RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_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 15.69 25.0823 0.907117
2 to 25 15.75 18.3307 0.631730
3 to 26 16.02 15.7440 0.457949
4 to 27 15.83 24.1440 0.884425
5 to 28 16.01 24.9922 0.905115
6 to 29 15.57 15.8029 0.462148
7 to 30 15.55 18.7930 0.659456
8 to 31 15.73 15.7487 0.458285
9 to 32 15.76 15.1975 0.418743
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.142276
Tough bday spacings test for dh-ranFile-2018-06-16_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 8 38 80 105 98 59 54 31 13 9 5
(O-E)^2/E 0.1 0.1 0.6 0.5 0.0 4.7 0.1 0.1 0.2 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 7.490, p= 0.322
RESULTS OF GCD FOR dh-ranFile-2018-06-16_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.061543
p-value, dist. of gcd's: 0.342810
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.400 0.531 0.586 0.509 0.468 0.951 0.154 0.089
Bits 8 to 15---> 0.791 0.143 0.310 0.059 0.467 0.001 0.876 0.100
Bits 16 to 23---> 0.102 0.387 0.723 0.383 0.052 0.985 0.039 0.072
Bits 24 to 31---> 0.511 0.552 0.762 0.271 0.857 0.378 0.530 0.122
KS test for the above 32 p values: 0.907
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_11:31,
p-values for 5 runs: 0.0194, 0.8057, 0.7396, 0.5093, 0.6750
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 189 211.4 2.377 2.377
r= 29 5223 5134.0 1.542 3.920
r= 30 23080 23103.0 0.023 3.943
r= 31 11508 11551.5 0.164 4.107
chi-square = 4.107 with df = 3; p-value = 0.750
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 192 211.4 1.783 1.783
r= 30 5118 5134.0 0.050 1.833
r= 31 23127 23103.0 0.025 1.858
r= 32 11563 11551.5 0.011 1.870
chi-square = 1.870 with df = 3; p-value = 0.400
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_11:31
b-rank test for bits 1 to 8, p=0.52326
b-rank test for bits 2 to 9, p=0.68006
b-rank test for bits 3 to 10, p=0.22020
b-rank test for bits 4 to 11, p=0.22014
b-rank test for bits 5 to 12, p=0.15220
b-rank test for bits 6 to 13, p=0.73577
b-rank test for bits 7 to 14, p=0.11177
b-rank test for bits 8 to 15, p=0.45241
b-rank test for bits 9 to 16, p=0.88946
b-rank test for bits 10 to 17, p=0.62784
b-rank test for bits 11 to 18, p=0.30537
b-rank test for bits 12 to 19, p=0.84163
b-rank test for bits 13 to 20, p=0.34452
b-rank test for bits 14 to 21, p=0.09026
b-rank test for bits 15 to 22, p=0.33325
b-rank test for bits 16 to 23, p=0.56416
b-rank test for bits 17 to 24, p=0.10078
b-rank test for bits 18 to 25, p=0.79333
b-rank test for bits 19 to 26, p=0.17211
b-rank test for bits 20 to 27, p=0.25709
b-rank test for bits 21 to 28, p=0.89681
b-rank test for bits 22 to 29, p=0.52826
b-rank test for bits 23 to 30, p=0.82650
b-rank test for bits 24 to 31, p=0.60994
b-rank test for bits 25 to 32, p=0.35749
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 = 0.722377
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_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 141380 -1.24 0.108090
2 141802 -0.25 0.400996
3 141830 -0.19 0.426477
4 141235 -1.58 0.057566
5 142007 0.23 0.590255
6 142067 0.37 0.643708
7 141769 -0.33 0.371504
8 141760 -0.35 0.363582
9 142031 0.28 0.611900
10 142181 0.63 0.737202
11 141717 -0.45 0.326583
12 142281 0.87 0.807409
13 142000 0.21 0.583886
14 141438 -1.10 0.135396
