RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.86 26.2397 0.929797
2 to 25 15.76 22.2553 0.824900
3 to 26 15.82 18.7293 0.655712
4 to 27 16.15 35.1056 0.993974
5 to 28 15.74 25.6110 0.918155
6 to 29 15.43 30.7286 0.978455
7 to 30 15.61 21.7704 0.806290
8 to 31 15.80 15.9052 0.469435
9 to 32 15.95 8.2650 0.039452
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.007339
Tough bday spacings test for dh-ranFile-2018-07-08_10:31: 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 30 65 101 102 88 61 23 7 6 5
(O-E)^2/E 0.9 1.2 0.9 0.1 0.2 1.2 1.5 1.5 4.2 0.1 0.2
Birthday Spacings: Sum(O-E)^2/E= 12.070, p= 0.720
RESULTS OF GCD FOR dh-ranFile-2018-07-08_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.989357
p-value, dist. of gcd's: 0.691220
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.676 0.649 0.814 0.298 0.096 0.439 0.829 0.597
Bits 8 to 15---> 0.476 0.268 0.252 0.410 0.787 0.384 0.410 0.579
Bits 16 to 23---> 0.398 0.543 0.598 0.298 0.690 0.644 0.487 0.904
Bits 24 to 31---> 0.724 0.554 0.095 0.049 0.383 0.459 0.798 0.633
KS test for the above 32 p values: 0.794
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_10:31,
p-values for 5 runs: 0.2287, 0.3007, 0.9046, 0.7506, 0.9616
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 219 211.4 0.272 0.272
r= 29 5227 5134.0 1.684 1.956
r= 30 23097 23103.0 0.002 1.958
r= 31 11457 11551.5 0.773 2.731
chi-square = 2.731 with df = 3; p-value = 0.565
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 225 211.4 0.873 0.873
r= 30 4984 5134.0 4.383 5.256
r= 31 23136 23103.0 0.047 5.303
r= 32 11655 11551.5 0.927 6.230
chi-square = 6.230 with df = 3; p-value = 0.899
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_10:31
b-rank test for bits 1 to 8, p=0.13363
b-rank test for bits 2 to 9, p=0.68506
b-rank test for bits 3 to 10, p=0.36441
b-rank test for bits 4 to 11, p=0.63218
b-rank test for bits 5 to 12, p=0.89764
b-rank test for bits 6 to 13, p=0.09572
b-rank test for bits 7 to 14, p=0.23687
b-rank test for bits 8 to 15, p=0.33703
b-rank test for bits 9 to 16, p=0.35178
b-rank test for bits 10 to 17, p=0.84063
b-rank test for bits 11 to 18, p=0.66379
b-rank test for bits 12 to 19, p=0.98850
b-rank test for bits 13 to 20, p=0.45627
b-rank test for bits 14 to 21, p=0.94308
b-rank test for bits 15 to 22, p=0.73668
b-rank test for bits 16 to 23, p=0.40834
b-rank test for bits 17 to 24, p=0.33354
b-rank test for bits 18 to 25, p=0.43414
b-rank test for bits 19 to 26, p=0.72040
b-rank test for bits 20 to 27, p=0.96058
b-rank test for bits 21 to 28, p=0.91252
b-rank test for bits 22 to 29, p=0.85933
b-rank test for bits 23 to 30, p=0.97595
b-rank test for bits 24 to 31, p=0.64725
b-rank test for bits 25 to 32, p=0.00955
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 = 0.190777
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_10:31
(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 141077 -1.94 0.025906
2 141889 -0.05 0.481057
3 142463 1.29 0.902102
4 141933 0.06 0.522052
5 142120 0.49 0.688718
6 141573 -0.79 0.215987
7 141875 -0.08 0.468035
8 142384 1.11 0.866294
9 141854 -0.13 0.448570
10 142004 0.22 0.587528
11 141952 0.10 0.539707
12 142164 0.60 0.724086
13 142009 0.23 0.592070
14 142837 2.17 0.984900
15 142222 0.73 0.767469
16 141931 0.05 0.520190
