RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_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 15.91 23.8018 0.875079
2 to 25 15.76 15.9424 0.472081
3 to 26 15.75 20.3709 0.744299
4 to 27 15.87 11.9204 0.195066
5 to 28 15.90 15.4403 0.436199
6 to 29 15.97 26.2650 0.930235
7 to 30 15.66 21.0128 0.774281
8 to 31 15.69 19.1339 0.679097
9 to 32 15.66 28.8991 0.964532
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.121868
Tough bday spacings test for dh-ranFile-2018-07-05_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 6 45 80 106 97 59 57 25 18 5 2
(O-E)^2/E 1.1 1.9 0.6 0.7 0.0 4.7 0.5 0.8 0.7 0.4 1.0
Birthday Spacings: Sum(O-E)^2/E= 12.346, p= 0.737
RESULTS OF GCD FOR dh-ranFile-2018-07-05_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.956469
p-value, dist. of gcd's: 0.344783
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.602 0.533 0.772 0.767 0.756 0.304 0.669 0.027
Bits 8 to 15---> 0.482 0.619 0.816 0.001 0.551 0.353 0.120 0.700
Bits 16 to 23---> 0.798 0.866 0.947 0.477 0.542 0.441 0.670 0.049
Bits 24 to 31---> 0.731 0.370 0.373 0.652 0.275 0.635 0.720 0.657
KS test for the above 32 p values: 0.823
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_23:31,
p-values for 5 runs: 0.9617, 0.7329, 0.2866, 0.4719, 0.0459
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5060 5134.0 1.067 2.367
r= 30 23093 23103.0 0.004 2.372
r= 31 11619 11551.5 0.394 2.766
chi-square = 2.766 with df = 3; p-value = 0.571
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5037 5134.0 1.833 1.843
r= 31 23252 23103.0 0.960 2.803
r= 32 11501 11551.5 0.221 3.024
chi-square = 3.024 with df = 3; p-value = 0.612
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_23:31
b-rank test for bits 1 to 8, p=0.16589
b-rank test for bits 2 to 9, p=0.69662
b-rank test for bits 3 to 10, p=0.50951
b-rank test for bits 4 to 11, p=0.87004
b-rank test for bits 5 to 12, p=0.78094
b-rank test for bits 6 to 13, p=0.68675
b-rank test for bits 7 to 14, p=0.38049
b-rank test for bits 8 to 15, p=0.87190
b-rank test for bits 9 to 16, p=0.13377
b-rank test for bits 10 to 17, p=0.87086
b-rank test for bits 11 to 18, p=0.94046
b-rank test for bits 12 to 19, p=0.05333
b-rank test for bits 13 to 20, p=0.59774
b-rank test for bits 14 to 21, p=0.10692
b-rank test for bits 15 to 22, p=0.20533
b-rank test for bits 16 to 23, p=0.00876
b-rank test for bits 17 to 24, p=0.73533
b-rank test for bits 18 to 25, p=0.98422
b-rank test for bits 19 to 26, p=0.26871
b-rank test for bits 20 to 27, p=0.50350
b-rank test for bits 21 to 28, p=0.57877
b-rank test for bits 22 to 29, p=0.48226
b-rank test for bits 23 to 30, p=0.41076
b-rank test for bits 24 to 31, p=0.08825
b-rank test for bits 25 to 32, p=0.11722
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 = 0.921033
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_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 142062 0.36 0.639344
2 142158 0.58 0.719381
3 142243 0.78 0.782188
4 142139 0.54 0.704232
5 140978 -2.18 0.014777
6 141624 -0.67 0.252495
7 142070 0.38 0.646317
8 141672 -0.55 0.289615
9 142119 0.49 0.687892
10 142137 0.53 0.702616
11 141935 0.06 0.523913
12 142245 0.78 0.783561
13 142262 0.82 0.795029
14 142315 0.95 0.828391
15 141817 -0.22 0.414601
16 141844 -0.15 0.439341
17 142556 1.51 0.934594
