RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.78 22.5192 0.834433
2 to 25 15.85 13.1360 0.272964
3 to 26 15.82 15.9844 0.475060
4 to 27 15.65 20.0747 0.729574
5 to 28 15.72 19.7505 0.712811
6 to 29 15.82 17.0816 0.551150
7 to 30 15.37 37.3567 0.996990
8 to 31 15.64 17.0336 0.547905
9 to 32 15.74 16.0563 0.480151
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.209474
Tough bday spacings test for dh-ranFile-2018-06-16_12:31: 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 13 43 78 106 77 81 49 25 20 7 1
(O-E)^2/E 1.6 1.1 0.3 0.7 4.4 0.1 0.2 0.8 1.8 0.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 13.258, p= 0.790
RESULTS OF GCD FOR dh-ranFile-2018-06-16_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.617493
p-value, dist. of gcd's: 0.017891
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.522 1.000 0.443 0.533 0.641 0.332 0.268 0.920
Bits 8 to 15---> 0.574 0.526 0.946 0.731 0.396 0.323 0.651 0.576
Bits 16 to 23---> 0.199 0.725 0.124 0.688 0.226 0.599 0.265 0.514
Bits 24 to 31---> 0.656 0.017 0.280 0.382 0.288 0.046 0.097 0.766
KS test for the above 32 p values: 0.463
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_12:31,
p-values for 5 runs: 0.7008, 0.8980, 0.7587, 0.6980, 0.0052
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5236 5134.0 2.026 3.327
r= 30 23102 23103.0 0.000 3.327
r= 31 11434 11551.5 1.196 4.522
chi-square = 4.522 with df = 3; p-value = 0.790
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5157 5134.0 0.103 0.375
r= 31 22952 23103.0 0.988 1.362
r= 32 11672 11551.5 1.257 2.619
chi-square = 2.619 with df = 3; p-value = 0.546
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_12:31
b-rank test for bits 1 to 8, p=0.94241
b-rank test for bits 2 to 9, p=0.97502
b-rank test for bits 3 to 10, p=0.30999
b-rank test for bits 4 to 11, p=0.26429
b-rank test for bits 5 to 12, p=0.06864
b-rank test for bits 6 to 13, p=0.12750
b-rank test for bits 7 to 14, p=0.10799
b-rank test for bits 8 to 15, p=0.80951
b-rank test for bits 9 to 16, p=0.32525
b-rank test for bits 10 to 17, p=0.53899
b-rank test for bits 11 to 18, p=0.14191
b-rank test for bits 12 to 19, p=0.55763
b-rank test for bits 13 to 20, p=0.61297
b-rank test for bits 14 to 21, p=0.93112
b-rank test for bits 15 to 22, p=0.59213
b-rank test for bits 16 to 23, p=0.91100
b-rank test for bits 17 to 24, p=0.25430
b-rank test for bits 18 to 25, p=0.28489
b-rank test for bits 19 to 26, p=0.13322
b-rank test for bits 20 to 27, p=0.23089
b-rank test for bits 21 to 28, p=0.34144
b-rank test for bits 22 to 29, p=0.98764
b-rank test for bits 23 to 30, p=0.50069
b-rank test for bits 24 to 31, p=0.47982
b-rank test for bits 25 to 32, p=0.71758
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 = 0.668373
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_12:31
(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 141704 -0.48 0.315705
2 141525 -0.90 0.184602
3 142252 0.80 0.788327
4 141870 -0.09 0.463392
5 142231 0.75 0.773844
6 141686 -0.52 0.300905
7 142694 1.83 0.966624
8 141503 -0.95 0.171216
9 141607 -0.71 0.239976
10 141436 -1.11 0.134382
11 142279 0.86 0.806128
12 141681 -0.53 0.296850
13 142079 0.40 0.654104
14 141167 -1.73 0.041422
15 141819 -0.21 0.416424
16 141602 -0.72 0.236360
17 142103 0.45 0.674546