17 142041 0.31 0.620822
18 141855 -0.13 0.449494
19 141356 -1.29 0.098035
20 141235 -1.58 0.057566
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_10:31
Bits used No. missing words z-score p-value
23 to 32 141802 -0.3701 0.355653
22 to 31 141557 -1.2149 0.112196
21 to 30 141875 -0.1184 0.452884
20 to 29 141942 0.1127 0.544848
19 to 28 141784 -0.4322 0.332808
18 to 27 142058 0.5127 0.695904
17 to 26 142001 0.3161 0.624038
16 to 25 141644 -0.9149 0.180114
15 to 24 141901 -0.0287 0.488542
14 to 23 141936 0.0920 0.536637
13 to 22 141840 -0.2391 0.405526
12 to 21 142236 1.1264 0.870012
11 to 20 142017 0.3713 0.644784
10 to 19 142280 1.2782 0.899406
9 to 18 142156 0.8506 0.802500
8 to 17 141831 -0.2701 0.393540
7 to 16 142131 0.7644 0.777679
6 to 15 142053 0.4954 0.689846
5 to 14 141604 -1.0529 0.146202
4 to 13 141574 -1.1563 0.123777
3 to 12 141825 -0.2908 0.385605
2 to 11 142071 0.5575 0.711401
1 to 10 142128 0.7540 0.774586
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_10:31
Bits used No. missing words z-score p-value
28 to 32 142715 2.7311 0.996844
27 to 31 142408 1.6904 0.954525
26 to 30 142161 0.8531 0.803203
25 to 29 142113 0.6904 0.755031
24 to 28 142497 1.9921 0.976820
23 to 27 141799 -0.3740 0.354202
22 to 26 142051 0.4802 0.684471
21 to 25 141931 0.0735 0.529279
20 to 24 142207 1.0091 0.843525
19 to 23 142052 0.4836 0.685675
18 to 22 141563 -1.1740 0.120198
17 to 21 141572 -1.1435 0.126417
16 to 20 141378 -1.8011 0.035842
15 to 19 142163 0.8599 0.805077
14 to 18 142442 1.8057 0.964514
13 to 17 141988 0.2667 0.605141
12 to 16 141796 -0.3842 0.350426
11 to 15 141767 -0.4825 0.314734
10 to 14 142434 1.7785 0.962343
9 to 13 141107 -2.7198 0.003266
8 to 12 142376 1.5819 0.943167
7 to 11 142258 1.1819 0.881384
6 to 10 142397 1.6531 0.950847
5 to 9 141972 0.2124 0.584118
4 to 8 141551 -1.2147 0.112244
3 to 7 141949 0.1345 0.553486
2 to 6 142177 0.9074 0.817891
1 to 5 142114 0.6938 0.756095
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_10:31
Bits used No. missing words z-score p-value
31 to 32 141655 -0.7502 0.226556
30 to 31 141625 -0.8387 0.200810
29 to 30 142009 0.2940 0.615626
28 to 29 141752 -0.4641 0.321288
27 to 28 141555 -1.0452 0.147960
26 to 27 141656 -0.7473 0.227445
25 to 26 142699 2.3294 0.990081
24 to 25 142209 0.8840 0.811647
23 to 24 142223 0.9253 0.822590
22 to 23 142232 0.9518 0.829408
21 to 22 141417 -1.4523 0.073209
20 to 21 141964 0.1613 0.564059
19 to 20 141742 -0.4936 0.310795
18 to 19 141246 -1.9567 0.025190
17 to 18 142437 1.5565 0.940211
16 to 17 142335 1.2557 0.895381
15 to 16 141697 -0.6263 0.265545
14 to 15 141921 0.0344 0.513731
13 to 14 141898 -0.0334 0.486669
12 to 13 141565 -1.0157 0.154881
11 to 12 142062 0.4504 0.673772
10 to 11 141840 -0.2045 0.418976
9 to 10 141985 0.2232 0.588316
8 to 9 141892 -0.0511 0.479615
7 to 8 142050 0.4150 0.660913
6 to 7 142243 0.9843 0.837510
5 to 6 142178 0.7925 0.785976
4 to 5 141864 -0.1337 0.446813
3 to 4 141412 -1.4671 0.071181
2 to 3 141567 -1.0098 0.156290
1 to 2 141978 0.2026 0.580263
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2560.40 0.854 0.803490
Test results for specific bytes for dh-ranFile-2018-07-08_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2618.53 1.676 0.953150
2 to 9 2453.28 -0.661 0.254418
3 to 10 2421.36 -1.112 0.133038