15 142031 0.28 0.611900
16 142257 0.81 0.791694
17 141907 -0.01 0.497828
18 142092 0.43 0.665237
19 141781 -0.30 0.382151
20 142264 0.83 0.796354
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_11:31
Bits used No. missing words z-score p-value
23 to 32 142412 1.7333 0.958483
22 to 31 142200 1.0023 0.841903
21 to 30 141848 -0.2115 0.416255
20 to 29 141785 -0.4287 0.334062
19 to 28 141896 -0.0460 0.481669
18 to 27 141458 -1.5563 0.059817
17 to 26 142982 3.6989 0.999892
16 to 25 141477 -1.4908 0.068008
15 to 24 142064 0.5333 0.703103
14 to 23 142402 1.6989 0.955327
13 to 22 141460 -1.5494 0.060641
12 to 21 142065 0.5368 0.704295
11 to 20 142138 0.7885 0.784803
10 to 19 141823 -0.2977 0.382970
9 to 18 142284 1.2920 0.901815
8 to 17 141509 -1.3804 0.083724
7 to 16 141420 -1.6873 0.045769
6 to 15 141373 -1.8494 0.032199
5 to 14 142133 0.7713 0.779728
4 to 13 142550 2.2092 0.986420
3 to 12 141557 -1.2149 0.112196
2 to 11 141838 -0.2460 0.402855
1 to 10 142076 0.5747 0.717261
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_11:31
Bits used No. missing words z-score p-value
28 to 32 142011 0.3446 0.634819
27 to 31 141636 -0.9265 0.177082
26 to 30 141744 -0.5604 0.287589
25 to 29 141481 -1.4520 0.073256
24 to 28 141999 0.3040 0.619423
23 to 27 141779 -0.4418 0.329318
22 to 26 142106 0.6667 0.747511
21 to 25 141532 -1.2791 0.100434
20 to 24 142345 1.4768 0.930142
19 to 23 141780 -0.4384 0.330546
18 to 22 141808 -0.3435 0.365614
17 to 21 141650 -0.8791 0.189678
16 to 20 141865 -0.1503 0.440275
15 to 19 142607 2.3650 0.990985
14 to 18 142172 0.8904 0.813376
13 to 17 142138 0.7752 0.780875
12 to 16 141774 -0.4587 0.323208
11 to 15 142374 1.5752 0.942389
10 to 14 142063 0.5209 0.698787
9 to 13 141365 -1.8452 0.032505
8 to 12 141666 -0.8248 0.204729
7 to 11 142175 0.9006 0.816093
6 to 10 141624 -0.9672 0.166717
5 to 9 141741 -0.5706 0.284132
4 to 8 142088 0.6057 0.727630
3 to 7 141711 -0.6723 0.250695
2 to 6 142136 0.7684 0.778867
1 to 5 142494 1.9819 0.976257
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_11:31
Bits used No. missing words z-score p-value
31 to 32 141717 -0.5673 0.285240
30 to 31 141858 -0.1514 0.439824
29 to 30 141656 -0.7473 0.227445
28 to 29 141967 0.1701 0.567541
27 to 28 142736 2.4386 0.992627
26 to 27 141994 0.2498 0.598615
25 to 26 141854 -0.1632 0.435174
24 to 25 141792 -0.3461 0.364632
23 to 24 141998 0.2616 0.603171
22 to 23 142076 0.4917 0.688517
21 to 22 141120 -2.3284 0.009945
20 to 21 141442 -1.3786 0.084016
19 to 20 142108 0.5860 0.721078
18 to 19 142174 0.7807 0.782522
17 to 18 141354 -1.6381 0.050696
16 to 17 142215 0.9017 0.816387
15 to 16 142085 0.5182 0.697841
14 to 15 142041 0.3884 0.651143
13 to 14 141842 -0.1986 0.421283
12 to 13 142154 0.7217 0.764773
11 to 12 142273 1.0728 0.858314
10 to 11 142408 1.4710 0.929355
9 to 10 142564 1.9312 0.973270
8 to 9 142145 0.6952 0.756532
7 to 8 142373 1.3678 0.914306
6 to 7 141189 -2.1249 0.016799
5 to 6 142105 0.5772 0.718097
4 to 5 141955 0.1347 0.553583
3 to 4 142498 1.7365 0.958761
2 to 3 142226 0.9341 0.824882
1 to 2 141756 -0.4523 0.325526
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2485.31 -0.208 0.417734
Test results for specific bytes for dh-ranFile-2018-06-16_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2484.24 -0.223 0.411816
2 to 9 2315.45 -2.610 0.004528
