RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.87 20.0647 0.729068
2 to 25 15.90 15.6669 0.452437
3 to 26 15.79 13.0449 0.266823
4 to 27 16.02 6.9974 0.016417
5 to 28 15.72 12.3022 0.218496
6 to 29 15.74 15.8844 0.467954
7 to 30 15.93 23.5524 0.867884
8 to 31 15.91 8.6667 0.049858
9 to 32 15.75 10.6823 0.127403
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.210785
Tough bday spacings test for dh-ranFile-2018-07-02_21:31: 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 32 56 94 118 75 54 36 6 6 10
(O-E)^2/E 1.6 0.6 4.1 0.1 4.2 0.1 0.1 1.3 5.3 0.1 8.7
Birthday Spacings: Sum(O-E)^2/E= 26.150, p= 0.996
RESULTS OF GCD FOR dh-ranFile-2018-07-02_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.591430
p-value, dist. of gcd's: 0.488764
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.472 0.272 0.208 0.608 0.999 0.907 0.805 0.028
Bits 8 to 15---> 0.091 0.420 0.301 0.755 0.618 0.129 0.869 0.732
Bits 16 to 23---> 0.237 0.809 0.002 0.794 0.750 0.924 0.297 0.758
Bits 24 to 31---> 0.701 0.440 0.985 0.068 0.225 0.204 0.902 0.783
KS test for the above 32 p values: 0.559
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_21:31,
p-values for 5 runs: 0.8076, 0.6297, 0.7857, 0.1530, 0.7675
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 235 211.4 2.630 2.630
r= 29 5253 5134.0 2.758 5.388
r= 30 22879 23103.0 2.173 7.561
r= 31 11633 11551.5 0.575 8.136
chi-square = 8.136 with df = 3; p-value = 0.957
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 194 211.4 1.435 1.435
r= 30 5112 5134.0 0.094 1.529
r= 31 23067 23103.0 0.056 1.586
r= 32 11627 11551.5 0.493 2.079
chi-square = 2.079 with df = 3; p-value = 0.444
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_21:31
b-rank test for bits 1 to 8, p=0.17323
b-rank test for bits 2 to 9, p=0.40277
b-rank test for bits 3 to 10, p=0.55160
b-rank test for bits 4 to 11, p=0.06237
b-rank test for bits 5 to 12, p=0.05172
b-rank test for bits 6 to 13, p=0.62565
b-rank test for bits 7 to 14, p=0.44649
b-rank test for bits 8 to 15, p=0.01156
b-rank test for bits 9 to 16, p=0.26212
b-rank test for bits 10 to 17, p=0.65771
b-rank test for bits 11 to 18, p=0.35551
b-rank test for bits 12 to 19, p=0.47292
b-rank test for bits 13 to 20, p=0.82721
b-rank test for bits 14 to 21, p=0.76422
b-rank test for bits 15 to 22, p=0.97430
b-rank test for bits 16 to 23, p=0.90297
b-rank test for bits 17 to 24, p=0.98494
b-rank test for bits 18 to 25, p=0.84287
b-rank test for bits 19 to 26, p=0.42510
b-rank test for bits 20 to 27, p=0.11312
b-rank test for bits 21 to 28, p=0.46692
b-rank test for bits 22 to 29, p=0.71850
b-rank test for bits 23 to 30, p=0.22286
b-rank test for bits 24 to 31, p=0.34585
b-rank test for bits 25 to 32, p=0.30953
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 = 0.978202
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_21:31
(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 142246 0.79 0.784246
2 141949 0.09 0.536924
3 142252 0.80 0.788327
4 142063 0.36 0.640218
5 142270 0.84 0.800298
6 142211 0.70 0.759544
7 141796 -0.26 0.395586
8 141449 -1.08 0.141067
9 141740 -0.40 0.346189
10 141310 -1.40 0.080711
11 142310 0.94 0.825401
12 141748 -0.38 0.353109
13 141822 -0.20 0.419160
14 141483 -1.00 0.159601
15 142084 0.41 0.658403
16 141541 -0.86 0.194734
