RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_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 15.91 19.9646 0.723956
2 to 25 15.77 23.1368 0.855149
3 to 26 15.78 14.7045 0.383244
4 to 27 15.57 17.2281 0.560980
5 to 28 15.99 15.1617 0.416166
6 to 29 16.11 13.9694 0.330730
7 to 30 15.77 15.5670 0.445288
8 to 31 15.72 17.8676 0.602759
9 to 32 15.71 21.1189 0.778985
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.373358
Tough bday spacings test for dh-ranFile-2018-07-09_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 9 38 95 99 96 71 46 25 13 5 3
(O-E)^2/E 0.0 0.1 6.4 0.0 0.0 0.7 0.7 0.8 0.2 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 9.595, p= 0.523
RESULTS OF GCD FOR dh-ranFile-2018-07-09_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.501620
p-value, dist. of gcd's: 0.240894
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.606 0.281 0.595 0.590 0.269 0.215 0.900 0.826
Bits 8 to 15---> 0.435 0.962 0.778 0.155 0.850 0.247 0.103 0.940
Bits 16 to 23---> 0.092 0.037 0.306 0.155 0.583 0.401 0.142 0.985
Bits 24 to 31---> 0.479 0.847 0.974 0.802 0.921 0.910 0.578 0.828
KS test for the above 32 p values: 0.737
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_16:31,
p-values for 5 runs: 0.2346, 0.6018, 0.6002, 0.4412, 0.1082
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5020 5134.0 2.532 3.807
r= 30 23179 23103.0 0.250 4.056
r= 31 11606 11551.5 0.257 4.313
chi-square = 4.313 with df = 3; p-value = 0.770
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5034 5134.0 1.948 2.565
r= 31 23124 23103.0 0.019 2.584
r= 32 11642 11551.5 0.709 3.293
chi-square = 3.293 with df = 3; p-value = 0.651
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_16:31
b-rank test for bits 1 to 8, p=0.37923
b-rank test for bits 2 to 9, p=0.20740
b-rank test for bits 3 to 10, p=0.52466
b-rank test for bits 4 to 11, p=0.39541
b-rank test for bits 5 to 12, p=0.83768
b-rank test for bits 6 to 13, p=0.20772
b-rank test for bits 7 to 14, p=0.20309
b-rank test for bits 8 to 15, p=0.56350
b-rank test for bits 9 to 16, p=0.13716
b-rank test for bits 10 to 17, p=0.39363
b-rank test for bits 11 to 18, p=0.48505
b-rank test for bits 12 to 19, p=0.11781
b-rank test for bits 13 to 20, p=0.00141
b-rank test for bits 14 to 21, p=0.81044
b-rank test for bits 15 to 22, p=0.47864
b-rank test for bits 16 to 23, p=0.09582
b-rank test for bits 17 to 24, p=0.69511
b-rank test for bits 18 to 25, p=0.69391
b-rank test for bits 19 to 26, p=0.15133
b-rank test for bits 20 to 27, p=0.12420
b-rank test for bits 21 to 28, p=0.78451
b-rank test for bits 22 to 29, p=0.42409
b-rank test for bits 23 to 30, p=0.42663
b-rank test for bits 24 to 31, p=0.73338
b-rank test for bits 25 to 32, p=0.13998
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 = 0.100784
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_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 141824 -0.20 0.420987
2 141662 -0.58 0.281675
3 141202 -1.65 0.049202
4 141854 -0.13 0.448570
5 142325 0.97 0.834274
6 141826 -0.19 0.422815
7 141857 -0.12 0.451344
8 142601 1.62 0.946958
9 141021 -2.08 0.018968
10 141884 -0.06 0.476404
11 141641 -0.63 0.265350
12 142112 0.47 0.682082
13 141453 -1.07 0.143169
14 142025 0.27 0.606519
15 141678 -0.54 0.294429
16 142014 0.24 0.596600
