RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.45 21.7426 0.805178
2 to 25 15.60 23.7191 0.872729
3 to 26 15.71 10.9861 0.142713
4 to 27 16.06 15.3827 0.432060
5 to 28 16.29 15.9857 0.475149
6 to 29 16.10 20.9331 0.770704
7 to 30 15.76 18.2598 0.627372
8 to 31 15.69 16.6376 0.520830
9 to 32 15.68 16.3807 0.502974
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.498633
Tough bday spacings test for dh-ranFile-2018-06-17_23:31: 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 11 32 95 87 102 71 43 32 17 10 0
(O-E)^2/E 0.4 0.6 6.4 1.2 0.2 0.7 1.6 0.2 0.3 1.7 4.1
Birthday Spacings: Sum(O-E)^2/E= 17.272, p= 0.931
RESULTS OF GCD FOR dh-ranFile-2018-06-17_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.218590
p-value, dist. of gcd's: 0.851687
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.531 0.900 0.772 0.750 0.317 0.589 0.337 0.500
Bits 8 to 15---> 0.229 0.096 0.692 0.659 0.169 0.139 0.953 0.696
Bits 16 to 23---> 0.599 0.696 0.760 0.717 0.947 0.619 0.038 0.964
Bits 24 to 31---> 0.396 0.386 0.900 0.947 0.255 0.784 0.454 0.824
KS test for the above 32 p values: 0.815
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_23:31,
p-values for 5 runs: 0.9672, 0.4848, 0.9681, 0.6662, 0.2228
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 230 211.4 1.633 1.633
r= 29 5167 5134.0 0.212 1.845
r= 30 23085 23103.0 0.014 1.859
r= 31 11518 11551.5 0.097 1.957
chi-square = 1.957 with df = 3; p-value = 0.419
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5186 5134.0 0.526 0.731
r= 31 23096 23103.0 0.002 0.734
r= 32 11500 11551.5 0.230 0.963
chi-square = 0.963 with df = 3; p-value = 0.190
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_23:31
b-rank test for bits 1 to 8, p=0.39583
b-rank test for bits 2 to 9, p=0.50227
b-rank test for bits 3 to 10, p=0.37224
b-rank test for bits 4 to 11, p=0.56948
b-rank test for bits 5 to 12, p=0.63977
b-rank test for bits 6 to 13, p=0.31732
b-rank test for bits 7 to 14, p=0.75611
b-rank test for bits 8 to 15, p=0.44428
b-rank test for bits 9 to 16, p=0.83332
b-rank test for bits 10 to 17, p=0.92304
b-rank test for bits 11 to 18, p=0.87930
b-rank test for bits 12 to 19, p=0.28630
b-rank test for bits 13 to 20, p=0.61949
b-rank test for bits 14 to 21, p=0.79097
b-rank test for bits 15 to 22, p=0.71702
b-rank test for bits 16 to 23, p=0.81772
b-rank test for bits 17 to 24, p=0.60744
b-rank test for bits 18 to 25, p=0.38780
b-rank test for bits 19 to 26, p=0.74236
b-rank test for bits 20 to 27, p=0.81541
b-rank test for bits 21 to 28, p=0.19652
b-rank test for bits 22 to 29, p=0.45797
b-rank test for bits 23 to 30, p=0.76463
b-rank test for bits 24 to 31, p=0.43516
b-rank test for bits 25 to 32, p=0.89681
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 = 0.049318
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_23:31
(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 142022 0.26 0.603820
2 143058 2.68 0.996361
3 141925 0.04 0.514603
4 141230 -1.59 0.056231
5 142144 0.55 0.708255
6 142446 1.25 0.895061
7 142229 0.75 0.772436
8 141623 -0.67 0.251749
9 141799 -0.26 0.398288
10 142097 0.44 0.669481
11 142397 1.14 0.872735
12 141482 -1.00 0.159034
13 141985 0.18 0.570167
14 141868 -0.10 0.461536
15 141940 0.07 0.528563
16 141743 -0.39 0.348778
17 142030 0.28 0.611005
