RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-09-09_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.65 13.3963 0.290722
2 to 25 15.72 13.1780 0.275811
3 to 26 15.62 19.5144 0.700181
4 to 27 15.81 8.8812 0.056084
5 to 28 15.99 11.9124 0.194590
6 to 29 16.05 12.1336 0.208018
7 to 30 15.86 17.7851 0.597485
8 to 31 15.81 24.5058 0.893669
9 to 32 15.90 18.5056 0.642361
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.721951
Tough bday spacings test for dh-ranFile-2017-09-09_05:31: 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 13 34 74 114 97 77 44 24 14 8 1
(O-E)^2/E 1.6 0.2 0.0 2.7 0.0 0.0 1.3 1.1 0.1 0.3 2.3
Birthday Spacings: Sum(O-E)^2/E= 9.587, p= 0.523
RESULTS OF GCD FOR dh-ranFile-2017-09-09_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.483373
p-value, dist. of gcd's: 0.665601
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-09-09_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.756 0.592 0.850 0.800 0.807 0.076 0.817 0.679
Bits 8 to 15---> 0.287 0.123 0.135 0.814 0.912 0.729 0.681 0.978
Bits 16 to 23---> 0.718 0.186 0.097 0.898 0.956 0.359 0.992 0.322
Bits 24 to 31---> 0.827 0.711 0.873 0.610 0.447 0.856 0.536 0.103
KS test for the above 32 p values: 0.969
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-09-09_05:31,
p-values for 5 runs: 0.7666, 0.1588, 0.1794, 0.5583, 0.0487
Rank test for binary matrices (31x31) for dh-ranFile-2017-09-09_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5245 5134.0 2.399 2.660
r= 30 23152 23103.0 0.104 2.763
r= 31 11399 11551.5 2.014 4.777
chi-square = 4.777 with df = 3; p-value = 0.811
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-09-09_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5112 5134.0 0.094 0.299
r= 31 23074 23103.0 0.037 0.336
r= 32 11596 11551.5 0.171 0.507
chi-square = 0.507 with df = 3; p-value = 0.083
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-09-09_05:31
b-rank test for bits 1 to 8, p=0.59628
b-rank test for bits 2 to 9, p=0.24805
b-rank test for bits 3 to 10, p=0.58189
b-rank test for bits 4 to 11, p=0.14002
b-rank test for bits 5 to 12, p=0.20855
b-rank test for bits 6 to 13, p=0.81391
b-rank test for bits 7 to 14, p=0.51129
b-rank test for bits 8 to 15, p=0.93094
b-rank test for bits 9 to 16, p=0.59133
b-rank test for bits 10 to 17, p=0.80340
b-rank test for bits 11 to 18, p=0.35623
b-rank test for bits 12 to 19, p=0.47446
b-rank test for bits 13 to 20, p=0.46044
b-rank test for bits 14 to 21, p=0.42474
b-rank test for bits 15 to 22, p=0.61717
b-rank test for bits 16 to 23, p=0.74785
b-rank test for bits 17 to 24, p=0.75243
b-rank test for bits 18 to 25, p=0.72757
b-rank test for bits 19 to 26, p=0.97828
b-rank test for bits 20 to 27, p=0.10055
b-rank test for bits 21 to 28, p=0.26972
b-rank test for bits 22 to 29, p=0.86256
b-rank test for bits 23 to 30, p=0.99692
b-rank test for bits 24 to 31, p=0.27530
b-rank test for bits 25 to 32, p=0.68212
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 = 0.396689
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-09-09_05:31
(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 142504 1.39 0.917647
2 141934 0.06 0.522982
3 142575 1.56 0.940063
4 142838 2.17 0.984989
5 142164 0.60 0.724086
6 141981 0.17 0.566493
7 142211 0.70 0.759544
8 141730 -0.42 0.337610
9 141977 0.16 0.562814
10 141464 -1.04 0.149056
11 142081 0.40 0.655826
12 141846 -0.15 0.441184