18 141886 -0.05 0.478265
19 141299 -1.43 0.076934
20 141085 -1.93 0.027052
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_23:31
Bits used No. missing words z-score p-value
23 to 32 142217 1.0609 0.855639
22 to 31 141819 -0.3115 0.377717
21 to 30 141515 -1.3598 0.086953
20 to 29 141570 -1.1701 0.120980
19 to 28 142339 1.4816 0.930779
18 to 27 142101 0.6609 0.745672
17 to 26 142139 0.7920 0.785810
16 to 25 141786 -0.4253 0.335318
15 to 24 141478 -1.4873 0.068462
14 to 23 142063 0.5299 0.701908
13 to 22 142245 1.1575 0.876462
12 to 21 141767 -0.4908 0.311786
11 to 20 141954 0.1540 0.561209
10 to 19 142295 1.3299 0.908224
9 to 18 141754 -0.5356 0.296110
8 to 17 142010 0.3471 0.635756
7 to 16 142233 1.1161 0.867811
6 to 15 141805 -0.3598 0.359514
5 to 14 141896 -0.0460 0.481669
4 to 13 141853 -0.1942 0.422994
3 to 12 141839 -0.2425 0.404190
2 to 11 141817 -0.3184 0.375099
1 to 10 142069 0.5506 0.709041
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_23:31
Bits used No. missing words z-score p-value
28 to 32 142117 0.7040 0.759273
27 to 31 142355 1.5107 0.934573
26 to 30 141743 -0.5638 0.286435
25 to 29 141871 -0.1299 0.448310
24 to 28 141998 0.3006 0.618131
23 to 27 141567 -1.1604 0.122935
22 to 26 141663 -0.8350 0.201854
21 to 25 141716 -0.6554 0.256119
20 to 24 142014 0.3548 0.638635
19 to 23 142159 0.8463 0.801318
18 to 22 142023 0.3853 0.650001
17 to 21 141864 -0.1537 0.438939
16 to 20 142138 0.7752 0.780875
15 to 19 142025 0.3921 0.652509
14 to 18 142606 2.3616 0.990902
13 to 17 141591 -1.0791 0.140275
12 to 16 141608 -1.0215 0.153519
11 to 15 142160 0.8497 0.802262
10 to 14 142426 1.7514 0.960064
9 to 13 141917 0.0260 0.510371
8 to 12 142176 0.9040 0.816993
7 to 11 141182 -2.4655 0.006841
6 to 10 141634 -0.9333 0.175327
5 to 9 142179 0.9141 0.819677
4 to 8 141758 -0.5130 0.303982
3 to 7 142226 1.0735 0.858467
2 to 6 142153 0.8260 0.795598
1 to 5 142145 0.7989 0.787820
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_23:31
Bits used No. missing words z-score p-value
31 to 32 141821 -0.2606 0.397216
30 to 31 142243 0.9843 0.837510
29 to 30 142175 0.7837 0.783388
28 to 29 141807 -0.3019 0.381380
27 to 28 141863 -0.1367 0.445647
26 to 27 142016 0.3147 0.623490
25 to 26 142008 0.2911 0.614498
24 to 25 141456 -1.3373 0.090569
23 to 24 141991 0.2409 0.595189
22 to 23 142334 1.2527 0.894845
21 to 22 141714 -0.5762 0.282242
20 to 21 141501 -1.2045 0.114196
19 to 20 142087 0.5241 0.699896
18 to 19 141409 -1.4759 0.069985
17 to 18 142036 0.3737 0.645671
16 to 17 141618 -0.8594 0.195065
15 to 16 141763 -0.4317 0.332997
14 to 15 141744 -0.4877 0.312882
13 to 14 141244 -1.9626 0.024845
12 to 13 141686 -0.6588 0.255015
11 to 12 142156 0.7276 0.766583
10 to 11 141459 -1.3284 0.092022
9 to 10 142007 0.2881 0.613370
8 to 9 141800 -0.3225 0.373534
7 to 8 141853 -0.1662 0.434014
6 to 7 142144 0.6922 0.755607
5 to 6 142091 0.5359 0.703986
4 to 5 142726 2.4091 0.992003
3 to 4 141736 -0.5113 0.304571
2 to 3 141625 -0.8387 0.200810
1 to 2 142453 1.6037 0.945615
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2530.21 0.427 0.665404
Test results for specific bytes for dh-ranFile-2018-07-05_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2397.09 -1.455 0.072791
2 to 9 2525.84 0.365 0.642618
3 to 10 2543.28 0.612 0.729774