18 141865 -0.10 0.458753
19 142195 0.67 0.747759
20 141756 -0.36 0.360079
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_23:31
Bits used No. missing words z-score p-value
23 to 32 141918 0.0299 0.511925
22 to 31 142111 0.6954 0.756602
21 to 30 142134 0.7747 0.780749
20 to 29 141496 -1.4253 0.077039
19 to 28 141723 -0.6425 0.260269
18 to 27 141520 -1.3425 0.089714
17 to 26 141652 -0.8873 0.187447
16 to 25 142373 1.5989 0.945074
15 to 24 141958 0.1678 0.566641
14 to 23 142076 0.5747 0.717261
13 to 22 141681 -0.7873 0.215540
12 to 21 141804 -0.3632 0.358225
11 to 20 141836 -0.2529 0.400187
10 to 19 141554 -1.2253 0.110236
9 to 18 141842 -0.2322 0.408202
8 to 17 142166 0.8851 0.811940
7 to 16 142110 0.6920 0.755521
6 to 15 141651 -0.8908 0.186520
5 to 14 142353 1.5299 0.936979
4 to 13 141675 -0.8080 0.209535
3 to 12 142040 0.4506 0.673856
2 to 11 141749 -0.5529 0.290179
1 to 10 141614 -1.0184 0.154249
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_23:31
Bits used No. missing words z-score p-value
28 to 32 141399 -1.7299 0.041821
27 to 31 142112 0.6870 0.753964
26 to 30 142002 0.3141 0.623291
25 to 29 141633 -0.9367 0.174453
24 to 28 141852 -0.1943 0.422955
23 to 27 142443 1.8091 0.964778
22 to 26 142261 1.1921 0.883389
21 to 25 141740 -0.5740 0.282984
20 to 24 141836 -0.2486 0.401844
19 to 23 142239 1.1175 0.868115
18 to 22 141342 -1.9232 0.027230
17 to 21 142086 0.5989 0.725374
16 to 20 141684 -0.7638 0.222484
15 to 19 142042 0.4497 0.673547
14 to 18 142107 0.6701 0.748593
13 to 17 142247 1.1446 0.873822
12 to 16 142227 1.0768 0.859226
11 to 15 141911 0.0057 0.502258
10 to 14 142080 0.5785 0.718551
9 to 13 141812 -0.3299 0.370726
8 to 12 142209 1.0158 0.845145
7 to 11 141665 -0.8282 0.203768
6 to 10 141510 -1.3537 0.087922
5 to 9 141891 -0.0621 0.475227
4 to 8 141740 -0.5740 0.282984
3 to 7 141737 -0.5842 0.279553
2 to 6 141962 0.1785 0.570852
1 to 5 141610 -1.0147 0.155130
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_23:31
Bits used No. missing words z-score p-value
31 to 32 141967 0.1701 0.567541
30 to 31 142113 0.6008 0.726012
29 to 30 141481 -1.2635 0.103203
28 to 29 141253 -1.9361 0.026429
27 to 28 142098 0.5565 0.711082
26 to 27 142113 0.6008 0.726012
25 to 26 142071 0.4769 0.683284
24 to 25 141700 -0.6175 0.268455
23 to 24 141153 -2.2311 0.012839
22 to 23 142094 0.5447 0.707037
21 to 22 141898 -0.0334 0.486669
20 to 21 142223 0.9253 0.822590
19 to 20 141700 -0.6175 0.268455
18 to 19 142334 1.2527 0.894845
17 to 18 141781 -0.3786 0.352509
16 to 17 142280 1.0934 0.862896
15 to 16 141803 -0.3137 0.376891
14 to 15 142298 1.1465 0.874210
13 to 14 141976 0.1967 0.577956
12 to 13 142480 1.6834 0.953850
11 to 12 142015 0.3117 0.622370
10 to 11 142113 0.6008 0.726012
9 to 10 141780 -0.3815 0.351415
8 to 9 141484 -1.2547 0.104801
7 to 8 142792 2.6037 0.995389
6 to 7 142072 0.4799 0.684334
5 to 6 141883 -0.0777 0.469045
4 to 5 141630 -0.8240 0.204975
3 to 4 141454 -1.3432 0.089611
2 to 3 142199 0.8545 0.803582
1 to 2 142040 0.3855 0.650051
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2475.77 -0.343 0.365934
Test results for specific bytes for dh-ranFile-2018-06-17_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2409.88 -1.274 0.101257
2 to 9 2426.37 -1.041 0.148874
3 to 10 2544.80 0.634 0.736805
4 to 11 2461.32 -0.547 0.292189
