RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.61 14.4847 0.367455
2 to 25 15.81 16.4233 0.505950
3 to 26 15.69 21.2831 0.786118
4 to 27 15.75 18.3177 0.630935
5 to 28 15.80 15.8987 0.468971
6 to 29 15.69 15.7438 0.457932
7 to 30 15.85 18.8632 0.663558
8 to 31 15.57 20.8702 0.767851
9 to 32 15.69 32.7695 0.987946
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.198929
Tough bday spacings test for dh-ranFile-2018-06-26_11:31: 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 7 41 86 85 80 81 52 37 17 10 4
(O-E)^2/E 0.5 0.5 2.2 1.6 3.2 0.1 0.0 1.8 0.3 1.7 0.0
Birthday Spacings: Sum(O-E)^2/E= 11.985, p= 0.714
RESULTS OF GCD FOR dh-ranFile-2018-06-26_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.925907
p-value, dist. of gcd's: 0.694299
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.965 0.646 0.546 0.358 0.015 0.232 0.934 0.742
Bits 8 to 15---> 0.169 0.690 0.218 0.575 0.420 0.413 0.377 0.083
Bits 16 to 23---> 0.021 0.099 0.929 0.881 0.629 0.998 0.921 0.494
Bits 24 to 31---> 0.060 0.101 0.774 0.105 0.228 0.748 0.779 0.018
KS test for the above 32 p values: 0.597
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_11:31,
p-values for 5 runs: 0.9711, 0.7945, 0.9313, 0.8065, 0.4950
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5166 5134.0 0.199 0.404
r= 30 23026 23103.0 0.257 0.661
r= 31 11590 11551.5 0.128 0.789
chi-square = 0.789 with df = 3; p-value = 0.148
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5144 5134.0 0.019 0.031
r= 31 22923 23103.0 1.403 1.434
r= 32 11720 11551.5 2.457 3.892
chi-square = 3.892 with df = 3; p-value = 0.727
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_11:31
b-rank test for bits 1 to 8, p=0.50553
b-rank test for bits 2 to 9, p=0.63365
b-rank test for bits 3 to 10, p=0.20070
b-rank test for bits 4 to 11, p=0.21043
b-rank test for bits 5 to 12, p=0.95077
b-rank test for bits 6 to 13, p=0.74435
b-rank test for bits 7 to 14, p=0.19044
b-rank test for bits 8 to 15, p=0.61647
b-rank test for bits 9 to 16, p=0.06922
b-rank test for bits 10 to 17, p=0.94087
b-rank test for bits 11 to 18, p=0.85507
b-rank test for bits 12 to 19, p=0.95648
b-rank test for bits 13 to 20, p=0.69741
b-rank test for bits 14 to 21, p=0.87842
b-rank test for bits 15 to 22, p=0.79555
b-rank test for bits 16 to 23, p=0.22548
b-rank test for bits 17 to 24, p=0.81588
b-rank test for bits 18 to 25, p=0.43555
b-rank test for bits 19 to 26, p=0.97965
b-rank test for bits 20 to 27, p=0.18767
b-rank test for bits 21 to 28, p=0.57500
b-rank test for bits 22 to 29, p=0.47430
b-rank test for bits 23 to 30, p=0.14424
b-rank test for bits 24 to 31, p=0.34112
b-rank test for bits 25 to 32, p=0.30172
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 = 0.566975
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_11:31
(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 141781 -0.30 0.382151
2 141979 0.16 0.564654
3 142146 0.55 0.709857
4 142010 0.24 0.592977
5 142257 0.81 0.791694
6 141909 -0.00 0.499692
7 142573 1.55 0.939505
8 141384 -1.23 0.109835
9 141312 -1.40 0.081413
10 141448 -1.08 0.140545
11 141847 -0.15 0.442106
12 141452 -1.07 0.142641
13 142523 1.43 0.924187
14 141859 -0.12 0.453195
15 142305 0.92 0.822377
16 142096 0.44 0.668634
17 141710 -0.47 0.320706
18 141491 -0.98 0.164184
