RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-11-28_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 15.46 21.9642 0.813899
2 to 25 15.62 21.9344 0.812746
3 to 26 15.51 34.5578 0.992892
4 to 27 15.79 19.2861 0.687642
5 to 28 15.82 23.8947 0.877676
6 to 29 15.90 13.8202 0.320213
7 to 30 15.85 17.1659 0.556815
8 to 31 16.03 20.6550 0.757896
9 to 32 15.95 16.5428 0.514268
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.052040
Tough bday spacings test for dh-ranFile-2017-11-28_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 8 36 75 94 106 74 60 33 8 2 4
(O-E)^2/E 0.1 0.0 0.0 0.1 0.7 0.2 1.2 0.4 3.2 3.2 0.0
Birthday Spacings: Sum(O-E)^2/E= 9.220, p= 0.489
RESULTS OF GCD FOR dh-ranFile-2017-11-28_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.577783
p-value, dist. of gcd's: 0.149904
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-11-28_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.121 0.741 0.954 0.774 0.186 0.767 0.321 0.283
Bits 8 to 15---> 0.443 0.858 0.156 0.545 0.428 0.280 0.170 0.639
Bits 16 to 23---> 0.123 0.813 0.220 0.485 0.042 0.222 0.346 0.944
Bits 24 to 31---> 0.060 0.108 0.736 0.394 0.322 0.421 0.323 0.762
KS test for the above 32 p values: 0.694
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-11-28_16:31,
p-values for 5 runs: 0.3743, 0.1223, 0.7764, 0.9117, 0.4899
Rank test for binary matrices (31x31) for dh-ranFile-2017-11-28_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 175 211.4 6.273 6.273
r= 29 5001 5134.0 3.446 9.719
r= 30 23169 23103.0 0.188 9.907
r= 31 11655 11551.5 0.927 10.834
chi-square = 10.834 with df = 3; p-value = 0.987
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-11-28_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 207 211.4 0.092 0.092
r= 30 5003 5134.0 3.343 3.435
r= 31 23162 23103.0 0.150 3.586
r= 32 11628 11551.5 0.506 4.092
chi-square = 4.092 with df = 3; p-value = 0.748
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-11-28_16:31
b-rank test for bits 1 to 8, p=0.14146
b-rank test for bits 2 to 9, p=0.26472
b-rank test for bits 3 to 10, p=0.83938
b-rank test for bits 4 to 11, p=0.72578
b-rank test for bits 5 to 12, p=0.71330
b-rank test for bits 6 to 13, p=0.74948
b-rank test for bits 7 to 14, p=0.10840
b-rank test for bits 8 to 15, p=0.26973
b-rank test for bits 9 to 16, p=0.28333
b-rank test for bits 10 to 17, p=0.28078
b-rank test for bits 11 to 18, p=0.61825
b-rank test for bits 12 to 19, p=0.05452
b-rank test for bits 13 to 20, p=0.31525
b-rank test for bits 14 to 21, p=0.69613
b-rank test for bits 15 to 22, p=0.72743
b-rank test for bits 16 to 23, p=0.57606
b-rank test for bits 17 to 24, p=0.77958
b-rank test for bits 18 to 25, p=0.06745
b-rank test for bits 19 to 26, p=0.65349
b-rank test for bits 20 to 27, p=0.46273
b-rank test for bits 21 to 28, p=0.55983
b-rank test for bits 22 to 29, p=0.39665
b-rank test for bits 23 to 30, p=0.51595
b-rank test for bits 24 to 31, p=0.67403
b-rank test for bits 25 to 32, p=0.88289
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 = 0.602417
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-11-28_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 142142 0.54 0.706649
2 141976 0.16 0.561893
3 142193 0.66 0.746264
4 141384 -1.23 0.109835
5 141572 -0.79 0.215303
6 141442 -1.09 0.137440
7 142501 1.38 0.916577
8 141560 -0.82 0.207195
9 141758 -0.35 0.361829
10 141687 -0.52 0.301719
