RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.96 14.1202 0.341426
2 to 25 15.87 11.4070 0.165359
3 to 26 15.87 13.3205 0.285518
4 to 27 15.94 26.6435 0.936493
5 to 28 15.78 17.5071 0.579446
6 to 29 16.08 24.8812 0.902600
7 to 30 15.40 26.2825 0.930534
8 to 31 15.63 18.2861 0.628987
9 to 32 15.84 19.9712 0.724295
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.392868
Tough bday spacings test for dh-ranFile-2018-06-22_19:31: 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 6 33 81 100 85 80 49 41 11 9 5
(O-E)^2/E 1.1 0.4 0.8 0.1 1.6 0.0 0.2 4.2 1.0 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 10.520, p= 0.604
RESULTS OF GCD FOR dh-ranFile-2018-06-22_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.380636
p-value, dist. of gcd's: 0.722030
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.245 0.895 0.508 0.513 0.027 0.678 0.679 0.271
Bits 8 to 15---> 0.106 0.899 0.909 0.112 0.537 0.954 0.332 0.212
Bits 16 to 23---> 0.441 0.356 0.294 0.107 0.145 0.050 0.879 0.982
Bits 24 to 31---> 0.442 0.792 0.923 0.315 0.448 0.048 0.394 0.680
KS test for the above 32 p values: 0.248
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_19:31,
p-values for 5 runs: 0.4491, 0.7130, 0.1940, 0.3653, 0.5911
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5157 5134.0 0.103 0.131
r= 30 22959 23103.0 0.898 1.029
r= 31 11675 11551.5 1.320 2.349
chi-square = 2.349 with df = 3; p-value = 0.497
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5131 5134.0 0.002 0.062
r= 31 23080 23103.0 0.023 0.085
r= 32 11574 11551.5 0.044 0.129
chi-square = 0.129 with df = 3; p-value = 0.012
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_19:31
b-rank test for bits 1 to 8, p=0.86561
b-rank test for bits 2 to 9, p=0.60632
b-rank test for bits 3 to 10, p=0.21875
b-rank test for bits 4 to 11, p=0.29753
b-rank test for bits 5 to 12, p=0.64992
b-rank test for bits 6 to 13, p=0.88988
b-rank test for bits 7 to 14, p=0.08580
b-rank test for bits 8 to 15, p=0.19930
b-rank test for bits 9 to 16, p=0.95628
b-rank test for bits 10 to 17, p=0.97090
b-rank test for bits 11 to 18, p=0.40876
b-rank test for bits 12 to 19, p=0.43416
b-rank test for bits 13 to 20, p=0.40357
b-rank test for bits 14 to 21, p=0.00161
b-rank test for bits 15 to 22, p=0.03616
b-rank test for bits 16 to 23, p=0.20996
b-rank test for bits 17 to 24, p=0.82370
b-rank test for bits 18 to 25, p=0.66300
b-rank test for bits 19 to 26, p=0.19771
b-rank test for bits 20 to 27, p=0.79964
b-rank test for bits 21 to 28, p=0.95955
b-rank test for bits 22 to 29, p=0.17332
b-rank test for bits 23 to 30, p=0.23403
b-rank test for bits 24 to 31, p=0.51273
b-rank test for bits 25 to 32, p=0.31868
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 = 0.688685
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_19:31
(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 141778 -0.31 0.379480
2 141842 -0.16 0.437499
3 142272 0.85 0.801603
4 142422 1.20 0.884508
5 142720 1.89 0.970893
6 142400 1.15 0.874190
7 142412 1.17 0.879895
8 142135 0.53 0.700996
9 141737 -0.40 0.343607
10 141946 0.09 0.534139
11 141909 -0.00 0.499692
12 142906 2.33 0.990062
13 141202 -1.65 0.049202
14 141959 0.12 0.546194
15 142403 1.15 0.875634
16 142400 1.15 0.874190
17 141836 -0.17 0.431981
18 141824 -0.20 0.420987
