RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.78 25.6762 0.919434
2 to 25 15.84 20.3511 0.743333
3 to 26 15.67 20.3981 0.745625
4 to 27 15.69 24.6298 0.896692
5 to 28 15.84 24.0387 0.881611
6 to 29 15.90 16.0830 0.482043
7 to 30 15.65 19.4508 0.696721
8 to 31 15.87 20.4430 0.747800
9 to 32 15.85 18.4412 0.638466
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.010686
Tough bday spacings test for dh-ranFile-2018-06-21_21:31: 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 12 41 78 82 104 70 48 38 17 5 5
(O-E)^2/E 0.9 0.5 0.3 2.5 0.4 0.8 0.3 2.3 0.3 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 8.992, p= 0.467
RESULTS OF GCD FOR dh-ranFile-2018-06-21_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.792173
p-value, dist. of gcd's: 0.138107
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.674 0.525 0.813 0.667 0.764 0.870 0.680 0.542
Bits 8 to 15---> 0.270 0.175 0.348 0.707 0.526 0.075 0.265 0.579
Bits 16 to 23---> 0.963 0.899 0.863 0.707 0.569 0.255 0.748 0.819
Bits 24 to 31---> 0.155 0.619 0.556 0.103 0.087 0.310 0.418 0.118
KS test for the above 32 p values: 0.254
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_21:31,
p-values for 5 runs: 0.4338, 0.8370, 0.4672, 0.6731, 0.7532
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5097 5134.0 0.267 1.016
r= 30 23234 23103.0 0.742 1.758
r= 31 11445 11551.5 0.982 2.740
chi-square = 2.740 with df = 3; p-value = 0.567
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5136 5134.0 0.001 1.973
r= 31 23131 23103.0 0.034 2.006
r= 32 11542 11551.5 0.008 2.014
chi-square = 2.014 with df = 3; p-value = 0.431
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_21:31
b-rank test for bits 1 to 8, p=0.06603
b-rank test for bits 2 to 9, p=0.76422
b-rank test for bits 3 to 10, p=0.19701
b-rank test for bits 4 to 11, p=0.48033
b-rank test for bits 5 to 12, p=0.87903
b-rank test for bits 6 to 13, p=0.80855
b-rank test for bits 7 to 14, p=0.82336
b-rank test for bits 8 to 15, p=0.52909
b-rank test for bits 9 to 16, p=0.47685
b-rank test for bits 10 to 17, p=0.92860
b-rank test for bits 11 to 18, p=0.69630
b-rank test for bits 12 to 19, p=0.37641
b-rank test for bits 13 to 20, p=0.57162
b-rank test for bits 14 to 21, p=0.39525
b-rank test for bits 15 to 22, p=0.74589
b-rank test for bits 16 to 23, p=0.10578
b-rank test for bits 17 to 24, p=0.62721
b-rank test for bits 18 to 25, p=0.96030
b-rank test for bits 19 to 26, p=0.90699
b-rank test for bits 20 to 27, p=0.37618
b-rank test for bits 21 to 28, p=0.09681
b-rank test for bits 22 to 29, p=0.23049
b-rank test for bits 23 to 30, p=0.69650
b-rank test for bits 24 to 31, p=0.44742
b-rank test for bits 25 to 32, p=0.62048
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 = 0.649660
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_21:31
(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 141860 -0.12 0.454121
2 141584 -0.76 0.223592
3 141621 -0.67 0.250261
4 141645 -0.62 0.268422
5 141714 -0.46 0.324059
6 141538 -0.87 0.192808
7 141520 -0.91 0.181504
8 142016 0.25 0.598408
9 141865 -0.10 0.458753
10 141651 -0.60 0.273063
11 141525 -0.90 0.184602
12 141857 -0.12 0.451344
13 141973 0.15 0.559129
14 142204 0.69 0.754425
15 141842 -0.16 0.437499
16 141657 -0.59 0.277744
17 142100 0.45 0.672017