19 141529 -0.89 0.187103
20 141787 -0.29 0.387509
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_11:31
Bits used No. missing words z-score p-value
23 to 32 141884 -0.0873 0.465199
22 to 31 141552 -1.2322 0.108942
21 to 30 141871 -0.1322 0.447424
20 to 29 141664 -0.8460 0.198786
19 to 28 142023 0.3920 0.652458
18 to 27 141824 -0.2942 0.384287
17 to 26 141808 -0.3494 0.363389
16 to 25 141987 0.2678 0.605584
15 to 24 142103 0.6678 0.747878
14 to 23 142013 0.3575 0.639635
13 to 22 141722 -0.6460 0.259151
12 to 21 141769 -0.4839 0.314230
11 to 20 142619 2.4471 0.992800
10 to 19 141773 -0.4701 0.319141
9 to 18 141964 0.1885 0.574764
8 to 17 141913 0.0127 0.505049
7 to 16 141643 -0.9184 0.179210
6 to 15 142251 1.1782 0.880636
5 to 14 141869 -0.1391 0.444698
4 to 13 142051 0.4885 0.687408
3 to 12 141587 -1.1115 0.133180
2 to 11 141701 -0.7184 0.236262
1 to 10 141780 -0.4460 0.327811
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_11:31
Bits used No. missing words z-score p-value
28 to 32 142157 0.8396 0.799422
27 to 31 141703 -0.6994 0.242144
26 to 30 142097 0.6362 0.737667
25 to 29 141214 -2.3571 0.009210
24 to 28 141044 -2.9333 0.001677
23 to 27 141842 -0.2282 0.409731
22 to 26 142214 1.0328 0.849147
21 to 25 141769 -0.4757 0.317146
20 to 24 142176 0.9040 0.816993
19 to 23 142032 0.4158 0.661233
18 to 22 141810 -0.3367 0.368167
17 to 21 142155 0.8328 0.797516
16 to 20 141792 -0.3977 0.345415
15 to 19 141651 -0.8757 0.190598
14 to 18 141818 -0.3096 0.378435
13 to 17 141995 0.2904 0.614248
12 to 16 141890 -0.0655 0.473878
11 to 15 142052 0.4836 0.685675
10 to 14 141928 0.0633 0.525232
9 to 13 142015 0.3582 0.639905
8 to 12 142310 1.3582 0.912800
7 to 11 141768 -0.4791 0.315939
6 to 10 142106 0.6667 0.747511
5 to 9 141813 -0.3265 0.372007
4 to 8 141577 -1.1265 0.129968
3 to 7 141930 0.0701 0.527930
2 to 6 141857 -0.1774 0.429601
1 to 5 142099 0.6429 0.739872
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_11:31
Bits used No. missing words z-score p-value
31 to 32 141524 -1.1367 0.127839
30 to 31 141978 0.2026 0.580263
29 to 30 142205 0.8722 0.808446
28 to 29 142652 2.1908 0.985766
27 to 28 141897 -0.0364 0.485493
26 to 27 142169 0.7660 0.778158
25 to 26 141461 -1.3225 0.093000
24 to 25 142081 0.5064 0.693713
23 to 24 141471 -1.2930 0.098004
22 to 23 142354 1.3117 0.905191
21 to 22 141390 -1.5319 0.062768
20 to 21 141843 -0.1957 0.422437
19 to 20 142151 0.7129 0.762043
18 to 19 141479 -1.2694 0.102147
17 to 18 141897 -0.0364 0.485493
16 to 17 141635 -0.8092 0.209191
15 to 16 141762 -0.4346 0.331926
14 to 15 142146 0.6981 0.757456
13 to 14 141583 -0.9626 0.167868
12 to 13 141875 -0.1013 0.459669
11 to 12 141507 -1.1868 0.117650
10 to 11 142346 1.2881 0.901147
9 to 10 141571 -0.9980 0.159134
8 to 9 142148 0.7040 0.759297
7 to 8 142035 0.3707 0.644573
6 to 7 142831 2.7188 0.996724
5 to 6 141929 0.0580 0.523135
4 to 5 141842 -0.1986 0.421283
3 to 4 142300 1.1524 0.875426
2 to 3 142350 1.2999 0.903184
1 to 2 141776 -0.3933 0.347048
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2407.87 -1.303 0.096294
Test results for specific bytes for dh-ranFile-2018-06-26_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2517.78 0.251 0.599269
2 to 9 2534.39 0.486 0.686625
3 to 10 2533.04 0.467 0.679820
4 to 11 2525.32 0.358 0.639880