13 141168 -1.73 0.041630
14 141895 -0.03 0.486645
15 142345 1.02 0.845642
16 140980 -2.17 0.014953
17 141662 -0.58 0.281675
18 140978 -2.18 0.014777
19 142261 0.82 0.794364
20 141770 -0.33 0.372387
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-09-09_05:31
Bits used No. missing words z-score p-value
23 to 32 142065 0.5368 0.704295
22 to 31 141801 -0.3736 0.354369
21 to 30 141883 -0.0908 0.463829
20 to 29 142190 0.9678 0.833435
19 to 28 141672 -0.8184 0.206570
18 to 27 142002 0.3196 0.625346
17 to 26 142183 0.9437 0.827336
16 to 25 141863 -0.1598 0.436536
15 to 24 142031 0.4196 0.662594
14 to 23 141969 0.2058 0.581510
13 to 22 142089 0.6196 0.732224
12 to 21 141431 -1.6494 0.049531
11 to 20 141276 -2.1839 0.014485
10 to 19 142016 0.3678 0.643499
9 to 18 141782 -0.4391 0.330306
8 to 17 142479 1.9644 0.975257
7 to 16 142128 0.7540 0.774586
6 to 15 141705 -0.7046 0.240534
5 to 14 141909 -0.0011 0.499546
4 to 13 141536 -1.2873 0.098987
3 to 12 141541 -1.2701 0.102024
2 to 11 141932 0.0782 0.531155
1 to 10 141951 0.1437 0.557127
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-09-09_05:31
Bits used No. missing words z-score p-value
28 to 32 141795 -0.3876 0.349171
27 to 31 141944 0.1175 0.546778
26 to 30 141911 0.0057 0.502258
25 to 29 141995 0.2904 0.614248
24 to 28 141855 -0.1842 0.426940
23 to 27 141697 -0.7198 0.235836
22 to 26 141774 -0.4587 0.323208
21 to 25 141808 -0.3435 0.365614
20 to 24 142059 0.5074 0.694048
19 to 23 141873 -0.1232 0.450993
18 to 22 141804 -0.3571 0.360527
17 to 21 141547 -1.2282 0.109679
16 to 20 141514 -1.3401 0.090106
15 to 19 142232 1.0938 0.862978
14 to 18 141840 -0.2350 0.407098
13 to 17 141888 -0.0723 0.471180
12 to 16 141765 -0.4893 0.312331
11 to 15 141889 -0.0689 0.472529
10 to 14 142098 0.6396 0.738770
9 to 13 141249 -2.2384 0.012597
8 to 12 141638 -0.9198 0.178848
7 to 11 141209 -2.3740 0.008798
6 to 10 141904 -0.0181 0.492792
5 to 9 141496 -1.4011 0.080589
4 to 8 141641 -0.9096 0.181519
3 to 7 141768 -0.4791 0.315939
2 to 6 142160 0.8497 0.802262
1 to 5 141942 0.1107 0.544091
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-09-09_05:31
Bits used No. missing words z-score p-value
31 to 32 141740 -0.4995 0.308714
30 to 31 141753 -0.4612 0.322345
29 to 30 141837 -0.2134 0.415522
28 to 29 141637 -0.8033 0.210891
27 to 28 141212 -2.0570 0.019842
26 to 27 142178 0.7925 0.785976
25 to 26 141521 -1.1455 0.125998
24 to 25 141848 -0.1809 0.428217
23 to 24 141770 -0.4110 0.340535
22 to 23 142370 1.3589 0.912912
21 to 22 142448 1.5890 0.943969
20 to 21 141875 -0.1013 0.459669
19 to 20 141674 -0.6942 0.243782
18 to 19 142391 1.4209 0.922321
17 to 18 142631 2.1288 0.983365
16 to 17 142697 2.3235 0.989924
15 to 16 142216 0.9046 0.817170
14 to 15 142121 0.6244 0.733816
13 to 14 141983 0.2173 0.586019
12 to 13 141801 -0.3196 0.374652
11 to 12 141637 -0.8033 0.210891
10 to 11 142147 0.7011 0.758377
9 to 10 142414 1.4887 0.931717
8 to 9 142141 0.6834 0.752821
7 to 8 142037 0.3766 0.646767
6 to 7 141989 0.2350 0.592901
5 to 6 141857 -0.1544 0.438661
4 to 5 141970 0.1790 0.571018
3 to 4 141574 -0.9892 0.161289
2 to 3 142305 1.1672 0.878429
1 to 2 142285 1.1082 0.866106
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-09-09_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2650.50 2.128 0.983345
Test results for specific bytes for dh-ranFile-2017-09-09_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2425.75 -1.050 0.146848
