RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.57 13.6585 0.308888
2 to 25 15.66 31.3001 0.981643
3 to 26 15.70 12.0416 0.202390
4 to 27 15.91 24.9144 0.903357
5 to 28 15.81 15.6792 0.453321
6 to 29 16.10 13.2670 0.281860
7 to 30 15.73 15.2379 0.421650
8 to 31 15.75 24.2214 0.886456
9 to 32 15.85 20.2385 0.737785
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.539106
Tough bday spacings test for dh-ranFile-2018-07-04_16:31: 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 36 83 99 80 93 56 24 11 6 3
(O-E)^2/E 0.0 0.0 1.3 0.0 3.2 2.8 0.3 1.1 1.0 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.111, p= 0.569
RESULTS OF GCD FOR dh-ranFile-2018-07-04_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.585596
p-value, dist. of gcd's: 0.204996
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.207 0.991 0.355 0.468 0.641 0.032 0.762 0.781
Bits 8 to 15---> 0.854 0.094 0.245 0.384 0.042 0.460 0.731 0.214
Bits 16 to 23---> 0.279 0.800 0.499 0.284 0.735 0.196 0.902 0.667
Bits 24 to 31---> 0.076 0.681 0.077 0.752 0.984 0.180 0.109 0.818
KS test for the above 32 p values: 0.256
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_16:31,
p-values for 5 runs: 0.4277, 0.0206, 0.6422, 0.9398, 0.7177
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5109 5134.0 0.122 0.470
r= 30 23111 23103.0 0.003 0.473
r= 31 11560 11551.5 0.006 0.479
chi-square = 0.479 with df = 3; p-value = 0.077
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 240 211.4 3.864 3.864
r= 30 5179 5134.0 0.394 4.258
r= 31 23073 23103.0 0.039 4.297
r= 32 11508 11551.5 0.164 4.461
chi-square = 4.461 with df = 3; p-value = 0.784
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_16:31
b-rank test for bits 1 to 8, p=0.13372
b-rank test for bits 2 to 9, p=0.40155
b-rank test for bits 3 to 10, p=0.70806
b-rank test for bits 4 to 11, p=0.43177
b-rank test for bits 5 to 12, p=0.45218
b-rank test for bits 6 to 13, p=0.50485
b-rank test for bits 7 to 14, p=0.80302
b-rank test for bits 8 to 15, p=0.81475
b-rank test for bits 9 to 16, p=0.28977
b-rank test for bits 10 to 17, p=0.07784
b-rank test for bits 11 to 18, p=0.12673
b-rank test for bits 12 to 19, p=0.62586
b-rank test for bits 13 to 20, p=0.75133
b-rank test for bits 14 to 21, p=0.51503
b-rank test for bits 15 to 22, p=0.41129
b-rank test for bits 16 to 23, p=0.33132
b-rank test for bits 17 to 24, p=0.03621
b-rank test for bits 18 to 25, p=0.88155
b-rank test for bits 19 to 26, p=0.72738
b-rank test for bits 20 to 27, p=0.91347
b-rank test for bits 21 to 28, p=0.27605
b-rank test for bits 22 to 29, p=0.59547
b-rank test for bits 23 to 30, p=0.26225
b-rank test for bits 24 to 31, p=0.71535
b-rank test for bits 25 to 32, p=0.57405
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 = 0.855002
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_16:31
(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 142108 0.46 0.678741
2 142358 1.05 0.852749
3 141328 -1.36 0.087193
4 141634 -0.64 0.260017
5 141626 -0.66 0.253990
6 141381 -1.23 0.108524
7 141807 -0.24 0.405518
8 142704 1.86 0.968323
9 141432 -1.12 0.132370
10 141840 -0.16 0.435658
11 142116 0.48 0.685407
12 141927 0.04 0.516466
13 142586 1.58 0.943062
14 141908 -0.00 0.498760
15 141735 -0.41 0.341889
16 141700 -0.49 0.312389
17 142016 0.25 0.598408