18 141510 -0.93 0.175406
19 140980 -2.17 0.014953
20 142102 0.45 0.673704
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_12:31
Bits used No. missing words z-score p-value
23 to 32 141498 -1.4184 0.078040
22 to 31 142096 0.6437 0.740112
21 to 30 141417 -1.6977 0.044783
20 to 29 142128 0.7540 0.774586
19 to 28 141701 -0.7184 0.236262
18 to 27 141557 -1.2149 0.112196
17 to 26 142397 1.6816 0.953679
16 to 25 141893 -0.0563 0.477547
15 to 24 142217 1.0609 0.855639
14 to 23 142016 0.3678 0.643499
13 to 22 141293 -2.1253 0.016782
12 to 21 142360 1.5540 0.939912
11 to 20 141774 -0.4667 0.320373
10 to 19 142056 0.5058 0.693487
9 to 18 141662 -0.8529 0.196868
8 to 17 141595 -1.0839 0.139205
7 to 16 141457 -1.5598 0.059408
6 to 15 141639 -0.9322 0.175624
5 to 14 142261 1.2127 0.887369
4 to 13 141653 -0.8839 0.188376
3 to 12 141884 -0.0873 0.465199
2 to 11 141785 -0.4287 0.334062
1 to 10 141846 -0.2184 0.413567
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_12:31
Bits used No. missing words z-score p-value
28 to 32 141678 -0.7842 0.216470
27 to 31 142001 0.3107 0.622003
26 to 30 141840 -0.2350 0.407098
25 to 29 141749 -0.5435 0.293396
24 to 28 141417 -1.6689 0.047567
23 to 27 141793 -0.3943 0.346665
22 to 26 141505 -1.3706 0.085248
21 to 25 141546 -1.2316 0.109044
20 to 24 141933 0.0802 0.531976
19 to 23 141644 -0.8994 0.184214
18 to 22 141895 -0.0486 0.480629
17 to 21 141722 -0.6350 0.262709
16 to 20 141446 -1.5706 0.058137
15 to 19 141891 -0.0621 0.475227
14 to 18 141360 -1.8621 0.031292
13 to 17 141803 -0.3604 0.359259
12 to 16 141215 -2.3537 0.009295
11 to 15 141823 -0.2926 0.384897
10 to 14 141406 -1.7062 0.043985
9 to 13 142645 2.4938 0.993681
8 to 12 141496 -1.4011 0.080589
7 to 11 141955 0.1548 0.561516
6 to 10 141856 -0.1808 0.428270
5 to 9 142257 1.1785 0.880710
4 to 8 141406 -1.7062 0.043985
3 to 7 141460 -1.5232 0.063860
2 to 6 141860 -0.1672 0.433598
1 to 5 141706 -0.6893 0.245332
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_12:31
Bits used No. missing words z-score p-value
31 to 32 141107 -2.3668 0.008972
30 to 31 141944 0.1023 0.540729
29 to 30 141717 -0.5673 0.285240
28 to 29 141741 -0.4965 0.309754
27 to 28 142093 0.5418 0.706022
26 to 27 142165 0.7542 0.774632
25 to 26 141878 -0.0924 0.463183
24 to 25 142006 0.2852 0.612240
23 to 24 142209 0.8840 0.811647
22 to 23 141219 -2.0364 0.020857
21 to 22 141283 -1.8476 0.032331
20 to 21 142876 2.8515 0.997825
19 to 20 142148 0.7040 0.759297
18 to 19 142086 0.5212 0.698869
17 to 18 142366 1.3471 0.911027
16 to 17 141785 -0.3668 0.356901
15 to 16 141966 0.1672 0.566381
14 to 15 141479 -1.2694 0.102147
13 to 14 141649 -0.7679 0.221263
12 to 13 141792 -0.3461 0.364632
11 to 12 142515 1.7866 0.963002
10 to 11 142750 2.4799 0.993428
9 to 10 141906 -0.0098 0.496081
8 to 9 142153 0.7188 0.763865
7 to 8 142221 0.9194 0.821052
6 to 7 142381 1.3914 0.917941
5 to 6 142124 0.6332 0.736713
4 to 5 141377 -1.5703 0.058173
3 to 4 141498 -1.2134 0.112496
2 to 3 141432 -1.4081 0.079558
1 to 2 141760 -0.4405 0.329787
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2528.80 0.407 0.658079
Test results for specific bytes for dh-ranFile-2018-06-16_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2511.81 0.167 0.566300
2 to 9 2515.62 0.221 0.587440
3 to 10 2559.40 0.840 0.799566