5 to 12 2571.99 1.018 0.845686
6 to 13 2470.80 -0.413 0.339834
7 to 14 2504.81 0.068 0.527115
8 to 15 2410.25 -1.269 0.102172
9 to 16 2624.07 1.755 0.960333
10 to 17 2593.93 1.328 0.907969
11 to 18 2577.01 1.089 0.861943
12 to 19 2595.50 1.351 0.911591
13 to 20 2526.95 0.381 0.648444
14 to 21 2566.39 0.939 0.826110
15 to 22 2470.99 -0.410 0.340822
16 to 23 2560.18 0.851 0.802652
17 to 24 2532.52 0.460 0.677185
18 to 25 2471.97 -0.396 0.345891
19 to 26 2581.90 1.158 0.876619
20 to 27 2508.13 0.115 0.545792
21 to 28 2332.29 -2.372 0.008851
22 to 29 2572.15 1.020 0.846228
23 to 30 2437.41 -0.885 0.188036
24 to 31 2489.45 -0.149 0.440705
25 to 32 2499.47 -0.007 0.497017
CDPARK for dh-ranFile-2018-06-17_23:31: 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
3550 1.2329 0.891189
3538 0.6849 0.753306
3529 0.2740 0.607947
3532 0.4110 0.659449
3533 0.4566 0.676028
3512 -0.5023 0.307734
3509 -0.6393 0.261324
3543 0.9132 0.819442
3510 -0.5936 0.276387
3530 0.3196 0.625377
Square side=100, avg. no. parked=3528.60 sample std.=13.39
p-value of the KSTEST for those 10 p-values: 0.358588
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_23:31
0.3685,0.7050,0.1744,0.0666,0.4266,0.3103,0.9709,0.5737,0.2937,0.9456,
The KS test for those 10 p-values: 0.885594
The 3DSPHERES test for dh-ranFile-2018-06-17_23:31
sample no r^3 equiv. uni.
1 45.152 0.777995
2 10.757 0.301324
3 61.110 0.869581
4 23.147 0.537707
5 33.060 0.667790
6 14.058 0.374130
7 7.013 0.208454
8 26.320 0.584112
9 52.522 0.826355
10 2.207 0.070939
11 21.770 0.516005
12 1.254 0.040938
13 8.097 0.236544
14 28.012 0.606914
15 18.942 0.468154
16 34.557 0.683963
17 27.451 0.599501
18 14.890 0.391234
19 51.680 0.821409
20 11.626 0.321269
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.721552
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -0.7 -2.0 -0.1 -0.5 0.2
-1.4 -0.6 1.0 -0.2 -0.1 0.2
-0.2 0.6 -0.0 0.1 0.5 -0.4
-0.4 0.1 0.2 -0.8 -0.6 2.4
0.3 -1.0 -0.1 -0.5 0.7 0.8
-0.3 -1.0 -2.1 1.0 1.0 0.4
-1.4 0.5 -1.2 -0.1 1.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:36.494026
z-score=-0.600751, p-value=0.289253
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_23:31
Test no p-value
1 0.255437
2 0.694339
3 0.091495
4 0.096120
5 0.002673
6 0.468754
7 0.118566
8 0.174532
9 0.811722
10 0.038500
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.010034
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_23:31:
(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 66643 0.01 66457 0.66
3 25000.00 25058 0.13 25278 3.09
4 6666.67 6605 0.57 6604 0.59
5 1388.89 1446 2.35 1367 0.35
6 238.10 214 2.44 254 1.06
7 34.72 30 0.64 34 0.01
8 4.96 3 0.77 5 0.00
p=0.67135 p=0.54970
Number of rngs required: 688642, p-value: 0.608
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_23:31
No. of wins: Observed Expected
98243 98585.9
z-score=-1.533, pvalue=0.06258
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66689 66666.7 0.007 0.007
2 37781 37654.3 0.426 0.434
3 27013 26954.7 0.126 0.560
4 19253 19313.5 0.189 0.749
5 13987 13851.4 1.327 2.076
6 9851 9943.5 0.861 2.937
7 7034 7145.0 1.725 4.662
8 5115 5139.1 0.113 4.775
9 3755 3699.9 0.822 5.597
10 2657 2666.3 0.032 5.629
11 1925 1923.3 0.001 5.631
12 1341 1388.7 1.641 7.272
13 1016 1003.7 0.150 7.422
14 663 726.1 5.490 12.913