17 142343 1.01 0.844529
18 141859 -0.12 0.453195
19 141751 -0.37 0.355717
20 141844 -0.15 0.439341
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_21:31
Bits used No. missing words z-score p-value
23 to 32 141806 -0.3563 0.360804
22 to 31 141796 -0.3908 0.347975
21 to 30 141804 -0.3632 0.358225
20 to 29 142216 1.0575 0.854854
19 to 28 141989 0.2747 0.608236
18 to 27 142233 1.1161 0.867811
17 to 26 141887 -0.0770 0.469312
16 to 25 141796 -0.3908 0.347975
15 to 24 141487 -1.4563 0.072653
14 to 23 141364 -1.8804 0.030024
13 to 22 141383 -1.8149 0.034767
12 to 21 142509 2.0678 0.980672
11 to 20 142099 0.6540 0.743455
10 to 19 141943 0.1161 0.546215
9 to 18 141684 -0.7770 0.218579
8 to 17 141949 0.1368 0.554403
7 to 16 141852 -0.1977 0.421644
6 to 15 141838 -0.2460 0.402855
5 to 14 141823 -0.2977 0.382970
4 to 13 142105 0.6747 0.750075
3 to 12 141962 0.1816 0.572060
2 to 11 142110 0.6920 0.755521
1 to 10 141801 -0.3736 0.354369
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_21:31
Bits used No. missing words z-score p-value
28 to 32 141679 -0.7808 0.217466
27 to 31 142086 0.5989 0.725374
26 to 30 141746 -0.5537 0.289905
25 to 29 142168 0.8768 0.809715
24 to 28 142275 1.2396 0.892431
23 to 27 142196 0.9718 0.834416
22 to 26 141610 -1.0147 0.155130
21 to 25 141945 0.1209 0.548121
20 to 24 142046 0.4633 0.678421
19 to 23 141733 -0.5977 0.275010
18 to 22 141215 -2.3537 0.009295
17 to 21 142337 1.4497 0.926433
16 to 20 141829 -0.2723 0.392694
15 to 19 142652 2.5175 0.994091
14 to 18 141975 0.2226 0.588081
13 to 17 141759 -0.5096 0.305168
12 to 16 142161 0.8531 0.803203
11 to 15 141589 -1.0859 0.138770
10 to 14 141945 0.1209 0.548121
9 to 13 142058 0.5040 0.692857
8 to 12 141632 -0.9401 0.173583
7 to 11 141878 -0.1062 0.457711
6 to 10 142211 1.0226 0.846754
5 to 9 142210 1.0192 0.845951
4 to 8 141819 -0.3062 0.379725
3 to 7 141987 0.2633 0.603836
2 to 6 142396 1.6497 0.950501
1 to 5 142172 0.8904 0.813376
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_21:31
Bits used No. missing words z-score p-value
31 to 32 142018 0.3206 0.625728
30 to 31 141992 0.2439 0.596332
29 to 30 141776 -0.3933 0.347048
28 to 29 142181 0.8014 0.788546
27 to 28 141912 0.0079 0.503142
26 to 27 142145 0.6952 0.756532
25 to 26 141587 -0.9508 0.170846
24 to 25 141297 -1.8063 0.035437
23 to 24 141716 -0.5703 0.284239
22 to 23 141303 -1.7886 0.036841
21 to 22 141701 -0.6145 0.269428
20 to 21 141886 -0.0688 0.472566
19 to 20 141311 -1.7650 0.038783
18 to 19 141918 0.0256 0.510202
17 to 18 142434 1.5477 0.939153
16 to 17 141426 -1.4258 0.076970
15 to 16 142362 1.3353 0.909113
14 to 15 141695 -0.6322 0.263614
13 to 14 142052 0.4209 0.663070
12 to 13 142189 0.8250 0.795310
11 to 12 141807 -0.3019 0.381380
10 to 11 142005 0.2822 0.611110
9 to 10 141772 -0.4051 0.342701
8 to 9 142212 0.8928 0.814026
7 to 8 142051 0.4179 0.661992
6 to 7 141869 -0.1190 0.452651
5 to 6 142024 0.3383 0.632416
4 to 5 141946 0.1082 0.543070
3 to 4 142209 0.8840 0.811647
2 to 3 141847 -0.1839 0.427060
1 to 2 142132 0.6568 0.744359
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2405.05 -1.343 0.089661
Test results for specific bytes for dh-ranFile-2018-07-02_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2476.29 -0.335 0.368716
2 to 9 2463.40 -0.518 0.302378
3 to 10 2399.84 -1.416 0.078328
