RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.60 20.5592 0.753368
2 to 25 15.64 27.2323 0.945252
3 to 26 15.90 17.7931 0.597995
4 to 27 15.82 9.8549 0.090415
5 to 28 15.80 13.0448 0.266820
6 to 29 15.70 10.9966 0.143261
7 to 30 15.84 21.3765 0.790100
8 to 31 15.87 14.6123 0.376612
9 to 32 15.73 18.1166 0.618476
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.997505
Tough bday spacings test for dh-ranFile-2018-07-07_13:31: 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 38 82 102 87 80 43 32 14 4 6
(O-E)^2/E 0.9 0.1 1.0 0.2 1.2 0.0 1.6 0.2 0.1 1.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 7.141, p= 0.288
RESULTS OF GCD FOR dh-ranFile-2018-07-07_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.526772
p-value, dist. of gcd's: 0.553280
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.890 0.610 0.477 0.719 0.152 0.947 0.446 0.071
Bits 8 to 15---> 0.710 0.059 0.157 0.347 0.427 0.148 0.094 0.252
Bits 16 to 23---> 0.612 0.285 0.016 0.919 0.966 0.894 0.798 0.358
Bits 24 to 31---> 0.025 0.303 0.427 0.937 0.325 0.832 0.035 0.121
KS test for the above 32 p values: 0.710
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_13:31,
p-values for 5 runs: 0.9287, 0.5870, 0.3665, 0.1699, 0.5521
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 236 211.4 2.858 2.858
r= 29 5142 5134.0 0.012 2.871
r= 30 22891 23103.0 1.946 4.817
r= 31 11731 11551.5 2.789 7.605
chi-square = 7.605 with df = 3; p-value = 0.945
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5064 5134.0 0.955 1.227
r= 31 23113 23103.0 0.004 1.231
r= 32 11604 11551.5 0.238 1.469
chi-square = 1.469 with df = 3; p-value = 0.311
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_13:31
b-rank test for bits 1 to 8, p=0.35616
b-rank test for bits 2 to 9, p=0.72099
b-rank test for bits 3 to 10, p=0.71665
b-rank test for bits 4 to 11, p=0.22647
b-rank test for bits 5 to 12, p=0.64887
b-rank test for bits 6 to 13, p=0.60713
b-rank test for bits 7 to 14, p=0.49652
b-rank test for bits 8 to 15, p=0.32498
b-rank test for bits 9 to 16, p=0.26125
b-rank test for bits 10 to 17, p=0.80341
b-rank test for bits 11 to 18, p=0.66030
b-rank test for bits 12 to 19, p=0.88361
b-rank test for bits 13 to 20, p=0.99813
b-rank test for bits 14 to 21, p=0.01518
b-rank test for bits 15 to 22, p=0.19875
b-rank test for bits 16 to 23, p=0.89496
b-rank test for bits 17 to 24, p=0.90885
b-rank test for bits 18 to 25, p=0.68686
b-rank test for bits 19 to 26, p=0.54685
b-rank test for bits 20 to 27, p=0.30446
b-rank test for bits 21 to 28, p=0.26931
b-rank test for bits 22 to 29, p=0.28478
b-rank test for bits 23 to 30, p=0.53406
b-rank test for bits 24 to 31, p=0.73345
b-rank test for bits 25 to 32, p=0.44516
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 = 0.571611
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_13:31
(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 142298 0.91 0.818089
2 141775 -0.31 0.376816
3 142361 1.06 0.854357
4 142346 1.02 0.846197
5 141818 -0.21 0.415512
6 141694 -0.50 0.307444
7 141996 0.20 0.580237
8 142174 0.62 0.731840
9 141813 -0.23 0.410962
10 141970 0.14 0.556362
11 141721 -0.44 0.329960
12 141679 -0.54 0.295235
13 142621 1.66 0.951822
14 142240 0.77 0.780119
15 141999 0.21 0.582975
16 141484 -0.99 0.160169
17 141697 -0.50 0.309913
18 141688 -0.52 0.302534
19 142117 0.49 0.686236
20 142128 0.51 0.695293
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_13:31
Bits used No. missing words z-score p-value
23 to 32 142123 0.7368 0.769376
22 to 31 142034 0.4299 0.666365
21 to 30 141849 -0.2080 0.417601
20 to 29 141521 -1.3391 0.090274
19 to 28 141934 0.0851 0.533897
18 to 27 142115 0.7092 0.760902
17 to 26 141877 -0.1115 0.455617
16 to 25 141667 -0.8356 0.201684
15 to 24 142261 1.2127 0.887369
14 to 23 142381 1.6264 0.948073
13 to 22 141963 0.1851 0.573413
12 to 21 142162 0.8713 0.808198
11 to 20 142527 2.1299 0.983410
10 to 19 141874 -0.1218 0.451518
9 to 18 141863 -0.1598 0.436536
8 to 17 141804 -0.3632 0.358225
