RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.81 16.4567 0.508280
2 to 25 15.94 13.1426 0.273413
3 to 26 15.91 13.9963 0.332639
4 to 27 15.78 18.2590 0.627322
5 to 28 15.55 19.0572 0.674739
6 to 29 15.53 12.8227 0.252031
7 to 30 15.75 20.5738 0.754066
8 to 31 16.03 13.0016 0.263920
9 to 32 15.72 17.9728 0.609440
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.444468
Tough bday spacings test for dh-ranFile-2018-07-06_15:31: 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 43 68 96 98 74 48 34 19 5 3
(O-E)^2/E 0.9 1.1 0.4 0.0 0.0 0.2 0.3 0.6 1.1 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 5.352, p= 0.134
RESULTS OF GCD FOR dh-ranFile-2018-07-06_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.679549
p-value, dist. of gcd's: 0.936432
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.711 0.597 0.854 0.352 0.327 0.619 0.691 0.010
Bits 8 to 15---> 0.091 0.620 0.896 0.139 0.677 0.426 0.420 0.398
Bits 16 to 23---> 0.347 0.650 0.264 0.726 0.642 0.736 0.597 0.790
Bits 24 to 31---> 0.251 0.767 0.327 0.160 0.861 0.891 0.054 0.501
KS test for the above 32 p values: 0.368
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_15:31,
p-values for 5 runs: 0.3972, 0.5326, 0.4739, 0.2908, 0.8549
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 184 211.4 3.556 3.556
r= 29 5129 5134.0 0.005 3.561
r= 30 23268 23103.0 1.178 4.738
r= 31 11419 11551.5 1.520 6.259
chi-square = 6.259 with df = 3; p-value = 0.900
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 5270 5134.0 3.602 4.585
r= 31 23013 23103.0 0.351 4.936
r= 32 11520 11551.5 0.086 5.022
chi-square = 5.022 with df = 3; p-value = 0.830
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_15:31
b-rank test for bits 1 to 8, p=0.71182
b-rank test for bits 2 to 9, p=0.65732
b-rank test for bits 3 to 10, p=0.27192
b-rank test for bits 4 to 11, p=0.67682
b-rank test for bits 5 to 12, p=0.54259
b-rank test for bits 6 to 13, p=0.57359
b-rank test for bits 7 to 14, p=0.17063
b-rank test for bits 8 to 15, p=0.99146
b-rank test for bits 9 to 16, p=0.06605
b-rank test for bits 10 to 17, p=0.23423
b-rank test for bits 11 to 18, p=0.63376
b-rank test for bits 12 to 19, p=0.59563
b-rank test for bits 13 to 20, p=0.78553
b-rank test for bits 14 to 21, p=0.27529
b-rank test for bits 15 to 22, p=0.63120
b-rank test for bits 16 to 23, p=0.77083
b-rank test for bits 17 to 24, p=0.78276
b-rank test for bits 18 to 25, p=0.64666
b-rank test for bits 19 to 26, p=0.62180
b-rank test for bits 20 to 27, p=0.48784
b-rank test for bits 21 to 28, p=0.81772
b-rank test for bits 22 to 29, p=0.95387
b-rank test for bits 23 to 30, p=0.30914
b-rank test for bits 24 to 31, p=0.70521
b-rank test for bits 25 to 32, p=0.96670
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 = 0.099470
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_15:31
(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 141429 -1.12 0.130875
2 142500 1.38 0.916217
3 141580 -0.77 0.220809
4 141696 -0.50 0.309089
5 142016 0.25 0.598408
6 142227 0.74 0.771023
7 142239 0.77 0.779426
8 142405 1.16 0.876590
9 142001 0.21 0.584798
10 141682 -0.53 0.297659
11 142635 1.70 0.955009
12 141817 -0.22 0.414601
13 142819 2.13 0.983223
14 142439 1.24 0.892058
15 141925 0.04 0.514603
16 141784 -0.29 0.384827
17 141855 -0.13 0.449494