17 142411 1.17 0.879427
18 141602 -0.72 0.236360
19 142145 0.55 0.709057
20 141605 -0.71 0.238526
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_16:31
Bits used No. missing words z-score p-value
23 to 32 142074 0.5678 0.714924
22 to 31 141810 -0.3425 0.365981
21 to 30 142221 1.0747 0.858751
20 to 29 141825 -0.2908 0.385605
19 to 28 141581 -1.1322 0.128781
18 to 27 141994 0.2920 0.614844
17 to 26 141769 -0.4839 0.314230
16 to 25 141755 -0.5322 0.297303
15 to 24 141810 -0.3425 0.365981
14 to 23 142180 0.9333 0.824679
13 to 22 142023 0.3920 0.652458
12 to 21 141951 0.1437 0.557127
11 to 20 142338 1.4782 0.930319
10 to 19 142302 1.3540 0.912137
9 to 18 142667 2.6127 0.995508
8 to 17 141743 -0.5736 0.283136
7 to 16 142031 0.4196 0.662594
6 to 15 141939 0.1023 0.540745
5 to 14 141993 0.2885 0.613525
4 to 13 141902 -0.0253 0.489918
3 to 12 142045 0.4678 0.680046
2 to 11 142068 0.5471 0.707858
1 to 10 141917 0.0264 0.510550
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_16:31
Bits used No. missing words z-score p-value
28 to 32 142079 0.5752 0.717406
27 to 31 141903 -0.0215 0.491440
26 to 30 141449 -1.5604 0.059328
25 to 29 141965 0.1887 0.574841
24 to 28 142182 0.9243 0.822336
23 to 27 142251 1.1582 0.876610
22 to 26 142023 0.3853 0.650001
21 to 25 141985 0.2565 0.601221
20 to 24 141671 -0.8079 0.209575
19 to 23 141808 -0.3435 0.365614
18 to 22 141629 -0.9503 0.170987
17 to 21 142052 0.4836 0.685675
16 to 20 142010 0.3413 0.633544
15 to 19 141884 -0.0859 0.465787
14 to 18 141772 -0.4655 0.320778
13 to 17 141531 -1.2825 0.099838
12 to 16 142305 1.3413 0.910081
11 to 15 142510 2.0362 0.979133
10 to 14 141828 -0.2757 0.391391
9 to 13 142009 0.3379 0.632267
8 to 12 142052 0.4836 0.685675
7 to 11 141822 -0.2960 0.383602
6 to 10 142467 1.8904 0.970648
5 to 9 142271 1.2260 0.889901
4 to 8 142027 0.3989 0.655010
3 to 7 141982 0.2463 0.597290
2 to 6 141885 -0.0825 0.467135
1 to 5 142155 0.8328 0.797516
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_16:31
Bits used No. missing words z-score p-value
31 to 32 141574 -0.9892 0.161289
30 to 31 142168 0.7630 0.777280
29 to 30 142063 0.4533 0.674835
28 to 29 142118 0.6155 0.730903
27 to 28 141713 -0.5791 0.281246
26 to 27 141030 -2.5939 0.004745
25 to 26 141714 -0.5762 0.282242
24 to 25 141972 0.1849 0.573333
23 to 24 141820 -0.2635 0.396079
22 to 23 142083 0.5123 0.695780
21 to 22 142331 1.2439 0.893225
20 to 21 141780 -0.3815 0.351415
19 to 20 141299 -1.8004 0.035900
18 to 19 142605 2.0521 0.979921
17 to 18 141794 -0.3402 0.366851
16 to 17 141836 -0.2163 0.414372
15 to 16 142336 1.2586 0.895915
14 to 15 141787 -0.3609 0.359104
13 to 14 141931 0.0639 0.525484
12 to 13 141858 -0.1514 0.439824
11 to 12 141646 -0.7768 0.218643
10 to 11 142282 1.0993 0.864186
9 to 10 141756 -0.4523 0.325526
8 to 9 141596 -0.9243 0.177671
7 to 8 141923 0.0403 0.516083
6 to 7 142048 0.4091 0.658751
5 to 6 142247 0.9961 0.840394
4 to 5 141646 -0.7768 0.218643
3 to 4 141451 -1.3520 0.088187
2 to 3 142215 0.9017 0.816387
1 to 2 142338 1.2645 0.896977
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2515.20 0.215 0.585092
Test results for specific bytes for dh-ranFile-2018-07-09_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2715.64 3.050 0.998854
2 to 9 2573.95 1.046 0.852163
3 to 10 2523.52 0.333 0.630317