4 to 11 2436.03 -0.905 0.182813
5 to 12 2487.30 -0.180 0.428718
6 to 13 2378.33 -1.721 0.042655
7 to 14 2430.08 -0.989 0.161382
8 to 15 2507.85 0.111 0.544223
9 to 16 2489.82 -0.144 0.442753
10 to 17 2528.96 0.410 0.658927
11 to 18 2620.58 1.705 0.955921
12 to 19 2528.08 0.397 0.654369
13 to 20 2566.81 0.945 0.827639
14 to 21 2617.32 1.659 0.951456
15 to 22 2474.25 -0.364 0.357886
16 to 23 2631.93 1.866 0.968964
17 to 24 2599.48 1.407 0.920273
18 to 25 2585.33 1.207 0.886241
19 to 26 2601.99 1.442 0.925405
20 to 27 2541.12 0.581 0.719533
21 to 28 2594.98 1.343 0.910397
22 to 29 2636.00 1.923 0.972781
23 to 30 2513.29 0.188 0.574548
24 to 31 2482.43 -0.249 0.401856
25 to 32 2514.76 0.209 0.582664
CDPARK for dh-ranFile-2018-06-16_12:31: 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
3521 -0.0913 0.463617
3523 0.0000 0.500000
3517 -0.2740 0.392053
3521 -0.0913 0.463617
3539 0.7306 0.767486
3546 1.0502 0.853193
3502 -0.9589 0.168804
3515 -0.3653 0.357445
3511 -0.5479 0.291865
3540 0.7763 0.781201
Square side=100, avg. no. parked=3523.50 sample std.=13.28
p-value of the KSTEST for those 10 p-values: 0.619458
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_12:31
0.1285,0.4386,0.8343,0.7091,0.9194,0.2283,0.5778,0.3717,0.0299,0.7338,
The KS test for those 10 p-values: 0.999425
The 3DSPHERES test for dh-ranFile-2018-06-16_12:31
sample no r^3 equiv. uni.
1 19.350 0.475334
2 23.539 0.543718
3 2.410 0.077199
4 1.700 0.055090
5 3.434 0.108160
6 34.846 0.686991
7 31.855 0.654182
8 8.965 0.258310
9 1.960 0.063253
10 17.691 0.445514
11 17.299 0.438208
12 2.444 0.078235
13 35.257 0.691252
14 18.937 0.468068
15 35.585 0.694612
16 6.949 0.206760
17 16.198 0.417205
18 17.311 0.438433
19 38.796 0.725607
20 13.733 0.367315
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.092969
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 -1.6 -1.0 0.3 -0.9
0.5 2.1 0.0 -0.9 0.8 -1.3
-0.9 0.1 0.9 -0.9 0.6 -0.4
1.9 0.7 -1.7 0.7 0.1 -0.4
-0.5 0.1 1.5 -1.4 -0.6 -0.4
-1.1 0.3 -1.2 1.8 -0.1 0.6
-0.5 -0.1 -2.0 -0.7 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:39.830817
z-score=-0.236677, p-value=0.433393
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_12:31
Test no p-value
1 0.023803
2 0.654918
3 0.092820
4 0.496189
5 0.007038
6 0.635769
7 0.302813
8 0.516500
9 0.124125
10 0.628238
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.087128
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_12:31:
(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 66633 0.02 66776 0.18
3 25000.00 24953 0.09 24953 0.09
4 6666.67 6682 0.04 6598 0.71
5 1388.89 1446 2.35 1380 0.06
6 238.10 254 1.06 246 0.26
7 34.72 28 1.30 39 0.53
8 4.96 3 0.77 7 0.84
p=0.53370 p=0.14996
Number of rngs required: 688952, p-value: 0.737
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_12:31
No. of wins: Observed Expected
98653 98585.9
z-score= 0.300, pvalue=0.61802
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66521 66666.7 0.318 0.318
2 37757 37654.3 0.280 0.598
3 26987 26954.7 0.039 0.637
4 19294 19313.5 0.020 0.657
5 14081 13851.4 3.805 4.462
6 9839 9943.5 1.099 5.561
7 7100 7145.0 0.284 5.845
8 5033 5139.1 2.189 8.034
9 3716 3699.9 0.070 8.104
10 2675 2666.3 0.028 8.133
11 1938 1923.3 0.112 8.245
12 1397 1388.7 0.049 8.294
13 1003 1003.7 0.001 8.294