19 141880 -0.07 0.472683
20 141645 -0.62 0.268422
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-22_19:31
Bits used No. missing words z-score p-value
23 to 32 141924 0.0506 0.520172
22 to 31 141797 -0.3873 0.349251
21 to 30 142661 2.5920 0.995229
20 to 29 142113 0.7023 0.758757
19 to 28 142533 2.1506 0.984246
18 to 27 141326 -2.0115 0.022137
17 to 26 141686 -0.7701 0.220619
16 to 25 141403 -1.7460 0.040408
15 to 24 141261 -2.2356 0.012688
14 to 23 141809 -0.3460 0.364684
13 to 22 141795 -0.3942 0.346701
12 to 21 142000 0.3127 0.622729
11 to 20 142257 1.1989 0.884709
10 to 19 141140 -2.6529 0.003991
9 to 18 141760 -0.5149 0.303301
8 to 17 142035 0.4333 0.667618
7 to 16 141364 -1.8804 0.030024
6 to 15 141326 -2.0115 0.022137
5 to 14 141686 -0.7701 0.220619
4 to 13 141813 -0.3322 0.369880
3 to 12 142541 2.1782 0.985303
2 to 11 142502 2.0437 0.979508
1 to 10 142074 0.5678 0.714924
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-22_19:31
Bits used No. missing words z-score p-value
28 to 32 141796 -0.3842 0.350426
27 to 31 142038 0.4362 0.668643
26 to 30 141861 -0.1638 0.434932
25 to 29 141909 -0.0011 0.499554
24 to 28 142020 0.3752 0.646227
23 to 27 141743 -0.5638 0.286435
22 to 26 141678 -0.7842 0.216470
21 to 25 142280 1.2565 0.895534
20 to 24 141998 0.3006 0.618131
19 to 23 142046 0.4633 0.678421
18 to 22 141717 -0.6520 0.257212
17 to 21 142126 0.7345 0.768670
16 to 20 142100 0.6463 0.740970
15 to 19 141835 -0.2520 0.400534
14 to 18 142178 0.9107 0.818785
13 to 17 142411 1.7006 0.955489
12 to 16 141297 -2.0757 0.018961
11 to 15 141732 -0.6011 0.273881
10 to 14 142125 0.7311 0.767636
9 to 13 141828 -0.2757 0.391391
8 to 12 141868 -0.1401 0.444290
7 to 11 141646 -0.8926 0.186024
6 to 10 142284 1.2701 0.897970
5 to 9 142123 0.7243 0.765561
4 to 8 141631 -0.9435 0.172715
3 to 7 141591 -1.0791 0.140275
2 to 6 142245 1.1379 0.872411
1 to 5 141925 0.0531 0.521181
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-22_19:31
Bits used No. missing words z-score p-value
31 to 32 141428 -1.4199 0.077825
30 to 31 142203 0.8663 0.806833
29 to 30 142149 0.7070 0.760214
28 to 29 141842 -0.1986 0.421283
27 to 28 142373 1.3678 0.914306
26 to 27 141558 -1.0364 0.150014
25 to 26 142020 0.3265 0.627962
24 to 25 142093 0.5418 0.706022
23 to 24 141857 -0.1544 0.438661
22 to 23 141892 -0.0511 0.479615
21 to 22 142078 0.4976 0.690600
20 to 21 142197 0.8486 0.801944
19 to 20 142001 0.2704 0.606579
18 to 19 141882 -0.0806 0.467872
17 to 18 141726 -0.5408 0.294324
16 to 17 141067 -2.4847 0.006482
15 to 16 142140 0.6804 0.751888
14 to 15 141633 -0.8151 0.207498
13 to 14 141741 -0.4965 0.309754
12 to 13 142096 0.5506 0.709063
11 to 12 142045 0.4002 0.655498
10 to 11 142539 1.8574 0.968375
9 to 10 141955 0.1347 0.553583
8 to 9 141931 0.0639 0.525484
7 to 8 140985 -2.7266 0.003199
6 to 7 141439 -1.3874 0.082659
5 to 6 142303 1.1613 0.877234
4 to 5 141323 -1.7296 0.041852
3 to 4 142035 0.3707 0.644573
2 to 3 142288 1.1170 0.868007
1 to 2 141322 -1.7325 0.041589
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2564.06 0.906 0.817500
Test results for specific bytes for dh-ranFile-2018-06-22_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2443.31 -0.802 0.211347
2 to 9 2470.31 -0.420 0.337304
3 to 10 2529.75 0.421 0.663030
4 to 11 2544.14 0.624 0.733776