4 to 11 2512.45 0.176 0.569871
5 to 12 2501.43 0.020 0.508083
6 to 13 2551.15 0.723 0.765264
7 to 14 2486.95 -0.185 0.426797
8 to 15 2379.99 -1.697 0.044828
9 to 16 2621.37 1.716 0.956960
10 to 17 2653.39 2.169 0.984971
11 to 18 2619.44 1.689 0.954401
12 to 19 2474.27 -0.364 0.357977
13 to 20 2687.21 2.648 0.995946
14 to 21 2529.76 0.421 0.663052
15 to 22 2305.13 -2.756 0.002927
16 to 23 2499.27 -0.010 0.495908
17 to 24 2344.04 -2.206 0.013705
18 to 25 2462.01 -0.537 0.295547
19 to 26 2460.84 -0.554 0.289862
20 to 27 2659.60 2.257 0.988000
21 to 28 2506.56 0.093 0.536944
22 to 29 2458.70 -0.584 0.279597
23 to 30 2593.50 1.322 0.906966
24 to 31 2486.20 -0.195 0.422648
25 to 32 2601.40 1.434 0.924212
CDPARK for dh-ranFile-2018-07-05_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
3502 -0.9589 0.168804
3529 0.2740 0.607947
3522 -0.0457 0.481790
3501 -1.0046 0.157553
3538 0.6849 0.753306
3540 0.7763 0.781201
3522 -0.0457 0.481790
3533 0.4566 0.676028
3524 0.0457 0.518210
3537 0.6393 0.738676
Square side=100, avg. no. parked=3524.80 sample std.=13.20
p-value of the KSTEST for those 10 p-values: 0.476334
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_23:31
0.7333,0.9107,0.5889,0.7574,0.9425,0.5900,0.5064,0.3638,0.3136,0.1602,
The KS test for those 10 p-values: 0.599327
The 3DSPHERES test for dh-ranFile-2018-07-05_23:31
sample no r^3 equiv. uni.
1 40.098 0.737258
2 4.169 0.129730
3 2.541 0.081204
4 17.921 0.449733
5 5.088 0.155986
6 0.396 0.013110
7 6.689 0.199848
8 19.062 0.470276
9 11.875 0.326871
10 23.823 0.548011
11 5.813 0.176140
12 33.984 0.677875
13 15.987 0.413095
14 21.869 0.517596
15 0.560 0.018488
16 2.866 0.091125
17 52.659 0.827146
18 15.667 0.406815
19 20.111 0.488478
20 10.168 0.287480
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.032451
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 1.3 1.1 0.8 0.8
-1.4 -0.5 -0.1 -0.3 1.4 0.1
-0.6 0.0 0.4 -0.4 1.1 -0.7
-2.0 -0.3 0.1 1.1 -0.7 -0.1
1.0 0.7 1.4 0.8 0.4 -0.0
-2.5 1.1 -1.3 1.1 -1.0 -1.0
-1.4 -1.0 -1.2 1.0 0.1 1.0
-1.1
Chi-square with 42 degrees of freedom:41.171792
z-score=-0.090365, p-value=0.492809
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_23:31
Test no p-value
1 0.021255
2 0.934041
3 0.025805
4 0.575026
5 0.384457
6 0.015841
7 0.922286
8 0.855140
9 0.006274
10 0.085119
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.009022
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_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 66515 0.35 66754 0.11
3 25000.00 25250 2.50 24968 0.04
4 6666.67 6628 0.22 6599 0.69
5 1388.89 1344 1.45 1403 0.14
6 238.10 226 0.61 228 0.43
7 34.72 33 0.09 41 1.14
8 4.96 3 0.77 6 0.22
p=0.57618 p=0.16260
Number of rngs required: 690323, p-value: 0.989
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_23:31
No. of wins: Observed Expected
98607 98585.9
z-score= 0.095, pvalue=0.53767
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67029 66666.7 1.969 1.969
2 37543 37654.3 0.329 2.298
3 27093 26954.7 0.709 3.008
4 19170 19313.5 1.066 4.073
5 13551 13851.4 6.516 10.589
6 9971 9943.5 0.076 10.665
7 7090 7145.0 0.424 11.089
8 5201 5139.1 0.746 11.835
9 3726 3699.9 0.185 12.019
10 2720 2666.3 1.082 13.101
11 1922 1923.3 0.001 13.102
12 1365 1388.7 0.406 13.508
13 1024 1003.7 0.410 13.918