4 to 11 2451.85 -0.681 0.247970
5 to 12 2539.00 0.551 0.709350
6 to 13 2432.55 -0.954 0.170062
7 to 14 2420.31 -1.127 0.129889
8 to 15 2547.30 0.669 0.748207
9 to 16 2458.71 -0.584 0.279627
10 to 17 2504.60 0.065 0.525934
11 to 18 2511.07 0.156 0.562177
12 to 19 2477.92 -0.312 0.377424
13 to 20 2496.78 -0.046 0.481844
14 to 21 2514.69 0.208 0.582262
15 to 22 2400.30 -1.410 0.079266
16 to 23 2473.51 -0.375 0.353960
17 to 24 2464.39 -0.504 0.307274
18 to 25 2426.68 -1.037 0.149900
19 to 26 2455.47 -0.630 0.264409
20 to 27 2603.55 1.464 0.928469
21 to 28 2363.12 -1.936 0.026451
22 to 29 2489.72 -0.145 0.442213
23 to 30 2534.49 0.488 0.687153
24 to 31 2380.19 -1.694 0.045096
25 to 32 2492.21 -0.110 0.456152
CDPARK for dh-ranFile-2018-07-09_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
3506 -0.7763 0.218799
3515 -0.3653 0.357445
3522 -0.0457 0.481790
3541 0.8219 0.794438
3500 -1.0502 0.146807
3515 -0.3653 0.357445
3487 -1.6438 0.050105
3543 0.9132 0.819442
3494 -1.3242 0.092718
3521 -0.0913 0.463617
Square side=100, avg. no. parked=3514.40 sample std.=17.53
p-value of the KSTEST for those 10 p-values: 0.320126
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_16:31
0.8185,0.1799,0.6727,0.1218,0.9192,0.8341,0.4662,0.0839,0.1467,0.0131,
The KS test for those 10 p-values: 0.344542
The 3DSPHERES test for dh-ranFile-2018-07-09_16:31
sample no r^3 equiv. uni.
1 11.249 0.312696
2 1.898 0.061321
3 1.483 0.048241
4 38.059 0.718780
5 13.128 0.354414
6 21.086 0.504837
7 15.975 0.412856
8 17.265 0.437573
9 24.779 0.562181
10 26.146 0.581685
11 0.655 0.021581
12 76.813 0.922730
13 26.685 0.589136
14 79.162 0.928549
15 31.205 0.646602
16 31.709 0.652487
17 8.831 0.254994
18 1.000 0.032781
19 10.180 0.287762
20 10.366 0.292168
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.363159
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.7 0.3 -1.4 0.4 -0.7
-0.9 -1.6 0.3 -1.4 0.2 -0.5
2.7 -0.7 -0.1 0.6 0.5 0.7
-0.9 0.4 1.2 -1.2 -0.3 -0.6
1.8 -1.0 -0.9 0.6 -1.9 -0.3
-0.8 0.3 1.7 -2.2 0.1 -2.1
-0.7 0.2 1.3 0.4 -1.3 0.0
-0.1
Chi-square with 42 degrees of freedom:51.989874
z-score=1.089985, p-value=0.861118
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_16:31
Test no p-value
1 0.635058
2 0.004107
3 0.226291
4 0.002918
5 0.788963
6 0.269346
7 0.132800
8 0.870270
9 0.023907
10 0.007757
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001463
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_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 66659 0.00 66532 0.27
3 25000.00 24983 0.01 25117 0.55
4 6666.67 6668 0.00 6693 0.10
5 1388.89 1410 0.32 1381 0.04
6 238.10 232 0.16 237 0.01
7 34.72 43 1.97 36 0.05
8 4.96 4 0.19 3 0.77
p=0.14868 p=0.06246
Number of rngs required: 689136, p-value: 0.802
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_16:31
No. of wins: Observed Expected
98385 98585.9
z-score=-0.898, pvalue=0.18450
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66475 66666.7 0.551 0.551
2 37562 37654.3 0.226 0.777
3 27123 26954.7 1.050 1.828
4 19130 19313.5 1.743 3.571
5 13930 13851.4 0.446 4.016
6 10133 9943.5 3.610 7.626
7 7151 7145.0 0.005 7.631
8 5236 5139.1 1.828 9.459
9 3653 3699.9 0.594 10.053
10 2628 2666.3 0.550 10.603
11 1878 1923.3 1.068 11.671
12 1417 1388.7 0.575 12.246
13 1009 1003.7 0.028 12.274
