RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_14:31
(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 14.9415 0.400302
2 to 25 15.77 17.2898 0.565098
3 to 26 15.89 8.1019 0.035680
4 to 27 15.65 13.7370 0.314376
5 to 28 15.66 18.2949 0.629529
6 to 29 15.61 26.0731 0.926861
7 to 30 16.00 12.9380 0.259673
8 to 31 16.00 18.4087 0.636490
9 to 32 15.84 23.7571 0.873814
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.984100
Tough bday spacings test for dh-ranFile-2018-06-24_14:31: 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 43 68 93 108 78 41 34 10 8 6
(O-E)^2/E 0.4 1.1 0.4 0.2 1.1 0.0 2.4 0.6 1.6 0.3 0.9
Birthday Spacings: Sum(O-E)^2/E= 8.948, p= 0.463
RESULTS OF GCD FOR dh-ranFile-2018-06-24_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.035104
p-value, dist. of gcd's: 0.964592
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.115 0.806 0.676 0.361 0.570 0.528 0.618 0.465
Bits 8 to 15---> 0.852 0.915 0.696 0.894 0.409 0.097 0.545 0.230
Bits 16 to 23---> 0.554 0.103 0.588 0.010 0.556 0.218 0.802 0.084
Bits 24 to 31---> 0.490 0.694 0.236 0.543 0.679 0.369 0.480 0.072
KS test for the above 32 p values: 0.470
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_14:31,
p-values for 5 runs: 0.2752, 0.6278, 0.7565, 0.0840, 0.1255
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5053 5134.0 1.278 2.579
r= 30 23200 23103.0 0.407 2.986
r= 31 11519 11551.5 0.092 3.077
chi-square = 3.077 with df = 3; p-value = 0.620
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5214 5134.0 1.246 1.863
r= 31 23035 23103.0 0.200 2.063
r= 32 11551 11551.5 0.000 2.063
chi-square = 2.063 with df = 3; p-value = 0.441
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_14:31
b-rank test for bits 1 to 8, p=0.77620
b-rank test for bits 2 to 9, p=0.81962
b-rank test for bits 3 to 10, p=0.60363
b-rank test for bits 4 to 11, p=0.16047
b-rank test for bits 5 to 12, p=0.62405
b-rank test for bits 6 to 13, p=0.50332
b-rank test for bits 7 to 14, p=0.82997
b-rank test for bits 8 to 15, p=0.52649
b-rank test for bits 9 to 16, p=0.71497
b-rank test for bits 10 to 17, p=0.07041
b-rank test for bits 11 to 18, p=0.66923
b-rank test for bits 12 to 19, p=0.42806
b-rank test for bits 13 to 20, p=0.94005
b-rank test for bits 14 to 21, p=0.11731
b-rank test for bits 15 to 22, p=0.12688
b-rank test for bits 16 to 23, p=0.24491
b-rank test for bits 17 to 24, p=0.97943
b-rank test for bits 18 to 25, p=0.70054
b-rank test for bits 19 to 26, p=0.08874
b-rank test for bits 20 to 27, p=0.26850
b-rank test for bits 21 to 28, p=0.64707
b-rank test for bits 22 to 29, p=0.62650
b-rank test for bits 23 to 30, p=0.19815
b-rank test for bits 24 to 31, p=0.38494
b-rank test for bits 25 to 32, p=0.78485
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 = 0.914274
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_14:31
(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 142147 0.56 0.710657
2 141243 -1.56 0.059754
3 141041 -2.03 0.021239
4 141563 -0.81 0.209205