7 to 16 141937 0.0954 0.538007
6 to 15 141648 -0.9011 0.183758
5 to 14 141658 -0.8667 0.193066
4 to 13 142087 0.6127 0.729948
3 to 12 141229 -2.3460 0.009489
2 to 11 141704 -0.7080 0.239462
1 to 10 142073 0.5644 0.713752
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_13:31
Bits used No. missing words z-score p-value
28 to 32 141680 -0.7774 0.218464
27 to 31 141789 -0.4079 0.341674
26 to 30 141716 -0.6554 0.256119
25 to 29 141986 0.2599 0.602529
24 to 28 141673 -0.8011 0.211532
23 to 27 142333 1.4362 0.924523
22 to 26 142155 0.8328 0.797516
21 to 25 141710 -0.6757 0.249617
20 to 24 141764 -0.4926 0.311132
19 to 23 141773 -0.4621 0.321992
18 to 22 141772 -0.4655 0.320778
17 to 21 141873 -0.1232 0.450993
16 to 20 142214 1.0328 0.849147
15 to 19 142228 1.0802 0.859982
14 to 18 141634 -0.9333 0.175327
13 to 17 141535 -1.2689 0.102236
12 to 16 142052 0.4836 0.685675
11 to 15 142264 1.2023 0.885371
10 to 14 142067 0.5345 0.703493
9 to 13 141996 0.2938 0.615543
8 to 12 141952 0.1446 0.557504
7 to 11 141874 -0.1198 0.452336
6 to 10 141844 -0.2215 0.412368
5 to 9 141751 -0.5367 0.295733
4 to 8 141178 -2.4791 0.006586
3 to 7 141580 -1.1164 0.132131
2 to 6 142021 0.3785 0.647486
1 to 5 142413 1.7074 0.956122
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_13:31
Bits used No. missing words z-score p-value
31 to 32 141959 0.1465 0.558244
30 to 31 142017 0.3176 0.624610
29 to 30 141462 -1.3196 0.093491
28 to 29 141868 -0.1219 0.451482
27 to 28 142261 1.0374 0.850219
26 to 27 142177 0.7896 0.785116
25 to 26 141431 -1.4110 0.079122
24 to 25 141340 -1.6794 0.046533
23 to 24 141705 -0.6027 0.273340
22 to 23 142383 1.3973 0.918832
21 to 22 141542 -1.0836 0.139278
20 to 21 141083 -2.4376 0.007394
19 to 20 141897 -0.0364 0.485493
18 to 19 142030 0.3560 0.639064
17 to 18 141540 -1.0895 0.137974
16 to 17 142122 0.6273 0.734784
15 to 16 141870 -0.1160 0.453819
14 to 15 141942 0.0964 0.538387
13 to 14 141563 -1.0216 0.153480
12 to 13 142150 0.7099 0.761130
11 to 12 141801 -0.3196 0.374652
10 to 11 141773 -0.4022 0.343786
9 to 10 142292 1.1288 0.870513
8 to 9 141993 0.2468 0.597474
7 to 8 142200 0.8574 0.804397
6 to 7 141980 0.2085 0.582568
5 to 6 141987 0.2291 0.590610
4 to 5 141878 -0.0924 0.463183
3 to 4 141375 -1.5762 0.057490
2 to 3 142231 0.9489 0.828659
1 to 2 142512 1.7778 0.962281
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2506.20 0.088 0.534911
Test results for specific bytes for dh-ranFile-2018-07-07_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2507.21 0.102 0.540585
2 to 9 2457.41 -0.602 0.273490
3 to 10 2505.04 0.071 0.528398
4 to 11 2423.29 -1.085 0.139007
5 to 12 2450.51 -0.700 0.241998
6 to 13 2412.87 -1.232 0.108947
7 to 14 2453.05 -0.664 0.253370
8 to 15 2440.14 -0.847 0.198630
9 to 16 2415.54 -1.194 0.116149
10 to 17 2502.78 0.039 0.515668
11 to 18 2487.52 -0.177 0.429947
12 to 19 2424.41 -1.069 0.142535
13 to 20 2541.09 0.581 0.719402
14 to 21 2541.64 0.589 0.722013
15 to 22 2453.83 -0.653 0.256896
16 to 23 2466.41 -0.475 0.317392
17 to 24 2467.94 -0.453 0.325156
18 to 25 2511.11 0.157 0.562427
19 to 26 2546.38 0.656 0.744071
20 to 27 2615.19 1.629 0.948342
21 to 28 2514.46 0.204 0.580994
22 to 29 2533.79 0.478 0.683623
23 to 30 2518.75 0.265 0.604585
24 to 31 2454.79 -0.639 0.261315
25 to 32 2506.94 0.098 0.539090
CDPARK for dh-ranFile-2018-07-07_13:31: 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
3524 0.0457 0.518210
3500 -1.0502 0.146807
3512 -0.5023 0.307734
3541 0.8219 0.794438
3495 -1.2785 0.100530
3561 1.7352 0.958644
3551 1.2785 0.899470
3512 -0.5023 0.307734
3505 -0.8219 0.205562
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3522.00 sample std.=21.07
p-value of the KSTEST for those 10 p-values: 0.860733
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_13:31
0.8190,0.7843,0.8151,0.4516,0.5567,0.5935,0.1610,0.5785,0.3101,0.4057,
The KS test for those 10 p-values: 0.547823
The 3DSPHERES test for dh-ranFile-2018-07-07_13:31
sample no r^3 equiv. uni.