14 754 726.1 1.069 9.363
15 521 525.8 0.044 9.408
16 355 381.2 1.794 11.202
17 280 276.5 0.043 11.245
18 219 200.8 1.644 12.889
19 129 146.0 1.976 14.865
20 104 106.2 0.046 14.911
21 297 287.1 0.340 15.252
Chisq= 15.25 for 20 degrees of freedom, p= 0.23817
SUMMARY of craptest
p-value for no. of wins: 0.618024
p-value for throws/game: 0.238167
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_12:31
No. of wins: Observed Expected
98887 98585.9
z-score= 1.347, pvalue=0.91099
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66774 66666.7 0.173 0.173
2 37826 37654.3 0.783 0.956
3 27035 26954.7 0.239 1.195
4 19333 19313.5 0.020 1.214
5 13773 13851.4 0.444 1.658
6 9834 9943.5 1.207 2.865
7 7091 7145.0 0.409 3.274
8 5012 5139.1 3.142 6.416
9 3720 3699.9 0.110 6.525
10 2686 2666.3 0.146 6.671
11 1930 1923.3 0.023 6.694
12 1371 1388.7 0.227 6.921
13 995 1003.7 0.076 6.996
14 732 726.1 0.047 7.044
15 519 525.8 0.089 7.132
16 391 381.2 0.255 7.387
17 267 276.5 0.329 7.716
18 198 200.8 0.040 7.756
19 140 146.0 0.245 8.001
20 94 106.2 1.405 9.406
21 279 287.1 0.229 9.635
Chisq= 9.64 for 20 degrees of freedom, p= 0.02569
SUMMARY of craptest
p-value for no. of wins: 0.910991
p-value for throws/game: 0.025687
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0052,0.0070,0.0090,0.0093,0.0150,0.0168,0.0170,0.0179,0.0209,0.0238,
0.0257,0.0299,0.0313,0.0323,0.0414,0.0427,0.0440,0.0440,0.0448,0.0464,
0.0476,0.0551,0.0581,0.0582,0.0594,0.0633,0.0639,0.0686,0.0772,0.0780,
0.0782,0.0796,0.0806,0.0852,0.0871,0.0928,0.0930,0.0967,0.1021,0.1080,
0.1082,0.1090,0.1122,0.1125,0.1237,0.1241,0.1275,0.1285,0.1332,0.1344,
0.1392,0.1419,0.1500,0.1614,0.1688,0.1712,0.1754,0.1756,0.1828,0.1842,
0.1846,0.1884,0.1969,0.1992,0.2068,0.2095,0.2165,0.2213,0.2265,0.2283,
0.2309,0.2363,0.2364,0.2382,0.2400,0.2453,0.2543,0.2583,0.2627,0.2643,
0.2652,0.2679,0.2730,0.2802,0.2849,0.2852,0.2883,0.2919,0.2934,0.2969,
0.3009,0.3028,0.3098,0.3100,0.3157,0.3204,0.3232,0.3253,0.3298,0.3323,
0.3341,0.3414,0.3467,0.3569,0.3574,0.3579,0.3593,0.3646,0.3673,0.3717,
0.3821,0.3849,0.3921,0.3962,0.4019,0.4071,0.4136,0.4164,0.4172,0.4283,
0.4287,0.4334,0.4336,0.4382,0.4384,0.4386,0.4426,0.4428,0.4455,0.4627,
0.4632,0.4634,0.4636,0.4636,0.4652,0.4681,0.4751,0.4752,0.4753,0.4775,
0.4798,0.4802,0.4806,0.4961,0.4962,0.5000,0.5007,0.5144,0.5165,0.5225,
0.5256,0.5320,0.5332,0.5337,0.5390,0.5407,0.5437,0.5442,0.5458,0.5479,
0.5512,0.5576,0.5615,0.5663,0.5664,0.5737,0.5745,0.5757,0.5778,0.5827,
0.5874,0.5921,0.5990,0.6122,0.6130,0.6175,0.6180,0.6195,0.6220,0.6282,
0.6358,0.6407,0.6435,0.6506,0.6541,0.6542,0.6544,0.6549,0.6556,0.6581,
0.6589,0.6684,0.6737,0.6745,0.6870,0.6879,0.6913,0.6935,0.6946,0.6980,
0.6989,0.7008,0.7060,0.7091,0.7128,0.7176,0.7195,0.7249,0.7256,0.7296,
0.7315,0.7338,0.7367,0.7368,0.7401,0.7587,0.7593,0.7639,0.7657,0.7675,
0.7738,0.7746,0.7746,0.7812,0.7883,0.7897,0.7904,0.7996,0.8061,0.8095,
0.8116,0.8211,0.8276,0.8343,0.8344,0.8532,0.8556,0.8807,0.8862,0.8874,
0.8980,0.9104,0.9110,0.9110,0.9110,0.9179,0.9194,0.9200,0.9203,0.9254,
0.9311,0.9399,0.9424,0.9461,0.9515,0.9537,0.9559,0.9630,0.9666,0.9690,
0.9728,0.9750,0.9876,0.9934,0.9937,0.9970,0.9978,0.9994,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.083344
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.