RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 12.2666 0.216269
2 to 25 15.59 26.2463 0.929911
3 to 26 15.58 22.7923 0.843865
4 to 27 15.59 25.8342 0.922466
5 to 28 15.71 19.6072 0.705188
6 to 29 15.56 16.4699 0.509201
7 to 30 16.01 19.5146 0.700196
8 to 31 15.71 10.2361 0.106579
9 to 32 15.54 28.4927 0.960500
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.129330
Tough bday spacings test for dh-ranFile-2018-06-23_16:31: 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 49 64 96 87 80 59 26 16 9 1
(O-E)^2/E 1.6 4.2 1.2 0.0 1.2 0.0 0.9 0.5 0.1 0.9 2.3
Birthday Spacings: Sum(O-E)^2/E= 12.848, p= 0.768
RESULTS OF GCD FOR dh-ranFile-2018-06-23_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.707283
p-value, dist. of gcd's: 0.531702
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.963 0.183 0.510 0.014 0.856 0.072 0.087 0.346
Bits 8 to 15---> 0.379 0.418 0.417 0.892 0.211 0.788 0.249 0.225
Bits 16 to 23---> 0.260 0.358 0.428 0.791 0.872 0.923 0.213 0.166
Bits 24 to 31---> 0.926 0.806 0.830 0.904 0.289 0.485 0.440 0.630
KS test for the above 32 p values: 0.305
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_16:31,
p-values for 5 runs: 0.3139, 0.5908, 0.4423, 0.3807, 0.6570
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5083 5134.0 0.507 1.782
r= 30 23219 23103.0 0.582 2.364
r= 31 11503 11551.5 0.204 2.568
chi-square = 2.568 with df = 3; p-value = 0.537
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5105 5134.0 0.164 0.781
r= 31 23074 23103.0 0.037 0.817
r= 32 11621 11551.5 0.418 1.235
chi-square = 1.235 with df = 3; p-value = 0.255
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_16:31
b-rank test for bits 1 to 8, p=0.22361
b-rank test for bits 2 to 9, p=0.93732
b-rank test for bits 3 to 10, p=0.42190
b-rank test for bits 4 to 11, p=0.98794
b-rank test for bits 5 to 12, p=0.90279
b-rank test for bits 6 to 13, p=0.73738
b-rank test for bits 7 to 14, p=0.08874
b-rank test for bits 8 to 15, p=0.60959
b-rank test for bits 9 to 16, p=0.60810
b-rank test for bits 10 to 17, p=0.04658
b-rank test for bits 11 to 18, p=0.82863
b-rank test for bits 12 to 19, p=0.27712
b-rank test for bits 13 to 20, p=0.81436
b-rank test for bits 14 to 21, p=0.38354
b-rank test for bits 15 to 22, p=0.04511
b-rank test for bits 16 to 23, p=0.28256
b-rank test for bits 17 to 24, p=0.59411
b-rank test for bits 18 to 25, p=0.99762
b-rank test for bits 19 to 26, p=0.80349
b-rank test for bits 20 to 27, p=0.02809
b-rank test for bits 21 to 28, p=0.09844
b-rank test for bits 22 to 29, p=0.27079
b-rank test for bits 23 to 30, p=0.76099
b-rank test for bits 24 to 31, p=0.08255
b-rank test for bits 25 to 32, p=0.79473
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 = 0.432108
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_16:31
(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 141443 -1.09 0.137954
2 142185 0.64 0.740241
3 141578 -0.77 0.219425
4 141905 -0.01 0.495964
5 140927 -2.30 0.010862
6 142184 0.64 0.739483
7 141635 -0.64 0.260775
8 141692 -0.51 0.305804
9 141088 -1.92 0.027492
10 142131 0.52 0.697743
11 141648 -0.61 0.270738
12 142237 0.77 0.778038
13 142225 0.74 0.769605
14 142813 2.11 0.982630
15 142889 2.29 0.988959
16 141632 -0.65 0.258503
17 141076 -1.95 0.025765
18 141930 0.05 0.519259