18 141160 -1.75 0.039993
19 141572 -0.79 0.215303
20 142153 0.57 0.715431
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_21:31
Bits used No. missing words z-score p-value
23 to 32 141962 0.1816 0.572060
22 to 31 142010 0.3471 0.635756
21 to 30 142318 1.4092 0.920613
20 to 29 142018 0.3747 0.646067
19 to 28 141770 -0.4804 0.315454
18 to 27 142426 1.7816 0.962594
17 to 26 142325 1.4333 0.924120
16 to 25 142244 1.1540 0.875757
15 to 24 142008 0.3402 0.633163
14 to 23 142210 1.0368 0.850084
13 to 22 141736 -0.5977 0.275024
12 to 21 141893 -0.0563 0.477547
11 to 20 142240 1.1402 0.872907
10 to 19 142135 0.7782 0.781766
9 to 18 141923 0.0471 0.518798
8 to 17 142098 0.6506 0.742343
7 to 16 141725 -0.6356 0.262512
6 to 15 142441 1.8333 0.966624
5 to 14 142263 1.2196 0.888683
4 to 13 142067 0.5437 0.706673
3 to 12 142164 0.8782 0.810075
2 to 11 142031 0.4196 0.662594
1 to 10 142121 0.7299 0.767273
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_21:31
Bits used No. missing words z-score p-value
28 to 32 141681 -0.7740 0.219465
27 to 31 141856 -0.1808 0.428270
26 to 30 141903 -0.0215 0.491440
25 to 29 141300 -2.0655 0.019437
24 to 28 141733 -0.5977 0.275010
23 to 27 141819 -0.3062 0.379725
22 to 26 141905 -0.0147 0.494145
21 to 25 141705 -0.6926 0.244267
20 to 24 142441 1.8023 0.964249
19 to 23 141903 -0.0215 0.491440
18 to 22 142168 0.8768 0.809715
17 to 21 142028 0.4023 0.656258
16 to 20 141823 -0.2926 0.384897
15 to 19 142049 0.4735 0.682057
14 to 18 142253 1.1650 0.877987
13 to 17 141609 -1.0181 0.154323
12 to 16 141716 -0.6554 0.256119
11 to 15 142691 2.6497 0.995972
10 to 14 141828 -0.2757 0.391391
9 to 13 142175 0.9006 0.816093
8 to 12 141882 -0.0926 0.463093
7 to 11 141554 -1.2045 0.114197
6 to 10 141583 -1.1062 0.134319
5 to 9 141581 -1.1130 0.132858
4 to 8 141556 -1.1977 0.115511
3 to 7 141613 -1.0045 0.157567
2 to 6 141904 -0.0181 0.492792
1 to 5 142065 0.5277 0.701145
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_21:31
Bits used No. missing words z-score p-value
31 to 32 141680 -0.6765 0.249365
30 to 31 141791 -0.3491 0.363524
29 to 30 141819 -0.2665 0.394942
28 to 29 142139 0.6775 0.750953
27 to 28 141794 -0.3402 0.366851
26 to 27 141816 -0.2753 0.391539
25 to 26 142674 2.2557 0.987954
24 to 25 141485 -1.2517 0.105338
23 to 24 141896 -0.0393 0.484317
22 to 23 141891 -0.0541 0.478439
21 to 22 140990 -2.7119 0.003345
20 to 21 141712 -0.5821 0.280252
19 to 20 141954 0.1318 0.552417
18 to 19 142236 0.9636 0.832384
17 to 18 141475 -1.2812 0.100060
16 to 17 141880 -0.0865 0.465527
15 to 16 141754 -0.4582 0.323404
14 to 15 142131 0.6539 0.743410
13 to 14 142179 0.7955 0.786835
12 to 13 141589 -0.9449 0.172348
11 to 12 142138 0.6745 0.750017
10 to 11 142177 0.7896 0.785116
9 to 10 141718 -0.5644 0.286243
8 to 9 141910 0.0020 0.500789
7 to 8 142110 0.5919 0.723057
6 to 7 141744 -0.4877 0.312882
5 to 6 142383 1.3973 0.918832
4 to 5 141816 -0.2753 0.391539
3 to 4 142223 0.9253 0.822590
2 to 3 142705 2.3471 0.990540
1 to 2 141313 -1.7591 0.039282
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2350.23 -2.118 0.017086
Test results for specific bytes for dh-ranFile-2018-06-21_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2475.67 -0.344 0.365384
2 to 9 2335.95 -2.320 0.010171
3 to 10 2562.22 0.880 0.810531