4 to 11 2471.01 -0.410 0.340904
5 to 12 2393.59 -1.505 0.066178
6 to 13 2519.48 0.275 0.608533
7 to 14 2493.81 -0.088 0.465119
8 to 15 2493.09 -0.098 0.461066
9 to 16 2442.69 -0.811 0.208815
10 to 17 2504.60 0.065 0.525959
11 to 18 2683.43 2.594 0.995258
12 to 19 2422.81 -1.092 0.137484
13 to 20 2481.13 -0.267 0.394779
14 to 21 2460.81 -0.554 0.289720
15 to 22 2464.12 -0.507 0.305948
16 to 23 2586.49 1.223 0.889363
17 to 24 2438.38 -0.871 0.191766
18 to 25 2509.02 0.128 0.550742
19 to 26 2511.20 0.158 0.562926
20 to 27 2465.18 -0.492 0.311185
21 to 28 2502.62 0.037 0.514800
22 to 29 2482.38 -0.249 0.401605
23 to 30 2462.85 -0.525 0.299651
24 to 31 2533.57 0.475 0.682505
25 to 32 2509.59 0.136 0.553954
CDPARK for dh-ranFile-2018-07-08_10:31: 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
3520 -0.1370 0.445521
3495 -1.2785 0.100530
3521 -0.0913 0.463617
3532 0.4110 0.659449
3565 1.9178 0.972432
3544 0.9589 0.831196
3496 -1.2329 0.108811
3543 0.9132 0.819442
3558 1.5982 0.944998
3566 1.9635 0.975204
Square side=100, avg. no. parked=3534.00 sample std.=24.65
p-value of the KSTEST for those 10 p-values: 0.116725
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_10:31
0.3817,0.4152,0.8292,0.4404,0.5974,0.4105,0.8853,0.0549,0.1545,0.1437,
The KS test for those 10 p-values: 0.689275
The 3DSPHERES test for dh-ranFile-2018-07-08_10:31
sample no r^3 equiv. uni.
1 70.394 0.904294
2 10.711 0.300259
3 35.739 0.696172
4 27.851 0.604795
5 4.611 0.142470
6 1.949 0.062903
7 13.745 0.367548
8 8.212 0.239460
9 32.672 0.663470
10 63.332 0.878891
11 2.694 0.085871
12 1.348 0.043950
13 26.003 0.579689
14 64.129 0.882066
15 44.704 0.774655
16 8.444 0.245333
17 28.203 0.609414
18 8.427 0.244897
19 36.313 0.701930
20 31.626 0.651526
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.863702
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -2.0 0.3 0.5 0.8 -1.5
1.2 0.1 -0.5 -0.5 -0.1 0.3
1.1 -2.0 -0.8 0.0 0.4 -0.1
0.5 -0.7 0.2 -0.4 1.4 1.5
-0.2 0.2 -0.2 -2.1 1.2 0.8
-1.6 -0.8 1.5 1.6 2.3 -1.4
-1.2 -0.1 0.5 -1.3 -1.3 -1.0
-0.1
Chi-square with 42 degrees of freedom:50.322207
z-score=0.908027, p-value=0.822737
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_10:31
Test no p-value
1 0.118815
2 0.093251
3 0.093932
4 0.683919
5 0.986222
6 0.107954
7 0.076748
8 0.977739
9 0.953433
10 0.245434
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.038132
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_10:31:
(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 66621 0.03 66648 0.01
3 25000.00 25098 0.38 25004 0.00
4 6666.67 6648 0.05 6687 0.06
5 1388.89 1346 1.32 1399 0.07
6 238.10 248 0.41 224 0.83
7 34.72 35 0.00 32 0.21
8 4.96 3 0.77 5 0.00
p=0.18878 p=0.02259
Number of rngs required: 688604, p-value: 0.591
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_10:31
No. of wins: Observed Expected
98488 98585.9
z-score=-0.438, pvalue=0.33081
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66438 66666.7 0.784 0.784
2 37903 37654.3 1.642 2.427
3 26943 26954.7 0.005 2.432
4 19446 19313.5 0.910 3.341
5 13747 13851.4 0.787 4.128
6 9938 9943.5 0.003 4.132
7 7099 7145.0 0.296 4.428
8 5027 5139.1 2.444 6.872
9 3726 3699.9 0.185 7.057
10 2706 2666.3 0.591 7.648
11 1927 1923.3 0.007 7.655
12 1433 1388.7 1.411 9.065
13 964 1003.7 1.571 10.637