14 696 726.1 1.251 13.525
15 511 525.8 0.419 13.944
16 394 381.2 0.433 14.377
17 297 276.5 1.514 15.891
18 214 200.8 0.864 16.755
19 150 146.0 0.110 16.865
20 107 106.2 0.006 16.871
21 306 287.1 1.242 18.113
Chisq= 18.11 for 20 degrees of freedom, p= 0.42004
SUMMARY of craptest
p-value for no. of wins: 0.184498
p-value for throws/game: 0.420040
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_16:31
No. of wins: Observed Expected
98493 98585.9
z-score=-0.415, pvalue=0.33895
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66679 66666.7 0.002 0.002
2 37708 37654.3 0.077 0.079
3 26991 26954.7 0.049 0.128
4 19398 19313.5 0.370 0.498
5 13920 13851.4 0.340 0.837
6 9872 9943.5 0.515 1.352
7 7131 7145.0 0.028 1.379
8 4996 5139.1 3.983 5.363
9 3717 3699.9 0.079 5.442
10 2626 2666.3 0.609 6.051
11 1916 1923.3 0.028 6.079
12 1381 1388.7 0.043 6.122
13 991 1003.7 0.161 6.283
14 766 726.1 2.188 8.471
15 532 525.8 0.072 8.543
16 372 381.2 0.220 8.763
17 264 276.5 0.569 9.332
18 213 200.8 0.737 10.069
19 151 146.0 0.172 10.241
20 102 106.2 0.167 10.409
21 274 287.1 0.599 11.008
Chisq= 11.01 for 20 degrees of freedom, p= 0.05398
SUMMARY of craptest
p-value for no. of wins: 0.338955
p-value for throws/game: 0.053978
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0015,0.0029,0.0041,0.0047,0.0078,0.0131,0.0190,0.0216,0.0239,
0.0265,0.0328,0.0359,0.0366,0.0451,0.0482,0.0492,0.0501,0.0540,0.0593,
0.0613,0.0625,0.0793,0.0839,0.0882,0.0924,0.0927,0.0958,0.0998,0.1008,
0.1028,0.1082,0.1178,0.1218,0.1242,0.1288,0.1299,0.1328,0.1372,0.1400,
0.1422,0.1432,0.1467,0.1468,0.1487,0.1499,0.1513,0.1547,0.1554,0.1613,
0.1701,0.1710,0.1777,0.1799,0.1845,0.2031,0.2074,0.2077,0.2096,0.2149,
0.2186,0.2186,0.2188,0.2263,0.2346,0.2364,0.2385,0.2409,0.2470,0.2480,
0.2550,0.2644,0.2653,0.2688,0.2693,0.2796,0.2812,0.2812,0.2817,0.2822,
0.2831,0.2878,0.2922,0.2944,0.2973,0.3060,0.3073,0.3127,0.3142,0.3201,
0.3208,0.3255,0.3307,0.3390,0.3445,0.3514,0.3540,0.3544,0.3574,0.3574,
0.3591,0.3632,0.3656,0.3660,0.3660,0.3669,0.3734,0.3774,0.3792,0.3832,
0.3836,0.3856,0.3914,0.3936,0.3954,0.3961,0.4011,0.4129,0.4144,0.4162,
0.4200,0.4210,0.4228,0.4241,0.4266,0.4350,0.4376,0.4398,0.4412,0.4422,
0.4453,0.4486,0.4513,0.4562,0.4636,0.4658,0.4662,0.4671,0.4764,0.4786,
0.4791,0.4818,0.4818,0.4850,0.4899,0.4914,0.5016,0.5048,0.5106,0.5161,
0.5233,0.5247,0.5255,0.5259,0.5407,0.5571,0.5610,0.5622,0.5622,0.5635,
0.5733,0.5748,0.5781,0.5817,0.5823,0.5829,0.5851,0.5891,0.5899,0.5952,
0.5966,0.5973,0.6002,0.6012,0.6018,0.6028,0.6057,0.6065,0.6135,0.6148,
0.6303,0.6323,0.6335,0.6351,0.6466,0.6500,0.6513,0.6525,0.6525,0.6550,
0.6588,0.6626,0.6727,0.6748,0.6800,0.6821,0.6857,0.6857,0.6872,0.6939,
0.6951,0.6958,0.7079,0.7091,0.7093,0.7149,0.7174,0.7188,0.7240,0.7309,
0.7334,0.7367,0.7482,0.7704,0.7773,0.7785,0.7790,0.7845,0.7890,0.7944,
0.7975,0.8017,0.8018,0.8104,0.8164,0.8185,0.8194,0.8223,0.8247,0.8257,
0.8282,0.8341,0.8343,0.8377,0.8404,0.8474,0.8500,0.8522,0.8551,0.8588,
0.8611,0.8642,0.8703,0.8766,0.8794,0.8899,0.8932,0.8959,0.8970,0.8996,
0.9101,0.9104,0.9121,0.9192,0.9211,0.9227,0.9285,0.9285,0.9303,0.9403,
0.9470,0.9619,0.9706,0.9737,0.9791,0.9799,0.9853,0.9955,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.230706
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.