11 141297 -1.43 0.076261
12 140980 -2.17 0.014953
13 141771 -0.32 0.373272
14 141807 -0.24 0.405518
15 142944 2.42 0.992185
16 142490 1.36 0.912563
17 142201 0.68 0.752214
18 142277 0.86 0.804841
19 141698 -0.49 0.310737
20 141879 -0.07 0.471753
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-11-28_16:31
Bits used No. missing words z-score p-value
23 to 32 142510 2.0713 0.980833
22 to 31 142378 1.6161 0.946964
21 to 30 142028 0.4092 0.658806
20 to 29 141896 -0.0460 0.481669
19 to 28 142180 0.9333 0.824679
18 to 27 141831 -0.2701 0.393540
17 to 26 141705 -0.7046 0.240534
16 to 25 142142 0.8023 0.788813
15 to 24 142433 1.8058 0.964522
14 to 23 141929 0.0678 0.527039
13 to 22 141939 0.1023 0.540745
12 to 21 141878 -0.1080 0.456984
11 to 20 141919 0.0333 0.513300
10 to 19 142095 0.6402 0.738992
9 to 18 141882 -0.0942 0.462459
8 to 17 141381 -1.8218 0.034241
7 to 16 141368 -1.8667 0.030975
6 to 15 142491 2.0058 0.977559
5 to 14 141280 -2.1701 0.015000
4 to 13 141405 -1.7391 0.041011
3 to 12 141306 -2.0804 0.018742
2 to 11 142256 1.1954 0.884037
1 to 10 142405 1.7092 0.956294
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-11-28_16:31
Bits used No. missing words z-score p-value
28 to 32 141891 -0.0621 0.475227
27 to 31 142132 0.7548 0.774820
26 to 30 141332 -1.9571 0.025171
25 to 29 141970 0.2057 0.581472
24 to 28 141595 -1.0655 0.143319
23 to 27 141652 -0.8723 0.191521
22 to 26 142444 1.8124 0.965041
21 to 25 141830 -0.2689 0.393998
20 to 24 141947 0.1277 0.550805
19 to 23 141905 -0.0147 0.494145
18 to 22 142023 0.3853 0.650001
17 to 21 142568 2.2328 0.987218
16 to 20 141648 -0.8859 0.187845
15 to 19 142257 1.1785 0.880710
14 to 18 141979 0.2362 0.593349
13 to 17 142196 0.9718 0.834416
12 to 16 142061 0.5141 0.696421
11 to 15 141847 -0.2113 0.416331
10 to 14 142004 0.3209 0.625863
9 to 13 141550 -1.2181 0.111599
8 to 12 141815 -0.3198 0.374574
7 to 11 142158 0.8429 0.800372
6 to 10 142177 0.9074 0.817891
5 to 9 141715 -0.6587 0.255030
4 to 8 141941 0.1074 0.542747
3 to 7 141355 -1.8791 0.030116
2 to 6 142271 1.2260 0.889901
1 to 5 141936 0.0904 0.536018
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-11-28_16:31
Bits used No. missing words z-score p-value
31 to 32 141442 -1.3786 0.084016
30 to 31 142301 1.1554 0.876030
29 to 30 142265 1.0492 0.852951
28 to 29 141127 -2.3078 0.010506
27 to 28 141820 -0.2635 0.396079
26 to 27 142313 1.1908 0.883127
25 to 26 142002 0.2734 0.607713
24 to 25 142223 0.9253 0.822590
23 to 24 142396 1.4356 0.924443
22 to 23 142107 0.5831 0.720086
21 to 22 141457 -1.3343 0.091052
20 to 21 141999 0.2645 0.604308
19 to 20 141864 -0.1337 0.446813
18 to 19 142009 0.2940 0.615626
17 to 18 141668 -0.7119 0.238267
16 to 17 141964 0.1613 0.564059
15 to 16 142182 0.8043 0.789399
14 to 15 141295 -1.8122 0.034979
13 to 14 141899 -0.0305 0.487845
12 to 13 141653 -0.7561 0.224784
11 to 12 142115 0.6067 0.727974
10 to 11 141844 -0.1927 0.423592
9 to 10 141730 -0.5290 0.298404
8 to 9 141557 -1.0393 0.149328
7 to 8 141925 0.0462 0.518434
6 to 7 141436 -1.3963 0.081319
5 to 6 141499 -1.2104 0.113060
4 to 5 142344 1.2822 0.900116
3 to 4 141457 -1.3343 0.091052
2 to 3 141432 -1.4081 0.079558
1 to 2 141795 -0.3373 0.367962
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-11-28_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2454.32 -0.646 0.259115