18 141969 0.14 0.555439
19 142521 1.43 0.923517
20 141320 -1.38 0.084266
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_15:31
Bits used No. missing words z-score p-value
23 to 32 142125 0.7437 0.771468
22 to 31 141907 -0.0080 0.496795
21 to 30 142125 0.7437 0.771468
20 to 29 142036 0.4368 0.668869
19 to 28 142090 0.6230 0.733358
18 to 27 141026 -3.0460 0.001160
17 to 26 141810 -0.3425 0.365981
16 to 25 141721 -0.6494 0.258036
15 to 24 141358 -1.9011 0.028642
14 to 23 141935 0.0885 0.535267
13 to 22 142202 1.0092 0.843562
12 to 21 142395 1.6747 0.953006
11 to 20 141283 -2.1598 0.015396
10 to 19 142052 0.4920 0.688628
9 to 18 141564 -1.1908 0.116867
8 to 17 142250 1.1747 0.879947
7 to 16 142042 0.4575 0.676338
6 to 15 142050 0.4851 0.686186
5 to 14 141806 -0.3563 0.360804
4 to 13 141177 -2.5253 0.005780
3 to 12 142179 0.9299 0.823788
2 to 11 141713 -0.6770 0.249203
1 to 10 141370 -1.8598 0.031460
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_15:31
Bits used No. missing words z-score p-value
28 to 32 141761 -0.5028 0.307548
27 to 31 142092 0.6192 0.732114
26 to 30 141475 -1.4723 0.070469
25 to 29 142438 1.7921 0.963442
24 to 28 141476 -1.4689 0.070928
23 to 27 141805 -0.3537 0.361797
22 to 26 141376 -1.8079 0.035311
21 to 25 142032 0.4158 0.661233
20 to 24 141432 -1.6181 0.052824
19 to 23 141804 -0.3571 0.360527
18 to 22 142195 0.9684 0.833571
17 to 21 142343 1.4701 0.929228
16 to 20 142093 0.6226 0.733230
15 to 19 141754 -0.5265 0.299256
14 to 18 141790 -0.4045 0.342919
13 to 17 141803 -0.3604 0.359259
12 to 16 142125 0.7311 0.767636
11 to 15 142039 0.4396 0.669872
10 to 14 141931 0.0735 0.529279
9 to 13 141879 -0.1028 0.459056
8 to 12 141466 -1.5028 0.066444
7 to 11 141386 -1.7740 0.038032
6 to 10 141913 0.0124 0.504963
5 to 9 142640 2.4768 0.993373
4 to 8 141817 -0.3130 0.377147
3 to 7 142436 1.7853 0.962895
2 to 6 141747 -0.5503 0.291067
1 to 5 141549 -1.2215 0.110956
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_15:31
Bits used No. missing words z-score p-value
31 to 32 141790 -0.3520 0.362417
30 to 31 142034 0.3678 0.643473
29 to 30 142038 0.3796 0.647863
28 to 29 141538 -1.0954 0.136678
27 to 28 141579 -0.9744 0.164923
26 to 27 142083 0.5123 0.695780
25 to 26 141306 -1.7797 0.037560
24 to 25 141442 -1.3786 0.084016
23 to 24 141813 -0.2842 0.388144
22 to 23 142215 0.9017 0.816387
21 to 22 142201 0.8604 0.805211
20 to 21 141998 0.2616 0.603171
19 to 20 142312 1.1878 0.882547
18 to 19 141971 0.1819 0.572176
17 to 18 142117 0.6126 0.729928
16 to 17 141584 -0.9597 0.168609
15 to 16 142089 0.5300 0.701944
14 to 15 142104 0.5742 0.717100
13 to 14 142003 0.2763 0.608846
12 to 13 141506 -1.1898 0.117070
11 to 12 141807 -0.3019 0.381380
10 to 11 141711 -0.5850 0.279259
9 to 10 142462 1.6303 0.948480
8 to 9 141600 -0.9125 0.180759
7 to 8 141498 -1.2134 0.112496
6 to 7 142366 1.3471 0.911027
5 to 6 142046 0.4032 0.656583
4 to 5 141700 -0.6175 0.268455
3 to 4 141777 -0.3904 0.348137
2 to 3 142057 0.4356 0.668438
1 to 2 141829 -0.2370 0.406343
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2555.51 0.785 0.783767
Test results for specific bytes for dh-ranFile-2018-07-06_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2485.96 -0.199 0.421301
2 to 9 2617.76 1.665 0.952085
3 to 10 2512.72 0.180 0.571391