5 to 12 2491.55 -0.120 0.452431
6 to 13 2544.95 0.636 0.737491
7 to 14 2504.45 0.063 0.525110
8 to 15 2460.70 -0.556 0.289170
9 to 16 2464.32 -0.505 0.306932
10 to 17 2426.40 -1.041 0.148961
11 to 18 2550.38 0.713 0.761932
12 to 19 2471.81 -0.399 0.345059
13 to 20 2502.11 0.030 0.511888
14 to 21 2504.10 0.058 0.523136
15 to 22 2412.44 -1.238 0.107792
16 to 23 2444.61 -0.783 0.216706
17 to 24 2475.47 -0.347 0.364355
18 to 25 2485.52 -0.205 0.418885
19 to 26 2467.95 -0.453 0.325205
20 to 27 2442.49 -0.813 0.208022
21 to 28 2416.65 -1.179 0.119240
22 to 29 2495.66 -0.061 0.475551
23 to 30 2469.61 -0.430 0.333692
24 to 31 2462.73 -0.527 0.299058
25 to 32 2514.51 0.205 0.581298
CDPARK for dh-ranFile-2018-06-26_11:31: 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
3560 1.6895 0.954438
3516 -0.3196 0.374623
3514 -0.4110 0.340551
3486 -1.6895 0.045562
3494 -1.3242 0.092718
3533 0.4566 0.676028
3548 1.1416 0.873180
3530 0.3196 0.625377
3570 2.1461 0.984068
3548 1.1416 0.873180
Square side=100, avg. no. parked=3529.90 sample std.=26.16
p-value of the KSTEST for those 10 p-values: 0.361126
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_11:31
0.0647,0.0436,0.8553,0.6505,0.8146,0.5213,0.2539,0.0523,0.8716,0.0807,
The KS test for those 10 p-values: 0.200045
The 3DSPHERES test for dh-ranFile-2018-06-26_11:31
sample no r^3 equiv. uni.
1 1.131 0.036985
2 3.361 0.105974
3 26.693 0.589251
4 24.788 0.562316
5 9.158 0.263077
6 80.403 0.931444
7 77.918 0.925524
8 48.915 0.804170
9 5.300 0.161933
10 53.039 0.829323
11 11.166 0.310786
12 55.214 0.841257
13 23.123 0.537349
14 0.016 0.000544
15 28.923 0.618668
16 6.861 0.204445
17 5.850 0.177167
18 10.913 0.304939
19 7.843 0.230047
20 74.022 0.915194
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.567152
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 -0.1 0.9 0.1 0.8
-1.2 -1.7 1.1 -0.8 1.2 0.1
0.5 -0.5 -0.2 1.4 1.6 -0.0
-0.6 -1.4 -1.1 0.3 0.2 1.3
0.3 0.5 -1.0 -0.3 -1.7 -1.3
-0.6 0.8 -1.7 -0.8 -1.2 0.1
-1.2 -1.0 1.7 0.4 -0.6 2.0
-0.1
Chi-square with 42 degrees of freedom:42.086352
z-score=0.009422, p-value=0.532766
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_11:31
Test no p-value
1 0.011873
2 0.118047
3 0.834752
4 0.410623
5 0.214891
6 0.181345
7 0.051744
8 0.002718
9 0.099556
10 0.800097
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004825
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_11:31:
(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 66638 0.01 66353 1.48
3 25000.00 25065 0.17 25295 3.48
4 6666.67 6601 0.65 6610 0.48
5 1388.89 1443 2.11 1442 2.03
6 238.10 210 3.32 246 0.26
7 34.72 34 0.01 49 5.87
8 4.96 8 1.86 4 0.19
p=0.77124 p=0.96794
Number of rngs required: 689780, p-value: 0.947
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_11:31
No. of wins: Observed Expected
98761 98585.9
z-score= 0.783, pvalue=0.78328
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67169 66666.7 3.785 3.785
2 37618 37654.3 0.035 3.820
3 26963 26954.7 0.003 3.823
4 18938 19313.5 7.299 11.122
5 13803 13851.4 0.169 11.291
6 9979 9943.5 0.126 11.417
7 7127 7145.0 0.045 11.463
8 5172 5139.1 0.211 11.674
9 3715 3699.9 0.062 11.736
10 2714 2666.3 0.853 12.589
11 1889 1923.3 0.613 13.202
12 1361 1388.7 0.554 13.756
13 995 1003.7 0.076 13.832
14 711 726.1 0.316 14.148