5 142423 1.20 0.884962
6 141866 -0.10 0.459681
7 142153 0.57 0.715431
8 141109 -1.87 0.030747
9 141460 -1.05 0.146897
10 142404 1.16 0.876113
11 141740 -0.40 0.346189
12 140764 -2.68 0.003725
13 142088 0.42 0.661827
14 141525 -0.90 0.184602
15 142026 0.27 0.607417
16 141522 -0.90 0.182739
17 142092 0.43 0.665237
18 141923 0.03 0.512740
19 141650 -0.61 0.272287
20 141705 -0.48 0.316536
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_14:31
Bits used No. missing words z-score p-value
23 to 32 141152 -2.6115 0.004508
22 to 31 141952 0.1471 0.558488
21 to 30 141606 -1.0460 0.147789
20 to 29 141536 -1.2873 0.098987
19 to 28 142255 1.1920 0.883363
18 to 27 141915 0.0196 0.507800
17 to 26 141511 -1.3736 0.084790
16 to 25 141969 0.2058 0.581510
15 to 24 141874 -0.1218 0.451518
14 to 23 141497 -1.4218 0.077538
13 to 22 141994 0.2920 0.614844
12 to 21 141605 -1.0494 0.146994
11 to 20 141587 -1.1115 0.133180
10 to 19 141550 -1.2391 0.107660
9 to 18 141646 -0.9080 0.181930
8 to 17 142320 1.4161 0.921627
7 to 16 141300 -2.1011 0.017814
6 to 15 142051 0.4885 0.687408
5 to 14 141678 -0.7977 0.212525
4 to 13 141909 -0.0011 0.499546
3 to 12 141956 0.1609 0.563926
2 to 11 141460 -1.5494 0.060641
1 to 10 141986 0.2644 0.604256
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_14:31
Bits used No. missing words z-score p-value
28 to 32 141873 -0.1232 0.450993
27 to 31 141541 -1.2486 0.105910
26 to 30 141691 -0.7401 0.229619
25 to 29 142129 0.7446 0.771757
24 to 28 141632 -0.9401 0.173583
23 to 27 141832 -0.2621 0.396609
22 to 26 141669 -0.8147 0.207628
21 to 25 141844 -0.2215 0.412368
20 to 24 141179 -2.4757 0.006649
19 to 23 142060 0.5107 0.695236
18 to 22 141854 -0.1876 0.425611
17 to 21 141807 -0.3469 0.364340
16 to 20 141295 -2.0825 0.018650
15 to 19 141687 -0.7537 0.225526
14 to 18 141797 -0.3808 0.351683
13 to 17 141509 -1.3571 0.087383
12 to 16 142180 0.9175 0.820566
11 to 15 142555 2.1887 0.985691
10 to 14 141538 -1.2587 0.104061
9 to 13 141755 -0.5232 0.300434
8 to 12 141890 -0.0655 0.473878
7 to 11 142288 1.2836 0.900364
6 to 10 142404 1.6768 0.953214
5 to 9 142455 1.8497 0.967824
4 to 8 142148 0.8091 0.790757
3 to 7 141661 -0.8418 0.199951
2 to 6 142034 0.4226 0.663710
1 to 5 142041 0.4463 0.672324
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_14:31
Bits used No. missing words z-score p-value
31 to 32 141405 -1.4877 0.068415
30 to 31 142870 2.8338 0.997700
29 to 30 141928 0.0551 0.521960
28 to 29 141844 -0.1927 0.423592
27 to 28 142208 0.8810 0.810850
26 to 27 141955 0.1347 0.553583
25 to 26 141884 -0.0747 0.470219
24 to 25 142540 1.8604 0.968584
23 to 24 141731 -0.5260 0.299428
22 to 23 141700 -0.6175 0.268455
21 to 22 141668 -0.7119 0.238267
20 to 21 142124 0.6332 0.736713
19 to 20 141906 -0.0098 0.496081
18 to 19 141772 -0.4051 0.342701
17 to 18 141517 -1.1573 0.123572
16 to 17 141849 -0.1780 0.429375
15 to 16 142035 0.3707 0.644573
14 to 15 142303 1.1613 0.877234
13 to 14 141974 0.1908 0.575646
12 to 13 142038 0.3796 0.647863