Test results for specific bytes for dh-ranFile-2017-11-28_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2505.16 0.073 0.529109
2 to 9 2534.72 0.491 0.688313
3 to 10 2485.01 -0.212 0.416072
4 to 11 2433.97 -0.934 0.175219
5 to 12 2473.94 -0.369 0.356217
6 to 13 2467.17 -0.464 0.321238
7 to 14 2691.53 2.709 0.996622
8 to 15 2420.33 -1.127 0.129942
9 to 16 2525.29 0.358 0.639705
10 to 17 2603.25 1.460 0.927888
11 to 18 2478.94 -0.298 0.382915
12 to 19 2638.68 1.961 0.975072
13 to 20 2545.78 0.647 0.741329
14 to 21 2444.25 -0.788 0.215244
15 to 22 2444.48 -0.785 0.216174
16 to 23 2498.51 -0.021 0.491614
17 to 24 2585.83 1.214 0.887585
18 to 25 2416.30 -1.184 0.118261
19 to 26 2557.85 0.818 0.793364
20 to 27 2529.24 0.414 0.660380
21 to 28 2441.16 -0.832 0.202669
22 to 29 2466.80 -0.470 0.319326
23 to 30 2512.22 0.173 0.568603
24 to 31 2497.44 -0.036 0.485563
25 to 32 2538.70 0.547 0.707904
CDPARK for dh-ranFile-2017-11-28_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
3517 -0.2740 0.392053
3514 -0.4110 0.340551
3493 -1.3699 0.085365
3538 0.6849 0.753306
3535 0.5479 0.708135
3537 0.6393 0.738676
3522 -0.0457 0.481790
3503 -0.9132 0.180558
3529 0.2740 0.607947
3550 1.2329 0.891189
Square side=100, avg. no. parked=3523.80 sample std.=16.56
p-value of the KSTEST for those 10 p-values: 0.951120
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-11-28_16:31
0.0000,0.1951,0.6603,0.3189,0.4989,0.9036,0.5962,0.9230,0.1726,0.1641,
The KS test for those 10 p-values: 0.346690
The 3DSPHERES test for dh-ranFile-2017-11-28_16:31
sample no r^3 equiv. uni.
1 6.408 0.192327
2 29.356 0.624139
3 39.531 0.732249
4 90.786 0.951500
5 29.767 0.629248
6 10.196 0.288143
7 7.494 0.221031
8 3.825 0.119706
9 20.178 0.489625
10 0.732 0.024098
11 10.581 0.297207
12 117.658 0.980197
13 7.114 0.211126
14 22.599 0.529183
15 3.758 0.117751
16 76.058 0.920759
17 19.806 0.483246
18 31.547 0.650614
19 27.497 0.600107
20 16.478 0.422631
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.899545
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-11-28_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 -0.6 -1.0 1.6 0.5
0.1 -0.3 -0.9 0.6 0.5 -0.3
-0.8 0.5 0.0 -0.8 0.5 -1.6
-1.6 -0.7 1.8 3.1 0.6 -0.9
1.2 -0.5 -0.6 -1.4 1.1 1.8
-0.6 -0.9 -1.3 1.6 -0.8 -0.3
0.3 -0.4 0.1 -0.7 0.9 -1.0
2.7
Chi-square with 42 degrees of freedom:52.218627
z-score=1.114944, p-value=0.865847
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-11-28_16:31
Test no p-value
1 0.022613
2 0.010413
3 0.074286
4 0.029768
5 0.381720
6 0.663266
7 0.016257
8 0.178846
9 0.413598
10 0.001452
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000022
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-11-28_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 66734 0.07 66942 1.14
3 25000.00 25032 0.04 24651 4.87
4 6666.67 6603 0.61 6740 0.81
5 1388.89 1352 0.98 1397 0.05
6 238.10 241 0.04 227 0.52
7 34.72 32 0.21 38 0.31
8 4.96 5 0.00 4 0.19
p=0.07538 p=0.75265
Number of rngs required: 687836, p-value: 0.256
RESULTS OF CRAPS TEST for dh-ranFile-2017-11-28_16:31
No. of wins: Observed Expected
98438 98585.9
z-score=-0.661, pvalue=0.25421
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66580 66666.7 0.113 0.113
2 37600 37654.3 0.078 0.191
3 26925 26954.7 0.033 0.224
4 19481 19313.5 1.453 1.677
5 13768 13851.4 0.502 2.180
6 9867 9943.5 0.589 2.769
7 7184 7145.0 0.213 2.981
8 5188 5139.1 0.466 3.447
9 3711 3699.9 0.034 3.481
10 2746 2666.3 2.383 5.863