15 539 525.8 0.330 13.242
16 382 381.2 0.002 13.244
17 282 276.5 0.108 13.352
18 195 200.8 0.169 13.521
19 146 146.0 0.000 13.521
20 99 106.2 0.490 14.011
21 277 287.1 0.356 14.367
Chisq= 14.37 for 20 degrees of freedom, p= 0.18861
SUMMARY of craptest
p-value for no. of wins: 0.062581
p-value for throws/game: 0.188614
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_23:31
No. of wins: Observed Expected
98932 98585.9
z-score= 1.548, pvalue=0.93921
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66708 66666.7 0.026 0.026
2 37609 37654.3 0.055 0.080
3 26877 26954.7 0.224 0.304
4 19307 19313.5 0.002 0.307
5 13631 13851.4 3.508 3.814
6 10061 9943.5 1.387 5.202
7 7291 7145.0 2.982 8.184
8 5175 5139.1 0.251 8.435
9 3752 3699.9 0.735 9.170
10 2593 2666.3 2.015 11.185
11 1890 1923.3 0.578 11.762
12 1384 1388.7 0.016 11.778
13 1011 1003.7 0.053 11.831
14 739 726.1 0.228 12.059
15 511 525.8 0.419 12.478
16 412 381.2 2.497 14.974
17 278 276.5 0.008 14.982
18 205 200.8 0.087 15.069
19 147 146.0 0.007 15.076
20 106 106.2 0.000 15.076
21 313 287.1 2.334 17.410
Chisq= 17.41 for 20 degrees of freedom, p= 0.37379
SUMMARY of craptest
p-value for no. of wins: 0.939206
p-value for throws/game: 0.373791
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0027,0.0089,0.0100,0.0128,0.0264,0.0272,0.0385,0.0385,0.0409,0.0418,
0.0493,0.0562,0.0626,0.0666,0.0709,0.0770,0.0879,0.0896,0.0897,0.0915,
0.0961,0.0963,0.1013,0.1022,0.1032,0.1048,0.1102,0.1186,0.1388,0.1427,
0.1489,0.1542,0.1551,0.1590,0.1692,0.1744,0.1745,0.1745,0.1865,0.1874,
0.1880,0.1886,0.1899,0.1965,0.2038,0.2050,0.2085,0.2095,0.2155,0.2186,
0.2225,0.2228,0.2290,0.2365,0.2517,0.2548,0.2554,0.2603,0.2613,0.2685,
0.2685,0.2764,0.2796,0.2830,0.2830,0.2863,0.2893,0.2902,0.2922,0.2937,
0.3013,0.3077,0.3103,0.3166,0.3173,0.3213,0.3368,0.3398,0.3408,0.3459,
0.3488,0.3514,0.3525,0.3582,0.3586,0.3601,0.3659,0.3685,0.3707,0.3722,
0.3738,0.3741,0.3769,0.3865,0.3878,0.3912,0.3955,0.3958,0.3983,0.4002,
0.4018,0.4082,0.4185,0.4230,0.4266,0.4321,0.4352,0.4407,0.4443,0.4545,
0.4580,0.4588,0.4615,0.4682,0.4688,0.4690,0.4751,0.4752,0.4848,0.4867,
0.4970,0.4986,0.5002,0.5023,0.5023,0.5030,0.5119,0.5146,0.5160,0.5208,
0.5271,0.5286,0.5314,0.5377,0.5458,0.5497,0.5666,0.5675,0.5695,0.5702,
0.5709,0.5737,0.5780,0.5841,0.5888,0.5989,0.5995,0.6038,0.6069,0.6074,
0.6079,0.6084,0.6110,0.6186,0.6195,0.6224,0.6233,0.6254,0.6274,0.6398,
0.6484,0.6501,0.6594,0.6595,0.6662,0.6678,0.6695,0.6713,0.6735,0.6739,
0.6760,0.6772,0.6833,0.6840,0.6843,0.6925,0.6943,0.6956,0.6959,0.7050,
0.7070,0.7083,0.7111,0.7170,0.7173,0.7174,0.7186,0.7216,0.7254,0.7260,
0.7260,0.7260,0.7368,0.7424,0.7478,0.7486,0.7505,0.7533,0.7540,0.7555,
0.7561,0.7566,0.7603,0.7646,0.7707,0.7722,0.7724,0.7780,0.7807,0.7837,
0.7910,0.8027,0.8036,0.8052,0.8117,0.8119,0.8145,0.8154,0.8177,0.8194,
0.8214,0.8226,0.8242,0.8261,0.8264,0.8333,0.8451,0.8457,0.8462,0.8517,
0.8592,0.8619,0.8629,0.8681,0.8696,0.8727,0.8727,0.8738,0.8742,0.8766,
0.8793,0.8834,0.8856,0.8912,0.8948,0.8951,0.8968,0.8995,0.9000,0.9080,
0.9116,0.9230,0.9314,0.9370,0.9392,0.9451,0.9456,0.9470,0.9472,0.9525,
0.9539,0.9603,0.9641,0.9648,0.9672,0.9681,0.9709,0.9954,0.9964,
Overall p-value after applying KStest on 269 p-values = 0.150352
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.