2 to 9 2489.47 -0.149 0.440820
3 to 10 2494.84 -0.073 0.470921
4 to 11 2507.55 0.107 0.542535
5 to 12 2485.52 -0.205 0.418857
6 to 13 2494.53 -0.077 0.469176
7 to 14 2517.25 0.244 0.596386
8 to 15 2502.54 0.036 0.514328
9 to 16 2407.84 -1.303 0.096232
10 to 17 2507.06 0.100 0.539780
11 to 18 2559.10 0.836 0.798356
12 to 19 2407.80 -1.304 0.096141
13 to 20 2414.74 -1.206 0.113960
14 to 21 2483.95 -0.227 0.410228
15 to 22 2411.97 -1.245 0.106586
16 to 23 2536.04 0.510 0.694873
17 to 24 2506.34 0.090 0.535739
18 to 25 2584.28 1.192 0.883348
19 to 26 2515.55 0.220 0.587008
20 to 27 2605.10 1.486 0.931401
21 to 28 2501.36 0.019 0.507683
22 to 29 2348.40 -2.144 0.016016
23 to 30 2634.09 1.896 0.971042
24 to 31 2367.58 -1.873 0.030558
25 to 32 2557.34 0.811 0.791274
CDPARK for dh-ranFile-2017-09-09_05:31: 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
3518 -0.2283 0.409702
3564 1.8721 0.969407
3570 2.1461 0.984068
3510 -0.5936 0.276387
3531 0.3653 0.642555
3536 0.5936 0.723613
3562 1.7808 0.962529
3494 -1.3242 0.092718
3505 -0.8219 0.205562
3516 -0.3196 0.374623
Square side=100, avg. no. parked=3530.60 sample std.=25.44
p-value of the KSTEST for those 10 p-values: 0.321016
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-09-09_05:31
0.1840,0.8857,0.3170,0.2605,0.1509,0.7703,0.6100,0.8585,0.6997,0.3150,
The KS test for those 10 p-values: 0.895923
The 3DSPHERES test for dh-ranFile-2017-09-09_05:31
sample no r^3 equiv. uni.
1 1.853 0.059902
2 12.529 0.341398
3 6.104 0.184094
4 7.340 0.217046
5 77.717 0.925022
6 20.845 0.500850
7 6.457 0.193645
8 14.115 0.375310
9 37.204 0.710659
10 28.663 0.615353
11 59.426 0.862051
12 3.743 0.117310
13 10.022 0.284002
14 30.427 0.637318
15 1.499 0.048725
16 3.933 0.122884
17 31.515 0.650233
18 44.266 0.771345
19 27.047 0.594069
20 6.160 0.185620
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.355388
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-09-09_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.7 -0.3 -2.5 0.3 -0.6 2.0
1.0 -0.6 -0.2 -1.9 -0.4 -1.6
0.1 0.8 -1.3 -0.7 -1.0 1.9
-0.7 0.6 0.8 -0.0 -0.1 0.2
1.2 1.6 -1.3 0.2 0.5 0.5
2.2 -0.2 0.1 -1.0 1.0 1.0
0.5 -0.7 -0.4 -0.7 -1.3 1.0
-0.1
Chi-square with 42 degrees of freedom:53.459300
z-score=1.250312, p-value=0.889363
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-09-09_05:31
Test no p-value
1 0.009458
2 0.076666
3 0.792196
4 0.607009
5 0.006742
6 0.176030
7 0.202160
8 0.548123
9 0.053836
10 0.650030
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.019072
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-09-09_05:31:
(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 66811 0.31 66764 0.14
3 25000.00 24711 3.34 24822 1.27
4 6666.67 6789 2.24 6720 0.43
5 1388.89 1387 0.00 1419 0.65
6 238.10 258 1.66 241 0.04
7 34.72 37 0.15 31 0.40
8 4.96 6 0.22 2 1.77
p=0.75690 p=0.41576
Number of rngs required: 687899, p-value: 0.281
RESULTS OF CRAPS TEST for dh-ranFile-2017-09-09_05:31
No. of wins: Observed Expected
98455 98585.9
z-score=-0.585, pvalue=0.27918
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66718 66666.7 0.040 0.040
2 37746 37654.3 0.223 0.263
3 26955 26954.7 0.000 0.263
4 19273 19313.5 0.085 0.348
5 13903 13851.4 0.192 0.540
6 9944 9943.5 0.000 0.540
7 7186 7145.0 0.235 0.775
8 5081 5139.1 0.656 1.431
9 3677 3699.9 0.141 1.572
10 2614 2666.3 1.026 2.598