5 to 12 2540.25 0.569 0.715412
6 to 13 2507.54 0.107 0.542478
7 to 14 2597.99 1.386 0.917091
8 to 15 2451.48 -0.686 0.246282
9 to 16 2422.31 -1.099 0.135946
10 to 17 2480.21 -0.280 0.389812
11 to 18 2511.91 0.168 0.566871
12 to 19 2509.93 0.140 0.555829
13 to 20 2623.21 1.742 0.959282
14 to 21 2487.49 -0.177 0.429783
15 to 22 2538.41 0.543 0.706497
16 to 23 2426.70 -1.037 0.149946
17 to 24 2430.88 -0.978 0.164147
18 to 25 2462.00 -0.537 0.295507
19 to 26 2534.31 0.485 0.686253
20 to 27 2460.58 -0.557 0.288594
21 to 28 2511.40 0.161 0.564014
22 to 29 2528.00 0.396 0.653963
23 to 30 2448.64 -0.726 0.233806
24 to 31 2484.43 -0.220 0.412843
25 to 32 2420.41 -1.126 0.130186
CDPARK for dh-ranFile-2018-06-22_19:31: 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
3559 1.6438 0.949895
3542 0.8676 0.807188
3530 0.3196 0.625377
3529 0.2740 0.607947
3520 -0.1370 0.445521
3492 -1.4155 0.078457
3526 0.1370 0.554479
3525 0.0913 0.536383
3512 -0.5023 0.307734
3485 -1.7352 0.041356
Square side=100, avg. no. parked=3522.00 sample std.=20.69
p-value of the KSTEST for those 10 p-values: 0.930641
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_19:31
0.4182,0.4754,0.0351,0.8480,0.2937,0.8676,0.7913,0.0623,0.7641,0.4521,
The KS test for those 10 p-values: 0.866934
The 3DSPHERES test for dh-ranFile-2018-06-22_19:31
sample no r^3 equiv. uni.
1 31.613 0.651377
2 4.484 0.138827
3 9.820 0.279148
4 18.833 0.466222
5 4.531 0.140195
6 98.548 0.962557
7 71.671 0.908282
8 46.534 0.787991
9 20.835 0.500669
10 17.636 0.444488
11 2.489 0.079619
12 28.295 0.610603
13 18.065 0.452378
14 18.090 0.452831
15 2.441 0.078147
16 31.394 0.648828
17 7.834 0.229818
18 37.198 0.710595
19 22.947 0.534625
20 29.939 0.631366
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.806022
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -1.1 -1.9 -1.5 0.2
-1.4 -0.6 -1.0 -2.2 0.3 0.0
-0.9 -1.3 -0.3 -0.5 1.4 -0.7
0.1 2.1 -0.3 1.9 0.6 -1.5
0.6 1.7 -0.0 0.5 0.4 -0.3
-0.5 -0.3 1.8 0.9 -0.6 -0.8
-0.5 -1.3 -1.2 0.4 -1.3 0.0
1.8
Chi-square with 42 degrees of freedom:48.886013
z-score=0.751326, p-value=0.783970
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-22_19:31
Test no p-value
1 0.161264
2 0.123371
3 0.081537
4 0.015259
5 0.813101
6 0.002057
7 0.173738
8 0.000520
9 0.521709
10 0.528814
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000620
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_19:31:
(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 66644 0.01 66679 0.00
3 25000.00 25019 0.01 24974 0.03
4 6666.67 6652 0.03 6626 0.25
5 1388.89 1400 0.09 1425 0.94
6 238.10 245 0.20 249 0.50
7 34.72 34 0.01 37 0.15
8 4.96 5 0.00 9 3.29
p=0.00084 p=0.47604
Number of rngs required: 689364, p-value: 0.868
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_19:31
No. of wins: Observed Expected
98563 98585.9
z-score=-0.102, pvalue=0.45928
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66448 66666.7 0.717 0.717
2 37745 37654.3 0.218 0.936
3 26713 26954.7 2.168 3.103
4 19391 19313.5 0.311 3.415
5 13996 13851.4 1.509 4.924
6 9881 9943.5 0.393 5.317
7 7237 7145.0 1.184 6.501
8 5130 5139.1 0.016 6.517
9 3856 3699.9 6.589 13.106
10 2620 2666.3 0.804 13.910
11 1998 1923.3 2.899 16.809
12 1419 1388.7 0.659 17.468
13 918 1003.7 7.320 24.788
14 767 726.1 2.299 27.087