18 141020 -2.08 0.018860
19 142154 0.57 0.716223
20 141904 -0.01 0.495032
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_16:31
Bits used No. missing words z-score p-value
23 to 32 142126 0.7471 0.772510
22 to 31 142234 1.1196 0.868548
21 to 30 141692 -0.7494 0.226804
20 to 29 142053 0.4954 0.689846
19 to 28 141732 -0.6115 0.270440
18 to 27 141692 -0.7494 0.226804
17 to 26 142289 1.3092 0.904768
16 to 25 141636 -0.9425 0.172964
15 to 24 142087 0.6127 0.729948
14 to 23 141836 -0.2529 0.400187
13 to 22 142037 0.4402 0.670119
12 to 21 141884 -0.0873 0.465199
11 to 20 141928 0.0644 0.525666
10 to 19 141754 -0.5356 0.296110
9 to 18 141782 -0.4391 0.330306
8 to 17 141980 0.2437 0.596264
7 to 16 141950 0.1402 0.555765
6 to 15 142111 0.6954 0.756602
5 to 14 141575 -1.1529 0.124484
4 to 13 142040 0.4506 0.673856
3 to 12 142028 0.4092 0.658806
2 to 11 142348 1.5127 0.934816
1 to 10 142219 1.0678 0.857201
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_16:31
Bits used No. missing words z-score p-value
28 to 32 141960 0.1718 0.568188
27 to 31 142047 0.4667 0.679635
26 to 30 141980 0.2396 0.594664
25 to 29 142086 0.5989 0.725374
24 to 28 141951 0.1413 0.556166
23 to 27 142065 0.5277 0.701145
22 to 26 142261 1.1921 0.883389
21 to 25 141622 -0.9740 0.165028
20 to 24 141761 -0.5028 0.307548
19 to 23 142251 1.1582 0.876610
18 to 22 142130 0.7480 0.772780
17 to 21 141693 -0.7333 0.231681
16 to 20 141649 -0.8825 0.188760
15 to 19 142132 0.7548 0.774820
14 to 18 141647 -0.8893 0.186933
13 to 17 141409 -1.6960 0.044940
12 to 16 142175 0.9006 0.816093
11 to 15 141910 0.0023 0.500906
10 to 14 141101 -2.7401 0.003071
9 to 13 141989 0.2701 0.606446
8 to 12 142690 2.6463 0.995932
7 to 11 142269 1.2192 0.888620
6 to 10 141760 -0.5062 0.306357
5 to 9 142061 0.5141 0.696421
4 to 8 142115 0.6972 0.757157
3 to 7 142083 0.5887 0.721973
2 to 6 141848 -0.2079 0.417654
1 to 5 141416 -1.6723 0.047232
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_16:31
Bits used No. missing words z-score p-value
31 to 32 141283 -1.8476 0.032331
30 to 31 142018 0.3206 0.625728
29 to 30 141855 -0.1603 0.436336
28 to 29 141866 -0.1278 0.449147
27 to 28 141903 -0.0187 0.492551
26 to 27 141678 -0.6824 0.247496
25 to 26 141864 -0.1337 0.446813
24 to 25 142046 0.4032 0.656583
23 to 24 141847 -0.1839 0.427060
22 to 23 142683 2.2822 0.988762
21 to 22 142709 2.3589 0.990836
20 to 21 141815 -0.2783 0.390407
19 to 20 141926 0.0492 0.519610
18 to 19 141887 -0.0659 0.473741
17 to 18 141423 -1.4346 0.075700
16 to 17 141400 -1.5024 0.066491
15 to 16 142018 0.3206 0.625728
14 to 15 142066 0.4622 0.678014
13 to 14 142106 0.5801 0.719092
12 to 13 142201 0.8604 0.805211
11 to 12 142042 0.3914 0.652233
10 to 11 141896 -0.0393 0.484317
9 to 10 142066 0.4622 0.678014
8 to 9 141967 0.1701 0.567541
7 to 8 140983 -2.7325 0.003142
6 to 7 141845 -0.1898 0.424747
5 to 6 141730 -0.5290 0.298404
4 to 5 141998 0.2616 0.603171
3 to 4 141179 -2.1544 0.015606
2 to 3 142100 0.5624 0.713095
1 to 2 142480 1.6834 0.953850
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2539.60 0.560 0.712249
Test results for specific bytes for dh-ranFile-2018-07-04_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2514.95 0.211 0.583702
2 to 9 2489.61 -0.147 0.441598
3 to 10 2441.39 -0.829 0.203583