4 to 11 2505.68 0.080 0.531994
5 to 12 2524.11 0.341 0.633419
6 to 13 2493.36 -0.094 0.462611
7 to 14 2489.21 -0.153 0.439336
8 to 15 2579.87 1.130 0.870671
9 to 16 2556.66 0.801 0.788537
10 to 17 2512.03 0.170 0.567549
11 to 18 2505.29 0.075 0.529807
12 to 19 2421.24 -1.114 0.132688
13 to 20 2585.72 1.212 0.887307
14 to 21 2574.31 1.051 0.853334
15 to 22 2499.97 -0.000 0.499857
16 to 23 2405.31 -1.339 0.090265
17 to 24 2356.45 -2.030 0.021176
18 to 25 2483.34 -0.236 0.406891
19 to 26 2623.45 1.746 0.959579
20 to 27 2501.80 0.026 0.510177
21 to 28 2499.86 -0.002 0.499187
22 to 29 2563.32 0.896 0.814753
23 to 30 2535.49 0.502 0.692143
24 to 31 2322.55 -2.510 0.006044
25 to 32 2551.22 0.724 0.765568
CDPARK for dh-ranFile-2018-07-06_15:31: 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
3526 0.1370 0.554479
3501 -1.0046 0.157553
3531 0.3653 0.642555
3535 0.5479 0.708135
3524 0.0457 0.518210
3536 0.5936 0.723613
3565 1.9178 0.972432
3544 0.9589 0.831196
3510 -0.5936 0.276387
3536 0.5936 0.723613
Square side=100, avg. no. parked=3530.80 sample std.=16.75
p-value of the KSTEST for those 10 p-values: 0.326667
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_15:31
0.3131,0.9395,0.4666,0.8102,0.6351,0.4758,0.8697,0.3612,0.4597,0.5911,
The KS test for those 10 p-values: 0.350855
The 3DSPHERES test for dh-ranFile-2018-07-06_15:31
sample no r^3 equiv. uni.
1 3.176 0.100450
2 0.495 0.016349
3 5.966 0.180353
4 35.590 0.694658
5 34.590 0.684313
6 14.817 0.389749
7 21.417 0.510277
8 35.602 0.694786
9 35.039 0.689004
10 75.513 0.919308
11 21.888 0.517906
12 26.041 0.580230
13 2.628 0.083871
14 30.829 0.642147
15 17.661 0.444946
16 3.385 0.106713
17 9.211 0.264373
18 71.551 0.907915
19 50.637 0.815093
20 2.831 0.090065
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.721868
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.6 0.3 0.5 -0.4 -0.7
-1.3 -1.4 1.3 -0.0 1.5 0.7
-0.9 1.4 -0.4 -0.0 -0.9 -0.4
-1.6 -0.6 0.7 1.2 1.4 -0.5
-0.3 -0.6 0.5 0.2 0.2 0.2
0.5 0.4 0.5 -0.3 -1.0 -0.1
-0.7 -1.7 1.3 1.5 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:34.756919
z-score=-0.790285, p-value=0.221542
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_15:31
Test no p-value
1 0.289928
2 0.014799
3 0.036242
4 0.449852
5 0.166597
6 0.398387
7 0.268280
8 0.209416
9 0.000008
10 0.839573
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004448
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_15:31:
(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 66891 0.75 66566 0.15
3 25000.00 24876 0.62 24995 0.00
4 6666.67 6575 1.26 6762 1.36
5 1388.89 1396 0.04 1390 0.00
6 238.10 227 0.52 248 0.41
7 34.72 31 0.40 36 0.05
8 4.96 3 0.77 2 1.77
p=0.37151 p=0.28856
Number of rngs required: 688795, p-value: 0.674
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_15:31
No. of wins: Observed Expected
98555 98585.9
z-score=-0.138, pvalue=0.44511
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66647 66666.7 0.006 0.006
2 37682 37654.3 0.020 0.026
3 26923 26954.7 0.037 0.064
4 19083 19313.5 2.750 2.814
5 13883 13851.4 0.072 2.886
6 10074 9943.5 1.712 4.597
7 7168 7145.0 0.074 4.671
8 5119 5139.1 0.078 4.749
9 3728 3699.9 0.214 4.963
10 2648 2666.3 0.126 5.089
11 1859 1923.3 2.152 7.240
12 1420 1388.7 0.704 7.944
13 1071 1003.7 4.511 12.455