11 1887 1923.3 0.686 3.284
12 1369 1388.7 0.281 3.565
13 1018 1003.7 0.203 3.768
14 717 726.1 0.115 3.883
15 499 525.8 1.370 5.253
16 388 381.2 0.123 5.376
17 289 276.5 0.561 5.937
18 203 200.8 0.023 5.961
19 136 146.0 0.683 6.643
20 115 106.2 0.727 7.370
21 282 287.1 0.091 7.461
Chisq= 7.46 for 20 degrees of freedom, p= 0.00512
SUMMARY of craptest
p-value for no. of wins: 0.279181
p-value for throws/game: 0.005125
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-09-09_05:31
No. of wins: Observed Expected
98249 98585.9
z-score=-1.507, pvalue=0.06595
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66552 66666.7 0.197 0.197
2 37556 37654.3 0.257 0.454
3 26885 26954.7 0.180 0.634
4 19383 19313.5 0.250 0.885
5 13893 13851.4 0.125 1.010
6 9962 9943.5 0.034 1.044
7 7259 7145.0 1.818 2.862
8 5143 5139.1 0.003 2.865
9 3635 3699.9 1.137 4.002
10 2736 2666.3 1.822 5.824
11 1955 1923.3 0.522 6.346
12 1363 1388.7 0.477 6.823
13 1021 1003.7 0.298 7.121
14 755 726.1 1.147 8.267
15 518 525.8 0.117 8.384
16 385 381.2 0.039 8.423
17 274 276.5 0.023 8.446
18 201 200.8 0.000 8.447
19 137 146.0 0.553 9.000
20 99 106.2 0.490 9.490
21 288 287.1 0.003 9.492
Chisq= 9.49 for 20 degrees of freedom, p= 0.02353
SUMMARY of craptest
p-value for no. of wins: 0.065953
p-value for throws/game: 0.023529
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0051,0.0067,0.0088,0.0095,0.0126,0.0145,0.0148,0.0150,0.0160,0.0191,
0.0198,0.0235,0.0306,0.0416,0.0487,0.0487,0.0495,0.0538,0.0561,0.0599,
0.0660,0.0757,0.0767,0.0806,0.0827,0.0901,0.0927,0.0961,0.0962,0.0974,
0.0990,0.1005,0.1020,0.1030,0.1066,0.1097,0.1140,0.1173,0.1228,0.1229,
0.1260,0.1354,0.1400,0.1468,0.1491,0.1509,0.1588,0.1613,0.1760,0.1788,
0.1794,0.1815,0.1840,0.1841,0.1856,0.1856,0.1936,0.1946,0.2022,0.2056,
0.2066,0.2080,0.2086,0.2109,0.2109,0.2170,0.2358,0.2405,0.2438,0.2480,
0.2605,0.2697,0.2753,0.2758,0.2764,0.2792,0.2806,0.2817,0.2840,0.2868,
0.2907,0.3087,0.3123,0.3150,0.3159,0.3170,0.3210,0.3216,0.3223,0.3232,
0.3303,0.3376,0.3405,0.3414,0.3492,0.3544,0.3554,0.3562,0.3592,0.3605,
0.3656,0.3724,0.3746,0.3747,0.3753,0.3967,0.4071,0.4097,0.4102,0.4155,
0.4158,0.4189,0.4247,0.4269,0.4282,0.4365,0.4387,0.4408,0.4412,0.4468,
0.4510,0.4597,0.4604,0.4638,0.4692,0.4709,0.4712,0.4725,0.4745,0.4834,
0.4866,0.4928,0.4995,0.5009,0.5023,0.5077,0.5113,0.5143,0.5226,0.5230,
0.5312,0.5357,0.5360,0.5398,0.5425,0.5441,0.5468,0.5481,0.5571,0.5583,
0.5628,0.5665,0.5710,0.5815,0.5819,0.5860,0.5870,0.5913,0.5919,0.5929,
0.5941,0.5963,0.5964,0.5975,0.6070,0.6096,0.6100,0.6142,0.6154,0.6172,
0.6253,0.6373,0.6424,0.6426,0.6435,0.6468,0.6500,0.6502,0.6558,0.6626,
0.6656,0.6790,0.6808,0.6821,0.6940,0.6949,0.6997,0.7002,0.7043,0.7105,
0.7107,0.7181,0.7220,0.7236,0.7241,0.7276,0.7292,0.7322,0.7338,0.7388,
0.7478,0.7524,0.7528,0.7562,0.7569,0.7584,0.7595,0.7666,0.7703,0.7713,
0.7746,0.7860,0.7913,0.7922,0.7944,0.7984,0.7996,0.8023,0.8034,0.8073,
0.8112,0.8139,0.8142,0.8172,0.8172,0.8273,0.8275,0.8334,0.8456,0.8500,
0.8560,0.8585,0.8621,0.8626,0.8630,0.8661,0.8731,0.8784,0.8833,0.8857,
0.8894,0.8937,0.8959,0.8978,0.9121,0.9129,0.9176,0.9223,0.9250,0.9309,
0.9314,0.9317,0.9401,0.9440,0.9561,0.9625,0.9692,0.9694,0.9710,0.9753,
0.9782,0.9783,0.9833,0.9834,0.9841,0.9850,0.9899,0.9916,0.9969,
Overall p-value after applying KStest on 269 p-values = 0.953044
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.