3 to 10 2508.47 0.120 0.547651
4 to 11 2553.44 0.756 0.775094
5 to 12 2657.11 2.222 0.986855
6 to 13 2478.23 -0.308 0.379108
7 to 14 2495.21 -0.068 0.472989
8 to 15 2634.55 1.903 0.971472
9 to 16 2474.66 -0.358 0.360012
10 to 17 2553.27 0.753 0.774375
11 to 18 2586.65 1.225 0.889799
12 to 19 2422.31 -1.099 0.135949
13 to 20 2606.65 1.508 0.934263
14 to 21 2498.78 -0.017 0.493093
15 to 22 2461.27 -0.548 0.291935
16 to 23 2496.25 -0.053 0.478838
17 to 24 2479.24 -0.294 0.384520
18 to 25 2504.57 0.065 0.525783
19 to 26 2524.33 0.344 0.634605
20 to 27 2442.96 -0.807 0.209922
21 to 28 2346.81 -2.167 0.015136
22 to 29 2578.99 1.117 0.868023
23 to 30 2452.18 -0.676 0.249450
24 to 31 2429.87 -0.992 0.160641
25 to 32 2515.74 0.223 0.588065
CDPARK for dh-ranFile-2018-06-16_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
3533 0.4566 0.676028
3543 0.9132 0.819442
3488 -1.5982 0.055002
3515 -0.3653 0.357445
3536 0.5936 0.723613
3544 0.9589 0.831196
3518 -0.2283 0.409702
3572 2.2374 0.987371
3523 0.0000 0.500000
3543 0.9132 0.819442
Square side=100, avg. no. parked=3531.50 sample std.=21.22
p-value of the KSTEST for those 10 p-values: 0.305362
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_11:31
0.5819,0.5985,0.2018,0.4501,0.9146,0.1346,0.3240,0.4285,0.9215,0.2709,
The KS test for those 10 p-values: 0.850578
The 3DSPHERES test for dh-ranFile-2018-06-16_11:31
sample no r^3 equiv. uni.
1 33.166 0.668968
2 48.288 0.800030
3 13.244 0.356909
4 19.336 0.475101
5 44.003 0.769332
6 59.185 0.860937
7 31.275 0.647424
8 2.348 0.075293
9 11.701 0.322958
10 10.010 0.283706
11 5.603 0.170354
12 5.614 0.170666
13 0.378 0.012512
14 6.571 0.196709
15 12.123 0.332432
16 49.746 0.809515
17 11.338 0.314725
18 33.914 0.677123
19 4.814 0.148255
20 16.561 0.424216
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.381024
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.9 -0.4 1.2 -2.0 -1.0
0.9 -0.9 0.3 -1.2 -0.9 2.3
1.3 0.7 -0.8 -0.5 -0.4 -0.8
-1.7 1.5 0.4 1.5 0.4 -0.9
-0.5 -0.7 0.2 -0.2 -0.6 1.4
1.9 -1.4 -0.8 -1.2 0.8 -0.3
1.2 -1.3 -0.4 0.4 0.9 1.0
-0.1
Chi-square with 42 degrees of freedom:47.975961
z-score=0.652031, p-value=0.756611
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_11:31
Test no p-value
1 0.079740
2 0.590327
3 0.209406
4 0.878418
5 0.028971
6 0.014899
7 0.167323
8 0.910636
9 0.125488
10 0.106591
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.015065
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_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 66670 0.00 66835 0.43
3 25000.00 25076 0.23 24802 1.57
4 6666.67 6650 0.04 6697 0.14
5 1388.89 1338 1.86 1391 0.00
6 238.10 230 0.28 236 0.02
7 34.72 30 0.64 36 0.05
8 4.96 5 0.00 2 1.77
p=0.19806 p=0.31878
Number of rngs required: 688885, p-value: 0.711
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_11:31
No. of wins: Observed Expected
98677 98585.9
z-score= 0.408, pvalue=0.65823
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66607 66666.7 0.053 0.053
2 37286 37654.3 3.603 3.656
3 27172 26954.7 1.751 5.407
4 19468 19313.5 1.237 6.644
5 13735 13851.4 0.979 7.623
6 9946 9943.5 0.001 7.623
7 7160 7145.0 0.031 7.654
8 5103 5139.1 0.253 7.908
9 3826 3699.9 4.300 12.208
10 2694 2666.3 0.288 12.496
11 1935 1923.3 0.071 12.567
12 1346 1388.7 1.315 13.882
13 1011 1003.7 0.053 13.935