19 141296 -1.43 0.075927
20 141280 -1.47 0.070727
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_16:31
Bits used No. missing words z-score p-value
23 to 32 141536 -1.2873 0.098987
22 to 31 141734 -0.6046 0.272727
21 to 30 142455 1.8816 0.970056
20 to 29 141958 0.1678 0.566641
19 to 28 142071 0.5575 0.711401
18 to 27 141702 -0.7149 0.237326
17 to 26 141722 -0.6460 0.259151
16 to 25 141649 -0.8977 0.184676
15 to 24 141908 -0.0046 0.498170
14 to 23 142181 0.9368 0.825568
13 to 22 141929 0.0678 0.527039
12 to 21 141746 -0.5632 0.286647
11 to 20 142052 0.4920 0.688628
10 to 19 141808 -0.3494 0.363389
9 to 18 141830 -0.2736 0.392215
8 to 17 142040 0.4506 0.673856
7 to 16 141964 0.1885 0.574764
6 to 15 141708 -0.6942 0.243765
5 to 14 141871 -0.1322 0.447424
4 to 13 142006 0.3333 0.630563
3 to 12 142040 0.4506 0.673856
2 to 11 141843 -0.2287 0.409542
1 to 10 142467 1.9230 0.972760
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_16:31
Bits used No. missing words z-score p-value
28 to 32 141876 -0.1130 0.455022
27 to 31 141624 -0.9672 0.166717
26 to 30 142047 0.4667 0.679635
25 to 29 141828 -0.2757 0.391391
24 to 28 142479 1.9311 0.973264
23 to 27 141897 -0.0418 0.483330
22 to 26 141957 0.1616 0.564187
21 to 25 141565 -1.1672 0.121561
20 to 24 142111 0.6836 0.752895
19 to 23 142012 0.3480 0.636093
18 to 22 141970 0.2057 0.581472
17 to 21 141727 -0.6181 0.268265
16 to 20 141993 0.2836 0.611652
15 to 19 142571 2.2429 0.987550
14 to 18 141861 -0.1638 0.434932
13 to 17 141249 -2.2384 0.012597
12 to 16 142085 0.5955 0.724243
11 to 15 141577 -1.1265 0.129968
10 to 14 141629 -0.9503 0.170987
9 to 13 141642 -0.9062 0.182414
8 to 12 141662 -0.8384 0.200901
7 to 11 141951 0.1413 0.556166
6 to 10 141816 -0.3164 0.375860
5 to 9 142240 1.1209 0.868838
4 to 8 141795 -0.3876 0.349171
3 to 7 141711 -0.6723 0.250695
2 to 6 141900 -0.0316 0.487385
1 to 5 141892 -0.0587 0.476577
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_16:31
Bits used No. missing words z-score p-value
31 to 32 141917 0.0226 0.509025
30 to 31 141594 -0.9302 0.176140
29 to 30 141746 -0.4818 0.314974
28 to 29 142244 0.9872 0.838234
27 to 28 142165 0.7542 0.774632
26 to 27 141573 -0.9921 0.160569
25 to 26 142076 0.4917 0.688517
24 to 25 142247 0.9961 0.840394
23 to 24 141941 0.0934 0.537216
22 to 23 141527 -1.1278 0.129699
21 to 22 142374 1.3707 0.914767
20 to 21 141956 0.1377 0.554749
19 to 20 142111 0.5949 0.724044
18 to 19 141851 -0.1721 0.431693
17 to 18 141679 -0.6794 0.248430
16 to 17 141255 -1.9302 0.026792
15 to 16 141011 -2.6499 0.004025
14 to 15 142244 0.9872 0.838234
13 to 14 142115 0.6067 0.727974
12 to 13 142074 0.4858 0.686429
11 to 12 141845 -0.1898 0.424747
10 to 11 141945 0.1052 0.541900
9 to 10 141689 -0.6499 0.257865
8 to 9 141144 -2.2576 0.011985
7 to 8 141690 -0.6470 0.258819
6 to 7 142132 0.6568 0.744359
5 to 6 141773 -0.4022 0.343786
4 to 5 141564 -1.0187 0.154179
3 to 4 141627 -0.8328 0.202470
2 to 3 142037 0.3766 0.646767
1 to 2 141245 -1.9597 0.025017
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2449.53 -0.714 0.237710
Test results for specific bytes for dh-ranFile-2018-06-23_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2460.45 -0.559 0.287989
2 to 9 2428.03 -1.018 0.154374
3 to 10 2460.21 -0.563 0.286803
4 to 11 2518.17 0.257 0.601409