1 135.319 0.989008
2 8.496 0.246626
3 4.411 0.136742
4 87.237 0.945410
5 8.544 0.247828
6 16.348 0.420125
7 16.080 0.414915
8 16.072 0.414762
9 0.020 0.000682
10 12.601 0.342985
11 38.335 0.721362
12 12.580 0.342508
13 2.156 0.069345
14 20.339 0.492356
15 47.523 0.794869
16 28.675 0.615502
17 51.290 0.819074
18 25.417 0.571395
19 7.604 0.223895
20 4.610 0.142435
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.603683
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 0.1 0.0 -0.1 -1.4
1.7 -1.4 -1.0 -0.3 1.8 -0.1
0.4 -0.6 0.6 -0.6 1.3 0.7
-1.3 -0.5 -0.3 -2.3 -0.0 1.9
1.0 0.8 -0.1 -0.3 0.6 -0.9
-1.0 -0.4 1.4 0.8 1.0 0.4
-1.4 -0.1 0.5 -1.8 -1.3 1.0
0.8
Chi-square with 42 degrees of freedom:43.817915
z-score=0.198351, p-value=0.605697
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_13:31
Test no p-value
1 0.592551
2 0.556025
3 0.623612
4 0.419869
5 0.046086
6 0.243387
7 0.352367
8 0.496754
9 0.667515
10 0.574178
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.321424
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_13:31:
(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 66759 0.13 66623 0.03
3 25000.00 24841 1.01 25046 0.08
4 6666.67 6704 0.21 6681 0.03
5 1388.89 1441 1.96 1350 1.09
6 238.10 217 1.87 251 0.70
7 34.72 32 0.21 41 1.14
8 4.96 5 0.00 7 0.84
p=0.50462 p=0.31079
Number of rngs required: 689138, p-value: 0.802
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_13:31
No. of wins: Observed Expected
98709 98585.9
z-score= 0.551, pvalue=0.70910
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66946 66666.7 1.170 1.170
2 37609 37654.3 0.055 1.225
3 26822 26954.7 0.654 1.879
4 19336 19313.5 0.026 1.905
5 13796 13851.4 0.222 2.127
6 9901 9943.5 0.182 2.309
7 7134 7145.0 0.017 2.326
8 5136 5139.1 0.002 2.327
9 3733 3699.9 0.297 2.624
10 2716 2666.3 0.927 3.551
11 1896 1923.3 0.388 3.939
12 1371 1388.7 0.227 4.166
13 986 1003.7 0.313 4.478
14 724 726.1 0.006 4.485
15 494 525.8 1.927 6.412
16 392 381.2 0.309 6.721
17 256 276.5 1.526 8.246
18 205 200.8 0.087 8.333
19 151 146.0 0.172 8.505
20 98 106.2 0.635 9.141
21 298 287.1 0.413 9.554
Chisq= 9.55 for 20 degrees of freedom, p= 0.02444
SUMMARY of craptest
p-value for no. of wins: 0.709101
p-value for throws/game: 0.024436
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_13:31
No. of wins: Observed Expected
98688 98585.9
z-score= 0.457, pvalue=0.67611
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66716 66666.7 0.037 0.037
2 37500 37654.3 0.632 0.669
3 26995 26954.7 0.060 0.729
4 19378 19313.5 0.216 0.945
5 13901 13851.4 0.177 1.122
6 9985 9943.5 0.173 1.295