14 712 726.1 0.275 14.210
15 561 525.8 2.352 16.562
16 414 381.2 2.831 19.393
17 261 276.5 0.873 20.266
18 213 200.8 0.737 21.003
19 167 146.0 3.025 24.029
20 111 106.2 0.216 24.244
21 272 287.1 0.796 25.040
Chisq= 25.04 for 20 degrees of freedom, p= 0.80010
SUMMARY of craptest
p-value for no. of wins: 0.658230
p-value for throws/game: 0.800096
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_11:31
No. of wins: Observed Expected
98778 98585.9
z-score= 0.859, pvalue=0.80493
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67118 66666.7 3.056 3.056
2 37332 37654.3 2.759 5.815
3 26910 26954.7 0.074 5.889
4 19403 19313.5 0.415 6.304
5 13846 13851.4 0.002 6.306
6 9890 9943.5 0.288 6.594
7 7012 7145.0 2.477 9.071
8 5132 5139.1 0.010 9.081
9 3649 3699.9 0.699 9.780
10 2716 2666.3 0.927 10.707
11 1933 1923.3 0.049 10.755
12 1352 1388.7 0.972 11.727
13 1066 1003.7 3.865 15.592
14 754 726.1 1.069 16.661
15 537 525.8 0.237 16.898
16 386 381.2 0.062 16.960
17 258 276.5 1.243 18.203
18 163 200.8 7.126 25.329
19 143 146.0 0.061 25.390
20 99 106.2 0.490 25.880
21 301 287.1 0.672 26.551
Chisq= 26.55 for 20 degrees of freedom, p= 0.85164
SUMMARY of craptest
p-value for no. of wins: 0.804931
p-value for throws/game: 0.851636
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0045,0.0099,0.0125,0.0149,0.0151,0.0151,0.0168,0.0194,0.0290,
0.0322,0.0325,0.0392,0.0458,0.0507,0.0521,0.0550,0.0576,0.0594,0.0598,
0.0606,0.0615,0.0680,0.0715,0.0733,0.0753,0.0797,0.0837,0.0840,0.0887,
0.0903,0.1004,0.1004,0.1008,0.1019,0.1066,0.1081,0.1118,0.1122,0.1218,
0.1255,0.1346,0.1354,0.1359,0.1423,0.1427,0.1483,0.1522,0.1543,0.1606,
0.1667,0.1673,0.1704,0.1707,0.1721,0.1771,0.1897,0.1967,0.1981,0.2018,
0.2047,0.2094,0.2099,0.2201,0.2202,0.2274,0.2494,0.2507,0.2571,0.2709,
0.2712,0.2837,0.2841,0.2852,0.2876,0.2919,0.3054,0.3054,0.3105,0.3147,
0.3188,0.3215,0.3230,0.3232,0.3240,0.3255,0.3266,0.3293,0.3305,0.3324,
0.3333,0.3341,0.3428,0.3445,0.3569,0.3574,0.3575,0.3600,0.3636,0.3646,
0.3656,0.3715,0.3776,0.3791,0.3810,0.3822,0.3829,0.3830,0.3845,0.3866,
0.3999,0.4001,0.4010,0.4029,0.4097,0.4118,0.4163,0.4177,0.4187,0.4213,
0.4242,0.4265,0.4285,0.4352,0.4398,0.4403,0.4501,0.4524,0.4579,0.4583,
0.4621,0.4666,0.4678,0.4730,0.4751,0.4788,0.4817,0.4931,0.4978,0.5000,
0.5093,0.5094,0.5108,0.5233,0.5258,0.5283,0.5298,0.5313,0.5477,0.5521,
0.5536,0.5642,0.5675,0.5819,0.5839,0.5865,0.5881,0.5903,0.5903,0.5985,
0.5986,0.6032,0.6099,0.6119,0.6119,0.6194,0.6278,0.6317,0.6346,0.6348,
0.6437,0.6474,0.6511,0.6582,0.6595,0.6652,0.6690,0.6750,0.6760,0.6771,
0.6801,0.6885,0.6978,0.6988,0.7031,0.7043,0.7108,0.7173,0.7181,0.7211,
0.7224,0.7225,0.7236,0.7276,0.7358,0.7372,0.7396,0.7475,0.7498,0.7565,
0.7566,0.7623,0.7648,0.7693,0.7744,0.7751,0.7789,0.7797,0.7809,0.7825,
0.7848,0.7913,0.7917,0.7933,0.7964,0.8000,0.8001,0.8049,0.8057,0.8074,
0.8095,0.8134,0.8161,0.8164,0.8194,0.8194,0.8249,0.8265,0.8312,0.8416,
0.8419,0.8506,0.8516,0.8567,0.8583,0.8609,0.8680,0.8757,0.8784,0.8844,
0.8895,0.8898,0.8968,0.9018,0.9051,0.9071,0.9073,0.9106,0.9143,0.9146,
0.9215,0.9294,0.9301,0.9343,0.9424,0.9511,0.9553,0.9585,0.9588,0.9715,
0.9733,0.9763,0.9851,0.9864,0.9869,0.9874,0.9910,0.9926,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.820388
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.