5 to 12 2458.56 -0.586 0.278940
6 to 13 2494.30 -0.081 0.467882
7 to 14 2460.88 -0.553 0.290026
8 to 15 2523.48 0.332 0.630089
9 to 16 2523.33 0.330 0.629258
10 to 17 2446.70 -0.754 0.225476
11 to 18 2508.13 0.115 0.545778
12 to 19 2502.83 0.040 0.515977
13 to 20 2439.75 -0.852 0.197084
14 to 21 2536.00 0.509 0.694654
15 to 22 2539.22 0.555 0.710424
16 to 23 2538.32 0.542 0.706046
17 to 24 2480.77 -0.272 0.392856
18 to 25 2505.56 0.079 0.531312
19 to 26 2538.64 0.546 0.707609
20 to 27 2460.67 -0.556 0.289057
21 to 28 2455.90 -0.624 0.266403
22 to 29 2510.53 0.149 0.559187
23 to 30 2600.54 1.422 0.922473
24 to 31 2515.93 0.225 0.589134
25 to 32 2425.60 -1.052 0.146364
CDPARK for dh-ranFile-2018-06-23_16:31: 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
3540 0.7763 0.781201
3503 -0.9132 0.180558
3530 0.3196 0.625377
3531 0.3653 0.642555
3567 2.0091 0.977738
3499 -1.0959 0.136563
3499 -1.0959 0.136563
3525 0.0913 0.536383
3547 1.0959 0.863437
3581 2.6484 0.995956
Square side=100, avg. no. parked=3532.20 sample std.=26.43
p-value of the KSTEST for those 10 p-values: 0.279649
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_16:31
0.8270,0.9772,0.5875,0.2589,0.3175,0.8176,0.6277,0.1794,0.8379,0.7223,
The KS test for those 10 p-values: 0.340486
The 3DSPHERES test for dh-ranFile-2018-06-23_16:31
sample no r^3 equiv. uni.
1 58.533 0.857881
2 59.019 0.860168
3 23.629 0.545083
4 2.042 0.065815
5 9.505 0.271548
6 25.711 0.575577
7 3.506 0.110285
8 37.841 0.716734
9 7.750 0.227673
10 140.975 0.990897
11 34.341 0.681682
12 27.782 0.603890
13 3.141 0.099393
14 26.411 0.585372
15 9.907 0.281243
16 12.817 0.347687
17 24.052 0.551447
18 6.524 0.195450
19 12.795 0.347218
20 19.161 0.472029
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.838235
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -0.8 -0.3 1.9 -0.7
-0.3 -0.5 0.5 -1.2 -1.3 -1.7
-0.1 -0.1 1.2 -0.0 0.7 0.7
0.6 -1.3 -1.3 1.3 1.8 0.9
-0.3 -0.6 1.0 -1.8 -0.5 0.5
1.5 -2.0 -0.4 -0.9 -0.1 0.2
-0.9 0.8 0.9 -1.8 1.6 0.0
1.8
Chi-square with 42 degrees of freedom:47.454559
z-score=0.595141, p-value=0.739965
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_16:31
Test no p-value
1 0.032052
2 0.587025
3 0.076099
4 0.308735
5 0.643624
6 0.763736
7 0.214315
8 0.276809
9 0.718950
10 0.016717
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.164603
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_16:31:
(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 66469 0.59 66445 0.74
3 25000.00 25018 0.01 25151 0.91
4 6666.67 6824 3.71 6776 1.79
5 1388.89 1415 0.49 1366 0.38
6 238.10 233 0.11 231 0.21
7 34.72 36 0.05 23 3.96
8 4.96 4 0.19 7 0.84
p=0.47463 p=0.81639
Number of rngs required: 688947, p-value: 0.735
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_16:31
No. of wins: Observed Expected
98385 98585.9
z-score=-0.898, pvalue=0.18450
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66827 66666.7 0.386 0.386
2 37704 37654.3 0.066 0.451
3 26747 26954.7 1.601 2.052
4 19264 19313.5 0.127 2.179
5 13862 13851.4 0.008 2.187
6 9862 9943.5 0.669 2.856
7 7259 7145.0 1.818 4.674
8 5203 5139.1 0.795 5.469
9 3662 3699.9 0.388 5.856
10 2674 2666.3 0.022 5.879
11 1881 1923.3 0.932 6.810
12 1409 1388.7 0.296 7.106
13 983 1003.7 0.428 7.533
14 704 726.1 0.675 8.208