15 493 525.8 2.050 29.138
16 367 381.2 0.525 29.663
17 264 276.5 0.569 30.232
18 191 200.8 0.481 30.713
19 165 146.0 2.477 33.190
20 105 106.2 0.014 33.204
21 296 287.1 0.275 33.479
Chisq= 33.48 for 20 degrees of freedom, p= 0.97013
SUMMARY of craptest
p-value for no. of wins: 0.459284
p-value for throws/game: 0.970126
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_19:31
No. of wins: Observed Expected
99089 98585.9
z-score= 2.250, pvalue=0.98779
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66841 66666.7 0.456 0.456
2 37460 37654.3 1.003 1.459
3 26864 26954.7 0.305 1.764
4 19147 19313.5 1.435 3.199
5 13805 13851.4 0.156 3.354
6 9969 9943.5 0.065 3.420
7 7266 7145.0 2.048 5.468
8 5083 5139.1 0.612 6.080
9 3846 3699.9 5.772 11.852
10 2706 2666.3 0.591 12.443
11 1932 1923.3 0.039 12.482
12 1411 1388.7 0.357 12.839
13 1061 1003.7 3.269 16.108
14 755 726.1 1.147 17.255
15 531 525.8 0.051 17.306
16 347 381.2 3.060 20.366
17 259 276.5 1.112 21.478
18 194 200.8 0.232 21.710
19 143 146.0 0.061 21.771
20 99 106.2 0.490 22.261
21 281 287.1 0.130 22.392
Chisq= 22.39 for 20 degrees of freedom, p= 0.68036
SUMMARY of craptest
p-value for no. of wins: 0.987786
p-value for throws/game: 0.680360
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0006,0.0008,0.0016,0.0021,0.0032,0.0040,0.0065,0.0119,0.0127,
0.0153,0.0190,0.0221,0.0221,0.0271,0.0300,0.0351,0.0362,0.0404,0.0414,
0.0416,0.0419,0.0485,0.0492,0.0500,0.0623,0.0778,0.0781,0.0785,0.0796,
0.0815,0.0827,0.0858,0.1059,0.1071,0.1117,0.1234,0.1302,0.1359,0.1388,
0.1402,0.1403,0.1448,0.1499,0.1500,0.1613,0.1641,0.1654,0.1727,0.1733,
0.1737,0.1860,0.1940,0.1977,0.1993,0.2075,0.2100,0.2113,0.2115,0.2165,
0.2188,0.2206,0.2206,0.2298,0.2338,0.2340,0.2447,0.2463,0.2479,0.2572,
0.2684,0.2715,0.2739,0.2791,0.2855,0.2864,0.2886,0.2937,0.2943,0.2944,
0.2955,0.2975,0.3033,0.3077,0.3098,0.3150,0.3187,0.3319,0.3373,0.3414,
0.3436,0.3467,0.3493,0.3504,0.3556,0.3647,0.3653,0.3699,0.3795,0.3806,
0.3898,0.3914,0.3929,0.3938,0.4005,0.4036,0.4088,0.4128,0.4182,0.4210,
0.4213,0.4298,0.4320,0.4342,0.4349,0.4375,0.4387,0.4411,0.4423,0.4443,
0.4445,0.4455,0.4482,0.4491,0.4521,0.4524,0.4528,0.4593,0.4662,0.4679,
0.4727,0.4754,0.4760,0.4796,0.4967,0.4996,0.4997,0.5007,0.5084,0.5127,
0.5127,0.5202,0.5212,0.5217,0.5255,0.5288,0.5341,0.5346,0.5364,0.5373,
0.5425,0.5462,0.5536,0.5545,0.5558,0.5640,0.5669,0.5794,0.5911,0.6039,
0.6063,0.6066,0.6079,0.6106,0.6181,0.6227,0.6254,0.6280,0.6290,0.6314,
0.6446,0.6462,0.6488,0.6499,0.6514,0.6540,0.6555,0.6630,0.6630,0.6676,
0.6686,0.6782,0.6784,0.6786,0.6800,0.6804,0.6863,0.6887,0.6906,0.7010,
0.7060,0.7065,0.7091,0.7106,0.7130,0.7149,0.7154,0.7220,0.7243,0.7338,
0.7410,0.7519,0.7588,0.7602,0.7641,0.7656,0.7676,0.7687,0.7840,0.7880,
0.7913,0.7924,0.7996,0.8016,0.8019,0.8060,0.8068,0.8072,0.8131,0.8175,
0.8188,0.8237,0.8480,0.8656,0.8669,0.8676,0.8676,0.8680,0.8724,0.8742,
0.8742,0.8756,0.8772,0.8788,0.8799,0.8845,0.8847,0.8899,0.8947,0.8955,
0.8980,0.8988,0.9026,0.9083,0.9090,0.9143,0.9171,0.9231,0.9305,0.9306,
0.9365,0.9499,0.9539,0.9555,0.9563,0.9593,0.9595,0.9626,0.9684,0.9701,
0.9709,0.9709,0.9795,0.9822,0.9842,0.9853,0.9878,0.9901,0.9952,
Overall p-value after applying KStest on 269 p-values = 0.413250
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.