4 to 11 2473.77 -0.371 0.355314
5 to 12 2350.66 -2.112 0.017345
6 to 13 2572.00 1.018 0.845707
7 to 14 2477.77 -0.314 0.376631
8 to 15 2558.63 0.829 0.796498
9 to 16 2526.86 0.380 0.647980
10 to 17 2506.04 0.085 0.534056
11 to 18 2376.04 -1.753 0.039798
12 to 19 2472.51 -0.389 0.348738
13 to 20 2483.72 -0.230 0.408973
14 to 21 2564.89 0.918 0.820601
15 to 22 2466.40 -0.475 0.317319
16 to 23 2425.25 -1.057 0.145226
17 to 24 2441.41 -0.829 0.203665
18 to 25 2388.61 -1.575 0.057596
19 to 26 2528.92 0.409 0.658748
20 to 27 2618.92 1.682 0.953700
21 to 28 2510.22 0.145 0.557469
22 to 29 2589.06 1.259 0.896065
23 to 30 2459.81 -0.568 0.284893
24 to 31 2558.09 0.821 0.794319
25 to 32 2615.87 1.639 0.949350
CDPARK for dh-ranFile-2018-07-04_16:31: 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
3522 -0.0457 0.481790
3494 -1.3242 0.092718
3537 0.6393 0.738676
3521 -0.0913 0.463617
3509 -0.6393 0.261324
3552 1.3242 0.907282
3511 -0.5479 0.291865
3520 -0.1370 0.445521
3519 -0.1826 0.427537
3528 0.2283 0.590298
Square side=100, avg. no. parked=3521.30 sample std.=14.98
p-value of the KSTEST for those 10 p-values: 0.683912
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_16:31
0.8260,0.0317,0.7269,0.4077,0.8384,0.8308,0.3391,0.5284,0.2729,0.1808,
The KS test for those 10 p-values: 0.943652
The 3DSPHERES test for dh-ranFile-2018-07-04_16:31
sample no r^3 equiv. uni.
1 34.811 0.686627
2 22.199 0.522875
3 10.890 0.304405
4 42.093 0.754165
5 6.234 0.187624
6 6.052 0.182684
7 52.486 0.826144
8 7.236 0.214303
9 10.817 0.302708
10 17.716 0.445968
11 0.488 0.016149
12 0.774 0.025472
13 44.400 0.772362
14 29.841 0.630164
15 5.797 0.175703
16 91.912 0.953287
17 39.000 0.727466
18 35.053 0.689147
19 20.407 0.493499
20 35.037 0.688983
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.815327
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.9 -0.4 -0.7 -1.7 0.1
-0.5 0.1 0.8 -2.2 1.2 -0.5
0.8 -0.1 -0.9 0.8 0.7 0.1
-0.7 0.4 0.2 0.6 -0.9 0.1
0.6 -0.8 -0.0 0.5 -0.3 -1.5
-0.9 -1.0 1.1 0.3 1.2 -0.5
0.5 0.8 1.7 -1.3 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:31.992745
z-score=-1.091881, p-value=0.131629
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_16:31
Test no p-value
1 0.810895
2 0.758340
3 0.045948
4 0.837825
5 0.621413
6 0.664499
7 0.376220
8 0.163359
9 0.841586
10 0.001601
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.407648
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_16:31:
(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 66513 0.35 66868 0.61
3 25000.00 25057 0.13 24897 0.42
4 6666.67 6726 0.53 6608 0.52
5 1388.89 1414 0.45 1354 0.88
6 238.10 245 0.20 229 0.35
7 34.72 35 0.00 39 0.53
8 4.96 9 3.29 4 0.19
p=0.45096 p=0.25417
Number of rngs required: 687501, p-value: 0.148
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_16:31
No. of wins: Observed Expected
98442 98585.9
z-score=-0.643, pvalue=0.25998
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66758 66666.7 0.125 0.125
2 37594 37654.3 0.097 0.222
3 27012 26954.7 0.122 0.343
4 19245 19313.5 0.243 0.586
5 13811 13851.4 0.118 0.704
6 9970 9943.5 0.070 0.774
7 7162 7145.0 0.040 0.815
8 5109 5139.1 0.176 0.991
9 3786 3699.9 2.005 2.996
10 2692 2666.3 0.248 3.244
11 1904 1923.3 0.194 3.438
12 1378 1388.7 0.083 3.521
13 996 1003.7 0.059 3.580