4 to 11 2413.82 -1.219 0.111461
5 to 12 2571.57 1.012 0.844259
6 to 13 2594.09 1.331 0.908344
7 to 14 2505.48 0.077 0.530867
8 to 15 2391.25 -1.538 0.062032
9 to 16 2509.46 0.134 0.553208
10 to 17 2474.44 -0.361 0.358877
11 to 18 2520.46 0.289 0.613843
12 to 19 2518.19 0.257 0.601486
13 to 20 2519.81 0.280 0.610345
14 to 21 2494.59 -0.076 0.469535
15 to 22 2430.54 -0.982 0.162957
16 to 23 2361.32 -1.961 0.024925
17 to 24 2549.18 0.695 0.756625
18 to 25 2518.03 0.255 0.600611
19 to 26 2530.42 0.430 0.666481
20 to 27 2484.42 -0.220 0.412779
21 to 28 2414.72 -1.206 0.113889
22 to 29 2551.69 0.731 0.767598
23 to 30 2453.56 -0.657 0.255661
24 to 31 2562.41 0.883 0.811283
25 to 32 2649.51 2.114 0.982758
CDPARK for dh-ranFile-2018-06-21_21:31: 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
3521 -0.0913 0.463617
3578 2.5114 0.993988
3536 0.5936 0.723613
3551 1.2785 0.899470
3585 2.8311 0.997680
3563 1.8265 0.966111
3547 1.0959 0.863437
3526 0.1370 0.554479
3539 0.7306 0.767486
Square side=100, avg. no. parked=3545.60 sample std.=23.08
p-value of the KSTEST for those 10 p-values: 0.003279
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_21:31
0.7612,0.0273,0.4775,0.6698,0.8501,0.8724,0.1004,0.8988,0.1849,0.4079,
The KS test for those 10 p-values: 0.858272
The 3DSPHERES test for dh-ranFile-2018-06-21_21:31
sample no r^3 equiv. uni.
1 12.027 0.330287
2 22.733 0.531285
3 82.340 0.935731
4 29.277 0.623151
5 81.726 0.934401
6 47.029 0.791459
7 5.050 0.154930
8 47.720 0.796214
9 81.890 0.934759
10 1.084 0.035472
11 40.251 0.738595
12 23.481 0.542834
13 11.987 0.329389
14 16.905 0.430787
15 40.473 0.740523
16 0.943 0.030941
17 5.483 0.167040
18 73.169 0.912750
19 31.150 0.645954
20 69.632 0.901830
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.310776
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.2 -0.1 0.6 -0.7 0.3
0.5 -1.7 0.2 1.0 -0.8 0.1
-0.5 0.5 0.6 0.6 -0.4 2.0
1.1 -1.0 -0.3 -0.9 0.2 -1.1
1.0 -1.1 -0.4 -0.5 -0.4 -0.7
-0.4 -1.3 -0.2 0.4 -0.6 -0.7
-0.5 -1.7 1.3 0.4 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:29.379552
z-score=-1.377004, p-value=0.070666
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_21:31
Test no p-value
1 0.700201
2 0.136217
3 0.032621
4 0.867745
5 0.667121
6 0.290981
7 0.712207
8 0.422848
9 0.102828
10 0.149937
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.470691
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_21:31:
(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 66431 0.83 66470 0.58
3 25000.00 25178 1.27 25157 0.99
4 6666.67 6728 0.56 6723 0.48
5 1388.89 1387 0.00 1379 0.07
6 238.10 227 0.52 235 0.04
7 34.72 43 1.97 28 1.30
8 4.96 5 0.00 7 0.84
p=0.47644 p=0.36283
Number of rngs required: 688524, p-value: 0.555
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_21:31
No. of wins: Observed Expected
98693 98585.9
z-score= 0.479, pvalue=0.68410
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66902 66666.7 0.831 0.831
2 37567 37654.3 0.202 1.033
3 27035 26954.7 0.239 1.272
4 19291 19313.5 0.026 1.298
5 13740 13851.4 0.896 2.195
6 9851 9943.5 0.861 3.056
7 7043 7145.0 1.457 4.513
8 5202 5139.1 0.771 5.283
9 3774 3699.9 1.485 6.769
10 2717 2666.3 0.964 7.733
11 1842 1923.3 3.439 11.172
12 1424 1388.7 0.895 12.067
13 970 1003.7 1.132 13.200
14 743 726.1 0.391 13.591