14 740 726.1 0.265 10.901
15 546 525.8 0.773 11.675
16 387 381.2 0.090 11.764
17 251 276.5 2.359 14.123
18 211 200.8 0.515 14.638
19 178 146.0 7.021 21.659
20 92 106.2 1.902 23.562
21 298 287.1 0.413 23.975
Chisq= 23.97 for 20 degrees of freedom, p= 0.75650
SUMMARY of craptest
p-value for no. of wins: 0.330809
p-value for throws/game: 0.756500
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_10:31
No. of wins: Observed Expected
98596 98585.9
z-score= 0.045, pvalue=0.51809
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66870 66666.7 0.620 0.620
2 37597 37654.3 0.087 0.707
3 26961 26954.7 0.001 0.709
4 19393 19313.5 0.328 1.036
5 13771 13851.4 0.467 1.503
6 9995 9943.5 0.266 1.770
7 7074 7145.0 0.706 2.476
8 5017 5139.1 2.900 5.375
9 3645 3699.9 0.814 6.189
10 2736 2666.3 1.822 8.011
11 1929 1923.3 0.017 8.028
12 1370 1388.7 0.253 8.281
13 982 1003.7 0.470 8.751
14 722 726.1 0.024 8.774
15 527 525.8 0.003 8.777
16 395 381.2 0.503 9.280
17 281 276.5 0.072 9.352
18 197 200.8 0.073 9.425
19 152 146.0 0.248 9.673
20 96 106.2 0.982 10.655
21 290 287.1 0.029 10.684
Chisq= 10.68 for 20 degrees of freedom, p= 0.04600
SUMMARY of craptest
p-value for no. of wins: 0.518089
p-value for throws/game: 0.045997
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0033,0.0073,0.0095,0.0226,0.0252,0.0259,0.0358,0.0381,0.0395,0.0440,
0.0460,0.0494,0.0549,0.0576,0.0629,0.0662,0.0712,0.0732,0.0767,0.0859,
0.0933,0.0939,0.0952,0.0957,0.0961,0.0980,0.1005,0.1080,0.1088,0.1122,
0.1122,0.1167,0.1188,0.1202,0.1238,0.1264,0.1330,0.1336,0.1375,0.1425,
0.1437,0.1462,0.1480,0.1545,0.1549,0.1563,0.1801,0.1888,0.1908,0.1918,
0.2008,0.2088,0.2160,0.2266,0.2274,0.2287,0.2369,0.2395,0.2449,0.2453,
0.2454,0.2517,0.2544,0.2655,0.2677,0.2897,0.2981,0.2982,0.2997,0.3003,
0.3007,0.3059,0.3108,0.3112,0.3147,0.3213,0.3308,0.3328,0.3335,0.3370,
0.3409,0.3504,0.3518,0.3542,0.3557,0.3644,0.3675,0.3817,0.3833,0.3837,
0.3856,0.3935,0.3948,0.3981,0.4016,0.4055,0.4083,0.4099,0.4100,0.4105,
0.4152,0.4190,0.4341,0.4390,0.4404,0.4455,0.4468,0.4486,0.4495,0.4529,
0.4563,0.4591,0.4611,0.4636,0.4651,0.4680,0.4694,0.4757,0.4796,0.4811,
0.4867,0.4867,0.4885,0.5137,0.5148,0.5181,0.5202,0.5221,0.5260,0.5293,
0.5366,0.5397,0.5427,0.5448,0.5507,0.5535,0.5540,0.5544,0.5629,0.5641,
0.5651,0.5793,0.5797,0.5803,0.5841,0.5875,0.5883,0.5915,0.5921,0.5972,
0.5974,0.5981,0.6048,0.6051,0.6085,0.6094,0.6156,0.6208,0.6240,0.6322,
0.6331,0.6440,0.6448,0.6472,0.6495,0.6515,0.6557,0.6594,0.6609,0.6635,
0.6638,0.6738,0.6759,0.6825,0.6839,0.6845,0.6851,0.6857,0.6887,0.6893,
0.6898,0.6903,0.6912,0.6959,0.6962,0.7019,0.7114,0.7196,0.7204,0.7238,
0.7241,0.7367,0.7506,0.7550,0.7561,0.7565,0.7675,0.7746,0.7747,0.7777,
0.7860,0.7869,0.7936,0.7983,0.8025,0.8032,0.8035,0.8051,0.8063,0.8116,
0.8140,0.8179,0.8194,0.8226,0.8227,0.8249,0.8292,0.8294,0.8295,0.8312,
0.8375,0.8406,0.8435,0.8593,0.8637,0.8663,0.8700,0.8789,0.8814,0.8821,
0.8853,0.8894,0.8954,0.8976,0.8990,0.8994,0.9021,0.9043,0.9043,0.9046,
0.9125,0.9182,0.9298,0.9402,0.9431,0.9432,0.9450,0.9508,0.9532,0.9534,
0.9545,0.9606,0.9616,0.9623,0.9645,0.9724,0.9752,0.9759,0.9768,0.9777,
0.9785,0.9849,0.9862,0.9885,0.9894,0.9901,0.9940,0.9953,0.9968,
Overall p-value after applying KStest on 269 p-values = 0.148317
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.