277,0.1299,0.1304,0.1317,
0.1353,0.1380,0.1395,0.1410,0.1449,0.1449,0.1482,0.1539,0.1546,0.1572,
0.1602,0.1606,0.1671,0.1696,0.1702,0.1777,0.1792,0.1814,0.1947,0.1960,
0.1988,0.2039,0.2056,0.2059,0.2117,0.2166,0.2273,0.2295,0.2349,0.2351,
0.2383,0.2388,0.2390,0.2395,0.2527,0.2555,0.2585,0.2591,0.2615,0.2654,
0.2675,0.2685,0.2689,0.2761,0.2770,0.2784,0.2798,0.2831,0.2864,0.2887,
0.2919,0.3031,0.3051,0.3077,0.3077,0.3099,0.3101,0.3230,0.3240,0.3278,
0.3321,0.3342,0.3387,0.3389,0.3404,0.3442,0.3460,0.3516,0.3542,0.3566,
0.3582,0.3593,0.3634,0.3661,0.3691,0.3728,0.3758,0.3781,0.3814,0.3820,
0.4010,0.4012,0.4155,0.4163,0.4171,0.4214,0.4286,0.4293,0.4336,0.4479,
0.4480,0.4481,0.4483,0.4496,0.4515,0.4779,0.4818,0.4989,0.5000,0.5006,
0.5023,0.5028,0.5093,0.5114,0.5147,0.5190,0.5239,0.5259,0.5364,0.5397,
0.5427,0.5445,0.5498,0.5571,0.5573,0.5606,0.5614,0.5653,0.5673,0.5684,
0.5692,0.5749,0.5922,0.5963,0.5973,0.6012,0.6016,0.6047,0.6064,0.6096,
0.6124,0.6182,0.6195,0.6257,0.6280,0.6358,0.6409,0.6451,0.6538,0.6543,
0.6593,0.6687,0.6689,0.6723,0.6729,0.6785,0.6787,0.6791,0.6812,0.6850,
0.6850,0.6857,0.6905,0.6910,0.7035,0.7082,0.7116,0.7171,0.7181,0.7211,
0.7257,0.7281,0.7304,0.7319,0.7437,0.7480,0.7507,0.7524,0.7620,0.7652,
0.7659,0.7670,0.7675,0.7702,0.7797,0.7812,0.7820,0.7868,0.7908,0.7990,
0.8040,0.8172,0.8187,0.8218,0.8282,0.8298,0.8360,0.8365,0.8527,0.8536,
0.8588,0.8603,0.8612,0.8622,0.8738,0.8741,0.8744,0.8895,0.8938,0.9071,
0.9123,0.9134,0.9134,0.9251,0.9374,0.9386,0.9399,0.9418,0.9491,0.9522,
0.9533,0.9539,0.9543,0.9598,0.9628,0.9628,0.9698,0.9706,0.9726,0.9736,
0.9791,0.9821,0.9825,0.9852,0.9884,0.9887,0.9924,0.9983,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.262538
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.