4 to 11 2477.71 -0.315 0.376270
5 to 12 2538.00 0.537 0.704483
6 to 13 2508.96 0.127 0.550409
7 to 14 2403.99 -1.358 0.087270
8 to 15 2400.74 -1.404 0.080207
9 to 16 2565.48 0.926 0.822776
10 to 17 2463.05 -0.523 0.300627
11 to 18 2480.51 -0.276 0.391397
12 to 19 2480.83 -0.271 0.393158
13 to 20 2450.73 -0.697 0.242982
14 to 21 2559.20 0.837 0.798761
15 to 22 2507.73 0.109 0.543522
16 to 23 2494.27 -0.081 0.467715
17 to 24 2576.78 1.086 0.861234
18 to 25 2513.45 0.190 0.575416
19 to 26 2540.26 0.569 0.715447
20 to 27 2674.41 2.467 0.993179
21 to 28 2395.85 -1.473 0.070383
22 to 29 2544.48 0.629 0.735347
23 to 30 2461.19 -0.549 0.291558
24 to 31 2583.19 1.176 0.880286
25 to 32 2547.22 0.668 0.747849
CDPARK for dh-ranFile-2018-07-02_21:31: 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
3548 1.1416 0.873180
3509 -0.6393 0.261324
3524 0.0457 0.518210
3555 1.4612 0.928018
3575 2.3744 0.991212
3501 -1.0046 0.157553
3537 0.6393 0.738676
3515 -0.3653 0.357445
3524 0.0457 0.518210
3525 0.0913 0.536383
Square side=100, avg. no. parked=3531.30 sample std.=21.47
p-value of the KSTEST for those 10 p-values: 0.508410
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_21:31
0.0708,0.3246,0.1963,0.8180,0.1628,0.3929,0.8668,0.8517,0.5730,0.0464,
The KS test for those 10 p-values: 0.622878
The 3DSPHERES test for dh-ranFile-2018-07-02_21:31
sample no r^3 equiv. uni.
1 22.695 0.530699
2 44.107 0.770129
3 10.171 0.287538
4 77.554 0.924614
5 43.890 0.768463
6 21.831 0.516980
7 43.607 0.766261
8 81.402 0.933689
9 74.801 0.917367
10 30.029 0.632473
11 82.221 0.935475
12 3.432 0.108104
13 16.055 0.414423
14 7.568 0.222954
15 70.385 0.904263
16 7.911 0.231802
17 5.137 0.157367
18 141.343 0.991008
19 42.207 0.755097
20 6.117 0.184446
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.133699
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 -0.1 1.8 -0.3 1.8
-1.7 -0.3 0.6 0.5 0.5 1.8
0.4 0.3 -2.5 0.9 0.7 -0.5
-1.0 -0.3 0.0 0.6 0.8 0.6
-1.5 -1.1 -0.6 0.2 0.1 0.4
-0.1 1.9 -1.0 -1.2 0.6 -0.1
-1.9 -0.7 -1.2 -0.1 0.9 1.0
-0.1
Chi-square with 42 degrees of freedom:42.567139
z-score=0.061880, p-value=0.553434
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_21:31
Test no p-value
1 0.011530
2 0.212242
3 0.198886
4 0.121264
5 0.024832
6 0.208670
7 0.545201
8 0.303464
9 0.091600
10 0.965359
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.008168
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_21:31:
(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 66620 0.03 66706 0.02
3 25000.00 25088 0.31 24944 0.13
4 6666.67 6601 0.65 6708 0.26
5 1388.89 1426 0.99 1378 0.09
6 238.10 221 1.23 231 0.21
7 34.72 36 0.05 29 0.94
8 4.96 7 0.84 3 0.77
p=0.33611 p=0.12253
Number of rngs required: 688240, p-value: 0.426
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_21:31
No. of wins: Observed Expected
98827 98585.9
z-score= 1.079, pvalue=0.85960
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67132 66666.7 3.248 3.248
2 37395 37654.3 1.786 5.034
3 26839 26954.7 0.497 5.531
4 19398 19313.5 0.370 5.901
5 13900 13851.4 0.170 6.071
6 9792 9943.5 2.310 8.381
7 7163 7145.0 0.045 8.426
8 5021 5139.1 2.713 11.139
9 3733 3699.9 0.297 11.436
10 2611 2666.3 1.147 12.582
11 1959 1923.3 0.662 13.244
12 1429 1388.7 1.167 14.411
13 1041 1003.7 1.385 15.796