15 536 525.8 0.196 8.405
16 400 381.2 0.932 9.337
17 264 276.5 0.569 9.906
18 214 200.8 0.864 10.769
19 146 146.0 0.000 10.769
20 95 106.2 1.184 11.953
21 304 287.1 0.993 12.947
Chisq= 12.95 for 20 degrees of freedom, p= 0.12034
SUMMARY of craptest
p-value for no. of wins: 0.184498
p-value for throws/game: 0.120337
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_16:31
No. of wins: Observed Expected
98579 98585.9
z-score=-0.031, pvalue=0.48776
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66734 66666.7 0.068 0.068
2 37605 37654.3 0.065 0.133
3 26648 26954.7 3.490 3.623
4 19306 19313.5 0.003 3.626
5 14106 13851.4 4.679 8.305
6 9978 9943.5 0.119 8.424
7 7094 7145.0 0.364 8.789
8 5151 5139.1 0.028 8.816
9 3644 3699.9 0.844 9.660
10 2682 2666.3 0.092 9.752
11 1975 1923.3 1.388 11.141
12 1380 1388.7 0.055 11.196
13 992 1003.7 0.137 11.332
14 720 726.1 0.052 11.384
15 524 525.8 0.006 11.391
16 392 381.2 0.309 11.700
17 276 276.5 0.001 11.701
18 209 200.8 0.332 12.033
19 164 146.0 2.223 14.256
20 118 106.2 1.308 15.564
21 302 287.1 0.772 16.336
Chisq= 16.34 for 20 degrees of freedom, p= 0.30440
SUMMARY of craptest
p-value for no. of wins: 0.487764
p-value for throws/game: 0.304399
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0040,0.0109,0.0120,0.0126,0.0141,0.0167,0.0250,0.0258,0.0268,0.0275,
0.0281,0.0321,0.0451,0.0466,0.0658,0.0707,0.0716,0.0759,0.0761,0.0826,
0.0867,0.0887,0.0984,0.0990,0.0994,0.1066,0.1103,0.1203,0.1216,0.1293,
0.1297,0.1300,0.1366,0.1366,0.1380,0.1464,0.1542,0.1544,0.1606,0.1646,
0.1658,0.1667,0.1710,0.1761,0.1794,0.1806,0.1824,0.1828,0.1845,0.1847,
0.1954,0.1971,0.2009,0.2025,0.2112,0.2126,0.2143,0.2163,0.2194,0.2236,
0.2247,0.2255,0.2277,0.2373,0.2377,0.2438,0.2484,0.2485,0.2507,0.2554,
0.2579,0.2585,0.2588,0.2589,0.2592,0.2597,0.2608,0.2664,0.2683,0.2707,
0.2708,0.2715,0.2727,0.2768,0.2771,0.2789,0.2796,0.2812,0.2826,0.2866,
0.2868,0.2880,0.2889,0.2891,0.2900,0.3044,0.3050,0.3058,0.3087,0.3139,
0.3150,0.3175,0.3405,0.3438,0.3456,0.3472,0.3477,0.3492,0.3577,0.3634,
0.3759,0.3791,0.3807,0.3835,0.3914,0.3922,0.3929,0.4095,0.4168,0.4185,
0.4219,0.4247,0.4277,0.4317,0.4321,0.4349,0.4403,0.4423,0.4474,0.4550,
0.4679,0.4720,0.4746,0.4766,0.4833,0.4847,0.4874,0.4878,0.4960,0.4982,
0.5090,0.5092,0.5103,0.5160,0.5193,0.5270,0.5313,0.5317,0.5364,0.5368,
0.5372,0.5419,0.5451,0.5458,0.5514,0.5547,0.5562,0.5592,0.5642,0.5666,
0.5748,0.5756,0.5815,0.5854,0.5870,0.5875,0.5891,0.5908,0.5941,0.6014,
0.6039,0.6081,0.6096,0.6117,0.6254,0.6277,0.6293,0.6301,0.6302,0.6306,
0.6361,0.6426,0.6436,0.6468,0.6570,0.6739,0.6739,0.6796,0.6817,0.6864,
0.6885,0.6886,0.6947,0.6977,0.7002,0.7052,0.7060,0.7073,0.7076,0.7104,
0.7114,0.7167,0.7190,0.7223,0.7240,0.7242,0.7280,0.7349,0.7374,0.7395,
0.7400,0.7402,0.7444,0.7529,0.7610,0.7637,0.7677,0.7696,0.7746,0.7780,
0.7812,0.7881,0.7913,0.7947,0.8035,0.8060,0.8144,0.8164,0.8176,0.8256,
0.8270,0.8286,0.8305,0.8379,0.8382,0.8382,0.8382,0.8404,0.8439,0.8564,
0.8579,0.8602,0.8634,0.8688,0.8716,0.8921,0.9028,0.9039,0.9148,0.9225,
0.9225,0.9234,0.9256,0.9299,0.9373,0.9605,0.9633,0.9701,0.9728,0.9733,
0.9772,0.9777,0.9826,0.9875,0.9879,0.9890,0.9909,0.9960,0.9976,
Overall p-value after applying KStest on 269 p-values = 0.297397
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.