7 7223 7145.0 0.851 2.146
8 5105 5139.1 0.226 2.372
9 3563 3699.9 5.063 7.435
10 2679 2666.3 0.061 7.495
11 1897 1923.3 0.360 7.856
12 1418 1388.7 0.616 8.472
13 1002 1003.7 0.003 8.475
14 722 726.1 0.024 8.499
15 591 525.8 8.075 16.574
16 334 381.2 5.833 22.407
17 280 276.5 0.043 22.450
18 207 200.8 0.190 22.640
19 130 146.0 1.750 24.390
20 112 106.2 0.315 24.705
21 262 287.1 2.197 26.902
Chisq= 26.90 for 20 degrees of freedom, p= 0.86195
SUMMARY of craptest
p-value for no. of wins: 0.676106
p-value for throws/game: 0.861954
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0007,0.0066,0.0074,0.0095,0.0152,0.0159,0.0244,0.0248,0.0348,0.0461,
0.0465,0.0575,0.0589,0.0693,0.0707,0.0791,0.0903,0.0904,0.0935,0.0939,
0.1005,0.1022,0.1089,0.1161,0.1208,0.1321,0.1367,0.1380,0.1390,0.1393,
0.1424,0.1425,0.1433,0.1468,0.1479,0.1525,0.1535,0.1570,0.1602,0.1610,
0.1699,0.1753,0.1838,0.1931,0.1986,0.1987,0.2017,0.2056,0.2115,0.2185,
0.2239,0.2265,0.2395,0.2420,0.2434,0.2466,0.2478,0.2496,0.2524,0.2534,
0.2561,0.2569,0.2612,0.2613,0.2668,0.2693,0.2733,0.2735,0.2848,0.2854,
0.2879,0.2952,0.2957,0.3025,0.3034,0.3045,0.3074,0.3077,0.3077,0.3099,
0.3101,0.3106,0.3108,0.3111,0.3174,0.3208,0.3214,0.3220,0.3250,0.3252,
0.3252,0.3300,0.3417,0.3425,0.3430,0.3438,0.3473,0.3524,0.3562,0.3582,
0.3585,0.3665,0.3747,0.3766,0.3768,0.4057,0.4110,0.4124,0.4148,0.4149,
0.4155,0.4176,0.4199,0.4201,0.4267,0.4275,0.4275,0.4299,0.4365,0.4452,
0.4464,0.4510,0.4515,0.4515,0.4516,0.4523,0.4538,0.4556,0.4632,0.4773,
0.4855,0.4924,0.4965,0.4968,0.5046,0.5157,0.5182,0.5268,0.5284,0.5339,
0.5341,0.5349,0.5380,0.5384,0.5391,0.5406,0.5468,0.5478,0.5521,0.5533,
0.5560,0.5564,0.5567,0.5575,0.5582,0.5624,0.5714,0.5716,0.5734,0.5742,
0.5785,0.5802,0.5810,0.5826,0.5830,0.5870,0.5906,0.5926,0.5935,0.5975,
0.5980,0.6025,0.6037,0.6046,0.6057,0.6071,0.6099,0.6117,0.6155,0.6155,
0.6185,0.6236,0.6246,0.6391,0.6475,0.6489,0.6603,0.6664,0.6675,0.6761,
0.6836,0.6857,0.6862,0.6869,0.6953,0.7035,0.7091,0.7104,0.7104,0.7138,
0.7166,0.7194,0.7194,0.7210,0.7214,0.7220,0.7299,0.7318,0.7334,0.7348,
0.7441,0.7534,0.7609,0.7611,0.7694,0.7801,0.7843,0.7851,0.7901,0.7944,
0.7949,0.7975,0.7978,0.8023,0.8034,0.8044,0.8082,0.8151,0.8181,0.8190,
0.8191,0.8287,0.8318,0.8462,0.8491,0.8502,0.8544,0.8600,0.8607,0.8620,
0.8705,0.8836,0.8854,0.8874,0.8900,0.8941,0.8950,0.8995,0.9089,0.9186,
0.9188,0.9245,0.9287,0.9366,0.9451,0.9453,0.9454,0.9475,0.9481,0.9483,
0.9518,0.9561,0.9586,0.9623,0.9662,0.9834,0.9890,0.9975,0.9981,
Overall p-value after applying KStest on 269 p-values = 0.356682
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.