14 754 726.1 1.069 13.523
15 528 525.8 0.009 13.532
16 367 381.2 0.525 14.058
17 281 276.5 0.072 14.130
18 196 200.8 0.116 14.246
19 160 146.0 1.346 15.591
20 111 106.2 0.216 15.807
21 298 287.1 0.413 16.220
Chisq= 16.22 for 20 degrees of freedom, p= 0.29710
SUMMARY of craptest
p-value for no. of wins: 0.445113
p-value for throws/game: 0.297099
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_15:31
No. of wins: Observed Expected
98482 98585.9
z-score=-0.465, pvalue=0.32114
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66917 66666.7 0.940 0.940
2 37528 37654.3 0.424 1.364
3 26994 26954.7 0.057 1.421
4 19311 19313.5 0.000 1.421
5 13832 13851.4 0.027 1.449
6 9921 9943.5 0.051 1.500
7 7264 7145.0 1.981 3.481
8 4975 5139.1 5.238 8.719
9 3683 3699.9 0.077 8.796
10 2693 2666.3 0.267 9.063
11 1889 1923.3 0.613 9.676
12 1355 1388.7 0.820 10.496
13 997 1003.7 0.045 10.541
14 726 726.1 0.000 10.541
15 513 525.8 0.313 10.854
16 394 381.2 0.433 11.287
17 268 276.5 0.264 11.551
18 185 200.8 1.248 12.799
19 160 146.0 1.346 14.144
20 112 106.2 0.315 14.459
21 283 287.1 0.059 14.518
Chisq= 14.52 for 20 degrees of freedom, p= 0.19672
SUMMARY of craptest
p-value for no. of wins: 0.321139
p-value for throws/game: 0.196721
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0012,0.0044,0.0058,0.0060,0.0101,0.0148,0.0154,0.0163,0.0212,
0.0286,0.0315,0.0353,0.0362,0.0376,0.0380,0.0528,0.0544,0.0661,0.0664,
0.0705,0.0709,0.0839,0.0840,0.0843,0.0901,0.0903,0.0913,0.0995,0.1005,
0.1067,0.1110,0.1125,0.1169,0.1171,0.1309,0.1327,0.1336,0.1367,0.1386,
0.1576,0.1602,0.1649,0.1666,0.1686,0.1706,0.1804,0.1808,0.1967,0.2094,
0.2208,0.2215,0.2342,0.2492,0.2509,0.2520,0.2580,0.2639,0.2643,0.2644,
0.2683,0.2685,0.2719,0.2734,0.2753,0.2764,0.2793,0.2886,0.2899,0.2908,
0.2911,0.2971,0.2977,0.2993,0.3075,0.3091,0.3091,0.3131,0.3211,0.3267,
0.3271,0.3274,0.3326,0.3429,0.3472,0.3481,0.3509,0.3523,0.3593,0.3605,
0.3608,0.3612,0.3618,0.3624,0.3660,0.3684,0.3715,0.3771,0.3814,0.3848,
0.3881,0.3897,0.3972,0.3978,0.3984,0.4063,0.4069,0.4146,0.4205,0.4213,
0.4263,0.4393,0.4445,0.4449,0.4451,0.4495,0.4499,0.4591,0.4597,0.4626,
0.4666,0.4739,0.4758,0.4878,0.4968,0.4992,0.4999,0.5006,0.5050,0.5083,
0.5102,0.5103,0.5146,0.5179,0.5182,0.5293,0.5298,0.5320,0.5326,0.5353,
0.5426,0.5545,0.5554,0.5675,0.5714,0.5722,0.5736,0.5802,0.5848,0.5911,
0.5956,0.5971,0.5974,0.5984,0.6032,0.6088,0.6094,0.6185,0.6197,0.6218,
0.6273,0.6312,0.6334,0.6338,0.6351,0.6421,0.6421,0.6426,0.6435,0.6467,
0.6479,0.6503,0.6566,0.6573,0.6612,0.6684,0.6689,0.6699,0.6742,0.6747,
0.6763,0.6767,0.6768,0.6795,0.6843,0.6862,0.6886,0.6890,0.6908,0.6921,
0.6947,0.6948,0.6958,0.7019,0.7052,0.7081,0.7115,0.7118,0.7171,0.7219,
0.7236,0.7236,0.7265,0.7299,0.7321,0.7332,0.7334,0.7363,0.7541,0.7656,
0.7671,0.7676,0.7708,0.7710,0.7715,0.7715,0.7794,0.7828,0.7838,0.7855,
0.7885,0.7903,0.8052,0.8102,0.8148,0.8151,0.8164,0.8177,0.8238,0.8298,
0.8312,0.8336,0.8396,0.8436,0.8533,0.8540,0.8549,0.8607,0.8697,0.8707,
0.8766,0.8799,0.8825,0.8873,0.8914,0.8921,0.8959,0.9003,0.9079,0.9110,
0.9162,0.9193,0.9235,0.9292,0.9364,0.9395,0.9485,0.9521,0.9530,0.9539,
0.9550,0.9596,0.9629,0.9634,0.9667,0.9724,0.9832,0.9915,0.9934,
Overall p-value after applying KStest on 269 p-values = 0.419527
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.