11 1873 1923.3 1.317 7.180
12 1383 1388.7 0.024 7.204
13 1027 1003.7 0.540 7.744
14 752 726.1 0.921 8.665
15 543 525.8 0.560 9.225
16 387 381.2 0.090 9.315
17 300 276.5 1.990 11.305
18 184 200.8 1.410 12.716
19 136 146.0 0.683 13.399
20 121 106.2 2.058 15.457
21 244 287.1 6.474 21.931
Chisq= 21.93 for 20 degrees of freedom, p= 0.65572
SUMMARY of craptest
p-value for no. of wins: 0.254207
p-value for throws/game: 0.655719
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-11-28_16:31
No. of wins: Observed Expected
98407 98585.9
z-score=-0.800, pvalue=0.21187
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66525 66666.7 0.301 0.301
2 37775 37654.3 0.387 0.688
3 26867 26954.7 0.286 0.973
4 19361 19313.5 0.117 1.090
5 13910 13851.4 0.248 1.338
6 9829 9943.5 1.319 2.658
7 7220 7145.0 0.787 3.444
8 5181 5139.1 0.342 3.786
9 3657 3699.9 0.497 4.283
10 2730 2666.3 1.522 5.805
11 1874 1923.3 1.265 7.070
12 1379 1388.7 0.068 7.138
13 999 1003.7 0.022 7.161
14 742 726.1 0.346 7.507
15 551 525.8 1.204 8.711
16 387 381.2 0.090 8.801
17 269 276.5 0.206 9.007
18 189 200.8 0.697 9.703
19 167 146.0 3.025 12.729
20 116 106.2 0.901 13.630
21 272 287.1 0.796 14.426
Chisq= 14.43 for 20 degrees of freedom, p= 0.19173
SUMMARY of craptest
p-value for no. of wins: 0.211867
p-value for throws/game: 0.191730
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0000,0.0015,0.0104,0.0105,0.0150,0.0150,0.0163,0.0187,0.0226,
0.0241,0.0252,0.0298,0.0301,0.0310,0.0342,0.0350,0.0410,0.0419,0.0520,
0.0545,0.0602,0.0675,0.0743,0.0754,0.0763,0.0796,0.0813,0.0840,0.0854,
0.0911,0.0911,0.1078,0.1084,0.1098,0.1116,0.1131,0.1178,0.1183,0.1197,
0.1210,0.1223,0.1232,0.1299,0.1374,0.1415,0.1433,0.1493,0.1499,0.1559,
0.1641,0.1696,0.1726,0.1752,0.1788,0.1806,0.1856,0.1878,0.1915,0.1917,
0.1923,0.1951,0.2027,0.2072,0.2111,0.2119,0.2152,0.2153,0.2162,0.2199,
0.2210,0.2219,0.2248,0.2383,0.2405,0.2542,0.2550,0.2565,0.2591,0.2647,
0.2697,0.2805,0.2808,0.2833,0.2834,0.2881,0.2972,0.2984,0.3017,0.3107,
0.3153,0.3189,0.3193,0.3202,0.3211,0.3212,0.3218,0.3232,0.3406,0.3458,
0.3467,0.3562,0.3618,0.3680,0.3733,0.3743,0.3746,0.3817,0.3829,0.3921,
0.3935,0.3936,0.3940,0.3961,0.3967,0.4055,0.4136,0.4161,0.4163,0.4213,
0.4226,0.4236,0.4282,0.4429,0.4468,0.4570,0.4625,0.4627,0.4718,0.4752,
0.4817,0.4818,0.4832,0.4846,0.4856,0.4878,0.4887,0.4896,0.4899,0.4916,
0.4941,0.4989,0.5133,0.5143,0.5159,0.5184,0.5270,0.5291,0.5292,0.5360,
0.5407,0.5427,0.5450,0.5508,0.5568,0.5598,0.5619,0.5641,0.5686,0.5761,
0.5778,0.5815,0.5933,0.5962,0.6001,0.6024,0.6043,0.6077,0.6079,0.6156,
0.6182,0.6241,0.6259,0.6292,0.6395,0.6397,0.6500,0.6506,0.6535,0.6557,
0.6588,0.6603,0.6604,0.6633,0.6740,0.6876,0.6883,0.6939,0.6961,0.6964,
0.7066,0.7079,0.7081,0.7133,0.7201,0.7258,0.7274,0.7280,0.7322,0.7363,
0.7387,0.7390,0.7413,0.7413,0.7463,0.7483,0.7495,0.7522,0.7527,0.7533,
0.7579,0.7618,0.7668,0.7743,0.7748,0.7764,0.7796,0.7888,0.7894,0.7934,
0.8004,0.8048,0.8127,0.8129,0.8139,0.8179,0.8226,0.8247,0.8344,0.8394,
0.8530,0.8584,0.8658,0.8760,0.8777,0.8807,0.8829,0.8831,0.8840,0.8876,
0.8899,0.8912,0.8995,0.9001,0.9036,0.9117,0.9126,0.9166,0.9208,0.9230,
0.9244,0.9279,0.9440,0.9470,0.9511,0.9515,0.9535,0.9563,0.9645,0.9650,
0.9751,0.9776,0.9802,0.9808,0.9872,0.9873,0.9922,0.9929,0.9966,
Overall p-value after applying KStest on 269 p-values = 0.449186
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.