14 707 726.1 0.505 4.085
15 550 525.8 1.110 5.195
16 353 381.2 2.079 7.275
17 272 276.5 0.075 7.349
18 167 200.8 5.699 13.048
19 140 146.0 0.245 13.293
20 123 106.2 2.652 15.945
21 271 287.1 0.904 16.850
Chisq= 16.85 for 20 degrees of freedom, p= 0.33730
SUMMARY of craptest
p-value for no. of wins: 0.259976
p-value for throws/game: 0.337297
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_16:31
No. of wins: Observed Expected
98784 98585.9
z-score= 0.886, pvalue=0.81225
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66877 66666.7 0.664 0.664
2 37636 37654.3 0.009 0.673
3 26769 26954.7 1.280 1.952
4 19262 19313.5 0.137 2.089
5 13924 13851.4 0.380 2.470
6 9900 9943.5 0.191 2.660
7 7017 7145.0 2.294 4.954
8 5180 5139.1 0.326 5.280
9 3725 3699.9 0.171 5.451
10 2744 2666.3 2.264 7.716
11 1991 1923.3 2.381 10.097
12 1312 1388.7 4.241 14.337
13 1009 1003.7 0.028 14.365
14 731 726.1 0.033 14.397
15 554 525.8 1.508 15.906
16 439 381.2 8.780 24.686
17 257 276.5 1.381 26.067
18 169 200.8 5.045 31.111
19 118 146.0 5.364 36.476
20 103 106.2 0.097 36.573
21 283 287.1 0.059 36.632
Chisq= 36.63 for 20 degrees of freedom, p= 0.98705
SUMMARY of craptest
p-value for no. of wins: 0.812246
p-value for throws/game: 0.987052
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0031,0.0031,0.0156,0.0161,0.0173,0.0189,0.0206,0.0255,0.0315,
0.0317,0.0323,0.0362,0.0398,0.0423,0.0449,0.0459,0.0472,0.0576,0.0665,
0.0757,0.0762,0.0766,0.0768,0.0778,0.0872,0.0927,0.0940,0.1085,0.1092,
0.1245,0.1267,0.1316,0.1324,0.1337,0.1452,0.1478,0.1634,0.1650,0.1730,
0.1757,0.1804,0.1808,0.1827,0.1869,0.1876,0.1888,0.1960,0.2024,0.2036,
0.2037,0.2050,0.2072,0.2136,0.2143,0.2268,0.2268,0.2317,0.2447,0.2475,
0.2540,0.2542,0.2557,0.2600,0.2600,0.2613,0.2622,0.2704,0.2729,0.2761,
0.2793,0.2819,0.2843,0.2849,0.2898,0.2919,0.2961,0.2984,0.3027,0.3044,
0.3064,0.3075,0.3089,0.3124,0.3173,0.3303,0.3313,0.3373,0.3391,0.3419,
0.3487,0.3546,0.3553,0.3762,0.3766,0.3844,0.3904,0.4002,0.4016,0.4055,
0.4076,0.4077,0.4090,0.4113,0.4177,0.4217,0.4247,0.4271,0.4275,0.4277,
0.4318,0.4357,0.4363,0.4416,0.4455,0.4460,0.4468,0.4491,0.4510,0.4522,
0.4533,0.4601,0.4636,0.4652,0.4677,0.4737,0.4818,0.4843,0.4926,0.4935,
0.4950,0.4987,0.4988,0.5009,0.5048,0.5150,0.5165,0.5196,0.5229,0.5257,
0.5284,0.5341,0.5391,0.5558,0.5562,0.5575,0.5675,0.5682,0.5692,0.5740,
0.5837,0.5856,0.5903,0.5947,0.5955,0.5963,0.5984,0.6032,0.6064,0.6214,
0.6257,0.6257,0.6259,0.6302,0.6414,0.6422,0.6480,0.6522,0.6566,0.6587,
0.6588,0.6645,0.6674,0.6701,0.6739,0.6780,0.6780,0.6787,0.6796,0.6814,
0.6839,0.6854,0.6866,0.6890,0.6891,0.6898,0.6964,0.7011,0.7081,0.7122,
0.7131,0.7154,0.7162,0.7177,0.7191,0.7220,0.7254,0.7269,0.7274,0.7275,
0.7299,0.7311,0.7351,0.7378,0.7387,0.7513,0.7515,0.7542,0.7566,0.7572,
0.7583,0.7621,0.7724,0.7725,0.7728,0.7748,0.7806,0.7842,0.7943,0.7965,
0.8005,0.8030,0.8052,0.8109,0.8122,0.8148,0.8153,0.8161,0.8178,0.8206,
0.8260,0.8261,0.8308,0.8378,0.8384,0.8416,0.8457,0.8527,0.8541,0.8550,
0.8572,0.8685,0.8766,0.8815,0.8834,0.8865,0.8886,0.8961,0.9017,0.9034,
0.9048,0.9073,0.9135,0.9348,0.9398,0.9431,0.9437,0.9494,0.9533,0.9537,
0.9539,0.9683,0.9816,0.9838,0.9871,0.9888,0.9908,0.9912,0.9959,
Overall p-value after applying KStest on 269 p-values = 0.609603
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.