14 673 726.1 3.889 19.685
15 533 525.8 0.098 19.783
16 386 381.2 0.062 19.844
17 249 276.5 2.743 22.587
18 210 200.8 0.419 23.006
19 146 146.0 0.000 23.006
20 107 106.2 0.006 23.011
21 283 287.1 0.059 23.070
Chisq= 23.07 for 20 degrees of freedom, p= 0.71465
SUMMARY of craptest
p-value for no. of wins: 0.859600
p-value for throws/game: 0.714648
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_21:31
No. of wins: Observed Expected
98551 98585.9
z-score=-0.156, pvalue=0.43805
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66360 66666.7 1.411 1.411
2 37631 37654.3 0.014 1.425
3 27117 26954.7 0.977 2.402
4 19399 19313.5 0.379 2.781
5 13832 13851.4 0.027 2.808
6 9985 9943.5 0.173 2.981
7 7128 7145.0 0.041 3.021
8 5191 5139.1 0.525 3.546
9 3802 3699.9 2.819 6.366
10 2723 2666.3 1.206 7.571
11 1879 1923.3 1.022 8.593
12 1391 1388.7 0.004 8.597
13 951 1003.7 2.769 11.365
14 724 726.1 0.006 11.372
15 507 525.8 0.675 12.046
16 383 381.2 0.009 12.055
17 273 276.5 0.045 12.101
18 192 200.8 0.388 12.489
19 144 146.0 0.027 12.516
20 100 106.2 0.364 12.880
21 288 287.1 0.003 12.882
Chisq= 12.88 for 20 degrees of freedom, p= 0.11763
SUMMARY of craptest
p-value for no. of wins: 0.438053
p-value for throws/game: 0.117625
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0024,0.0082,0.0093,0.0115,0.0116,0.0164,0.0248,0.0276,0.0300,0.0348,
0.0354,0.0368,0.0388,0.0464,0.0499,0.0517,0.0624,0.0680,0.0704,0.0708,
0.0727,0.0770,0.0783,0.0802,0.0807,0.0873,0.0897,0.0908,0.0916,0.1081,
0.1131,0.1176,0.1213,0.1225,0.1274,0.1290,0.1337,0.1388,0.1411,0.1530,
0.1551,0.1574,0.1576,0.1596,0.1628,0.1708,0.1732,0.1736,0.1844,0.1947,
0.1963,0.1989,0.2039,0.2077,0.2087,0.2108,0.2122,0.2175,0.2185,0.2186,
0.2229,0.2230,0.2247,0.2318,0.2371,0.2430,0.2613,0.2621,0.2636,0.2668,
0.2694,0.2720,0.2750,0.2842,0.2875,0.2899,0.2916,0.2966,0.3006,0.3008,
0.3024,0.3035,0.3052,0.3095,0.3246,0.3361,0.3427,0.3459,0.3462,0.3470,
0.3480,0.3480,0.3531,0.3544,0.3555,0.3557,0.3574,0.3582,0.3608,0.3687,
0.3763,0.3797,0.3814,0.3830,0.3914,0.3927,0.3929,0.3932,0.3956,0.4028,
0.4029,0.4144,0.4192,0.4201,0.4216,0.4251,0.4256,0.4271,0.4381,0.4393,
0.4397,0.4438,0.4465,0.4524,0.4527,0.4532,0.4577,0.4669,0.4677,0.4680,
0.4693,0.4715,0.4726,0.4729,0.4888,0.5031,0.5084,0.5102,0.5170,0.5182,
0.5182,0.5307,0.5364,0.5369,0.5431,0.5435,0.5452,0.5462,0.5481,0.5481,
0.5504,0.5516,0.5534,0.5544,0.5593,0.5721,0.5730,0.5754,0.5881,0.5914,
0.5963,0.6038,0.6082,0.6085,0.6111,0.6182,0.6229,0.6257,0.6257,0.6297,
0.6324,0.6325,0.6402,0.6577,0.6584,0.6620,0.6631,0.6784,0.6929,0.7010,
0.7045,0.7146,0.7154,0.7185,0.7254,0.7291,0.7318,0.7353,0.7387,0.7435,
0.7444,0.7478,0.7501,0.7504,0.7551,0.7555,0.7555,0.7565,0.7585,0.7595,
0.7642,0.7663,0.7675,0.7685,0.7701,0.7830,0.7842,0.7857,0.7883,0.7885,
0.7937,0.7953,0.7988,0.8003,0.8032,0.8048,0.8076,0.8095,0.8097,0.8116,
0.8134,0.8140,0.8180,0.8228,0.8254,0.8272,0.8344,0.8429,0.8445,0.8460,
0.8468,0.8517,0.8549,0.8596,0.8612,0.8668,0.8678,0.8679,0.8688,0.8732,
0.8803,0.8924,0.9018,0.9030,0.9043,0.9071,0.9091,0.9174,0.9238,0.9246,
0.9264,0.9280,0.9337,0.9355,0.9392,0.9505,0.9567,0.9654,0.9743,0.9782,
0.9807,0.9849,0.9849,0.9910,0.9912,0.9932,0.9941,0.9965,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.946460
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.