15 504 525.8 0.907 14.498
16 379 381.2 0.012 14.510
17 286 276.5 0.324 14.834
18 221 200.8 2.026 16.859
19 142 146.0 0.109 16.968
20 104 106.2 0.046 17.014
21 263 287.1 2.025 19.040
Chisq= 19.04 for 20 degrees of freedom, p= 0.48075
SUMMARY of craptest
p-value for no. of wins: 0.684101
p-value for throws/game: 0.480752
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_21:31
No. of wins: Observed Expected
98418 98585.9
z-score=-0.751, pvalue=0.22640
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66178 66666.7 3.582 3.582
2 38107 37654.3 5.442 9.024
3 26934 26954.7 0.016 9.040
4 19378 19313.5 0.216 9.256
5 13930 13851.4 0.446 9.701
6 9901 9943.5 0.182 9.883
7 7193 7145.0 0.322 10.206
8 5015 5139.1 2.995 13.201
9 3730 3699.9 0.245 13.446
10 2636 2666.3 0.344 13.791
11 1976 1923.3 1.442 15.233
12 1416 1388.7 0.535 15.768
13 967 1003.7 1.343 17.111
14 723 726.1 0.014 17.125
15 516 525.8 0.184 17.309
16 426 381.2 5.277 22.586
17 278 276.5 0.008 22.594
18 196 200.8 0.116 22.710
19 126 146.0 2.736 25.446
20 93 106.2 1.644 27.090
21 281 287.1 0.130 27.220
Chisq= 27.22 for 20 degrees of freedom, p= 0.87082
SUMMARY of craptest
p-value for no. of wins: 0.226398
p-value for throws/game: 0.870818
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0033,0.0033,0.0102,0.0107,0.0171,0.0194,0.0249,0.0273,0.0309,0.0326,
0.0355,0.0393,0.0400,0.0620,0.0660,0.0707,0.0753,0.0870,0.0968,0.1001,
0.1004,0.1028,0.1028,0.1053,0.1058,0.1115,0.1139,0.1142,0.1155,0.1181,
0.1329,0.1343,0.1362,0.1381,0.1499,0.1543,0.1545,0.1549,0.1576,0.1630,
0.1670,0.1723,0.1748,0.1815,0.1846,0.1849,0.1928,0.1970,0.2153,0.2195,
0.2236,0.2264,0.2305,0.2443,0.2494,0.2503,0.2542,0.2551,0.2557,0.2561,
0.2625,0.2649,0.2684,0.2704,0.2731,0.2750,0.2750,0.2764,0.2777,0.2803,
0.2862,0.2910,0.3103,0.3108,0.3129,0.3155,0.3234,0.3241,0.3294,0.3303,
0.3482,0.3589,0.3628,0.3635,0.3654,0.3669,0.3762,0.3764,0.3797,0.3849,
0.3914,0.3915,0.3915,0.3949,0.3952,0.4079,0.4128,0.4176,0.4228,0.4283,
0.4306,0.4308,0.4338,0.4375,0.4474,0.4513,0.4541,0.4588,0.4631,0.4636,
0.4655,0.4672,0.4672,0.4695,0.4707,0.4764,0.4769,0.4775,0.4775,0.4784,
0.4803,0.4808,0.4820,0.4843,0.4914,0.4914,0.4928,0.4941,0.5008,0.5188,
0.5248,0.5260,0.5291,0.5309,0.5313,0.5421,0.5428,0.5524,0.5532,0.5545,
0.5554,0.5555,0.5591,0.5666,0.5688,0.5716,0.5721,0.5794,0.5984,0.6006,
0.6015,0.6103,0.6138,0.6186,0.6205,0.6232,0.6272,0.6332,0.6358,0.6385,
0.6460,0.6461,0.6497,0.6563,0.6626,0.6665,0.6669,0.6671,0.6698,0.6720,
0.6731,0.6739,0.6800,0.6821,0.6841,0.6963,0.6965,0.6967,0.7002,0.7011,
0.7067,0.7068,0.7072,0.7122,0.7154,0.7231,0.7236,0.7386,0.7405,0.7423,
0.7433,0.7434,0.7456,0.7459,0.7478,0.7480,0.7500,0.7510,0.7532,0.7544,
0.7566,0.7612,0.7641,0.7642,0.7673,0.7675,0.7676,0.7818,0.7851,0.7868,
0.7915,0.7922,0.7962,0.8085,0.8097,0.8101,0.8105,0.8113,0.8130,0.8161,
0.8192,0.8226,0.8234,0.8324,0.8370,0.8443,0.8501,0.8501,0.8583,0.8630,
0.8634,0.8677,0.8698,0.8708,0.8724,0.8729,0.8758,0.8780,0.8790,0.8816,
0.8887,0.8967,0.8987,0.8988,0.8995,0.9018,0.9070,0.9083,0.9127,0.9188,
0.9194,0.9206,0.9241,0.9286,0.9344,0.9348,0.9357,0.9603,0.9626,0.9630,
0.9642,0.9661,0.9666,0.9828,0.9880,0.9905,0.9940,0.9960,0.9977,
Overall p-value after applying KStest on 269 p-values = 0.226252
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.