14 691 726.1 1.701 15.618
15 518 525.8 0.117 15.735
16 377 381.2 0.045 15.780
17 287 276.5 0.396 16.176
18 188 200.8 0.820 16.996
19 134 146.0 0.984 17.980
20 110 106.2 0.135 18.114
21 290 287.1 0.029 18.143
Chisq= 18.14 for 20 degrees of freedom, p= 0.42204
SUMMARY of craptest
p-value for no. of wins: 0.537667
p-value for throws/game: 0.422039
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_23:31
No. of wins: Observed Expected
98422 98585.9
z-score=-0.733, pvalue=0.23182
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66463 66666.7 0.622 0.622
2 37733 37654.3 0.164 0.787
3 27104 26954.7 0.827 1.613
4 19161 19313.5 1.204 2.817
5 13987 13851.4 1.327 4.144
6 9871 9943.5 0.529 4.673
7 7251 7145.0 1.572 6.245
8 5144 5139.1 0.005 6.250
9 3706 3699.9 0.010 6.260
10 2713 2666.3 0.818 7.078
11 1883 1923.3 0.846 7.923
12 1352 1388.7 0.972 8.895
13 1007 1003.7 0.011 8.906
14 719 726.1 0.070 8.976
15 535 525.8 0.160 9.136
16 362 381.2 0.962 10.098
17 260 276.5 0.989 11.088
18 222 200.8 2.232 13.319
19 138 146.0 0.437 13.756
20 122 106.2 2.346 16.102
21 267 287.1 1.409 17.511
Chisq= 17.51 for 20 degrees of freedom, p= 0.38040
SUMMARY of craptest
p-value for no. of wins: 0.231819
p-value for throws/game: 0.380396
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0029,0.0063,0.0068,0.0088,0.0090,0.0131,0.0137,0.0148,0.0158,
0.0185,0.0213,0.0248,0.0258,0.0268,0.0271,0.0325,0.0448,0.0459,0.0486,
0.0533,0.0685,0.0700,0.0728,0.0769,0.0812,0.0851,0.0870,0.0882,0.0906,
0.0911,0.0920,0.1069,0.1142,0.1172,0.1195,0.1210,0.1219,0.1229,0.1297,
0.1338,0.1403,0.1535,0.1560,0.1576,0.1602,0.1626,0.1659,0.1688,0.1753,
0.1761,0.1951,0.1951,0.1998,0.2008,0.2019,0.2053,0.2318,0.2525,0.2550,
0.2561,0.2687,0.2747,0.2796,0.2822,0.2864,0.2866,0.2875,0.2896,0.2899,
0.2955,0.2961,0.3038,0.3040,0.3046,0.3118,0.3129,0.3136,0.3269,0.3330,
0.3353,0.3448,0.3527,0.3580,0.3595,0.3638,0.3699,0.3729,0.3735,0.3751,
0.3777,0.3804,0.3805,0.3814,0.3845,0.3972,0.4042,0.4068,0.4108,0.4131,
0.4146,0.4220,0.4226,0.4230,0.4268,0.4340,0.4362,0.4389,0.4393,0.4405,
0.4456,0.4483,0.4497,0.4703,0.4719,0.4721,0.4763,0.4774,0.4783,0.4817,
0.4818,0.4818,0.4821,0.4823,0.4885,0.4928,0.4959,0.5035,0.5064,0.5081,
0.5095,0.5104,0.5176,0.5182,0.5239,0.5334,0.5369,0.5377,0.5416,0.5480,
0.5511,0.5612,0.5699,0.5709,0.5750,0.5762,0.5788,0.5889,0.5900,0.5952,
0.5977,0.5993,0.6019,0.6079,0.6120,0.6134,0.6145,0.6181,0.6185,0.6235,
0.6350,0.6358,0.6386,0.6393,0.6426,0.6457,0.6463,0.6500,0.6523,0.6525,
0.6569,0.6631,0.6654,0.6686,0.6699,0.6760,0.6779,0.6791,0.6867,0.6879,
0.6966,0.6999,0.7003,0.7019,0.7026,0.7040,0.7042,0.7090,0.7194,0.7200,
0.7298,0.7311,0.7329,0.7333,0.7353,0.7373,0.7374,0.7387,0.7443,0.7457,
0.7533,0.7556,0.7562,0.7574,0.7593,0.7653,0.7666,0.7668,0.7725,0.7743,
0.7809,0.7809,0.7812,0.7822,0.7834,0.7836,0.7858,0.7878,0.7950,0.7956,
0.7978,0.8013,0.8023,0.8161,0.8170,0.8197,0.8227,0.8271,0.8284,0.8375,
0.8551,0.8556,0.8585,0.8656,0.8678,0.8700,0.8709,0.8719,0.8751,0.8765,
0.8948,0.9070,0.9082,0.9107,0.9210,0.9223,0.9242,0.9302,0.9308,0.9340,
0.9346,0.9346,0.9405,0.9425,0.9456,0.9465,0.9544,0.9565,0.9570,0.9601,
0.9617,0.9645,0.9842,0.9850,0.9880,0.9887,0.9909,0.9920,0.9959,
Overall p-value after applying KStest on 269 p-values = 0.321350
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.