15 486 525.8 3.018 17.165
16 387 381.2 0.090 17.255
17 274 276.5 0.023 17.278
18 199 200.8 0.017 17.295
19 138 146.0 0.437 17.732
20 102 106.2 0.167 17.899
21 260 287.1 2.561 20.460
Chisq= 20.46 for 20 degrees of freedom, p= 0.57047
SUMMARY of craptest
p-value for no. of wins: 0.783285
p-value for throws/game: 0.570475
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_11:31
No. of wins: Observed Expected
98896 98585.9
z-score= 1.387, pvalue=0.91730
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67011 66666.7 1.778 1.778
2 37417 37654.3 1.496 3.274
3 26845 26954.7 0.447 3.721
4 19284 19313.5 0.045 3.766
5 13638 13851.4 3.288 7.054
6 10007 9943.5 0.405 7.459
7 7136 7145.0 0.011 7.471
8 5228 5139.1 1.539 9.009
9 3758 3699.9 0.913 9.923
10 2715 2666.3 0.890 10.812
11 1946 1923.3 0.267 11.080
12 1381 1388.7 0.043 11.123
13 977 1003.7 0.711 11.834
14 756 726.1 1.228 13.062
15 532 525.8 0.072 13.134
16 363 381.2 0.864 13.998
17 247 276.5 3.155 17.154
18 204 200.8 0.050 17.204
19 144 146.0 0.027 17.231
20 121 106.2 2.058 19.289
21 290 287.1 0.029 19.318
Chisq= 19.32 for 20 degrees of freedom, p= 0.49873
SUMMARY of craptest
p-value for no. of wins: 0.917299
p-value for throws/game: 0.498731
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0017,0.0027,0.0048,0.0092,0.0119,0.0147,0.0177,0.0209,0.0370,
0.0436,0.0456,0.0517,0.0523,0.0595,0.0628,0.0647,0.0692,0.0807,0.0814,
0.0831,0.0927,0.0930,0.0963,0.0980,0.0987,0.0996,0.1006,0.1021,0.1051,
0.1060,0.1078,0.1089,0.1098,0.1177,0.1180,0.1192,0.1278,0.1300,0.1332,
0.1405,0.1426,0.1442,0.1480,0.1490,0.1591,0.1619,0.1642,0.1679,0.1687,
0.1772,0.1792,0.1813,0.1871,0.1877,0.1904,0.1906,0.1988,0.1989,0.2000,
0.2007,0.2044,0.2080,0.2092,0.2104,0.2149,0.2167,0.2178,0.2255,0.2279,
0.2300,0.2320,0.2363,0.2421,0.2539,0.2592,0.2631,0.2892,0.2991,0.3017,
0.3049,0.3069,0.3108,0.3142,0.3159,0.3171,0.3191,0.3207,0.3252,0.3278,
0.3319,0.3337,0.3406,0.3411,0.3451,0.3454,0.3470,0.3576,0.3611,0.3634,
0.3644,0.3675,0.3682,0.3720,0.3746,0.3765,0.3784,0.3822,0.3843,0.3875,
0.4097,0.4106,0.4125,0.4189,0.4196,0.4213,0.4224,0.4296,0.4355,0.4421,
0.4447,0.4474,0.4524,0.4532,0.4579,0.4597,0.4652,0.4690,0.4739,0.4743,
0.4756,0.4855,0.4855,0.4944,0.4950,0.4987,0.4997,0.5050,0.5055,0.5060,
0.5119,0.5213,0.5231,0.5231,0.5251,0.5252,0.5279,0.5328,0.5373,0.5456,
0.5623,0.5647,0.5670,0.5672,0.5705,0.5747,0.5748,0.5750,0.5803,0.5813,
0.5893,0.5930,0.5974,0.5993,0.6056,0.6142,0.6165,0.6187,0.6254,0.6293,
0.6309,0.6336,0.6396,0.6399,0.6399,0.6446,0.6456,0.6505,0.6525,0.6612,
0.6636,0.6686,0.6760,0.6798,0.6857,0.6866,0.6874,0.6902,0.6937,0.6943,
0.6974,0.7099,0.7139,0.7266,0.7375,0.7377,0.7399,0.7416,0.7444,0.7475,
0.7479,0.7483,0.7575,0.7593,0.7619,0.7620,0.7679,0.7712,0.7735,0.7782,
0.7790,0.7833,0.7861,0.7917,0.7945,0.7955,0.7975,0.7994,0.8001,0.8042,
0.8065,0.8084,0.8146,0.8159,0.8170,0.8224,0.8293,0.8348,0.8413,0.8491,
0.8551,0.8553,0.8716,0.8732,0.8732,0.8754,0.8784,0.8806,0.8811,0.9011,
0.9032,0.9052,0.9128,0.9152,0.9173,0.9205,0.9242,0.9255,0.9259,0.9290,
0.9313,0.9314,0.9336,0.9395,0.9409,0.9465,0.9508,0.9544,0.9565,0.9655,
0.9679,0.9711,0.9797,0.9841,0.9858,0.9879,0.9928,0.9967,0.9977,
Overall p-value after applying KStest on 269 p-values = 0.968324
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.