11 to 12 141917 0.0226 0.509025
10 to 11 142618 2.0905 0.981712
9 to 10 141002 -2.6765 0.003720
8 to 9 141956 0.1377 0.554749
7 to 8 142306 1.1701 0.879023
6 to 7 141875 -0.1013 0.459669
5 to 6 141967 0.1701 0.567541
4 to 5 142376 1.3766 0.915683
3 to 4 142130 0.6509 0.742459
2 to 3 141131 -2.2960 0.010839
1 to 2 142013 0.3058 0.620126
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2482.55 -0.247 0.402550
Test results for specific bytes for dh-ranFile-2018-06-24_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2482.70 -0.245 0.403364
2 to 9 2476.38 -0.334 0.369196
3 to 10 2503.49 0.049 0.519691
4 to 11 2499.97 -0.000 0.499830
5 to 12 2439.90 -0.850 0.197674
6 to 13 2591.63 1.296 0.902496
7 to 14 2445.46 -0.771 0.220264
8 to 15 2444.73 -0.782 0.217233
9 to 16 2431.84 -0.964 0.167558
10 to 17 2565.42 0.925 0.822576
11 to 18 2485.04 -0.212 0.416232
12 to 19 2534.47 0.488 0.687053
13 to 20 2511.08 0.157 0.562285
14 to 21 2559.44 0.841 0.799723
15 to 22 2449.22 -0.718 0.236338
16 to 23 2458.07 -0.593 0.276597
17 to 24 2512.99 0.184 0.572866
18 to 25 2531.33 0.443 0.671148
19 to 26 2440.60 -0.840 0.200433
20 to 27 2514.67 0.208 0.582193
21 to 28 2410.86 -1.261 0.103721
22 to 29 2401.94 -1.387 0.082761
23 to 30 2607.94 1.527 0.936561
24 to 31 2488.67 -0.160 0.436366
25 to 32 2371.23 -1.821 0.034302
CDPARK for dh-ranFile-2018-06-24_14:31: 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
3471 -2.3744 0.008788
3505 -0.8219 0.205562
3537 0.6393 0.738676
3494 -1.3242 0.092718
3529 0.2740 0.607947
3501 -1.0046 0.157553
3514 -0.4110 0.340551
3522 -0.0457 0.481790
3524 0.0457 0.518210
3484 -1.7808 0.037471
Square side=100, avg. no. parked=3508.10 sample std.=19.92
p-value of the KSTEST for those 10 p-values: 0.069269
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_14:31
0.5624,0.0870,0.6035,0.3299,0.3803,0.3042,0.7086,0.5751,0.9646,0.9582,
The KS test for those 10 p-values: 0.731084
The 3DSPHERES test for dh-ranFile-2018-06-24_14:31
sample no r^3 equiv. uni.
1 33.250 0.669890
2 1.292 0.042167
3 125.267 0.984633
4 55.239 0.841392
5 34.951 0.688089
6 25.779 0.576543
7 81.704 0.934353
8 48.712 0.802840
9 12.176 0.333593
10 8.625 0.249853
11 31.460 0.649591
12 49.540 0.808207
13 19.441 0.476929
14 52.179 0.824359
15 14.581 0.384928
16 81.548 0.934012
17 151.493 0.993589
18 13.083 0.353453
19 2.039 0.065707
20 5.409 0.164993
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.231438
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.9 0.3 1.5 -0.6 -0.5
-2.0 -0.1 -1.2 -0.3 0.6 -1.7
1.1 -0.3 -0.5 0.3 0.9 0.5
0.1 -0.6 -0.7 -0.6 0.8 0.2
0.9 -0.1 0.9 0.9 -0.2 1.5
0.7 -0.4 -1.1 -1.5 -0.1 -1.4
-0.2 0.5 -1.2 -0.7 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:32.968322
z-score=-0.985437, p-value=0.160524
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_14:31
Test no p-value
1 0.184206
2 0.287836
3 0.513128
4 0.014058
5 0.042303
6 0.386683
7 0.286305
8 0.719865
9 0.939091
10 0.024728
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.076006
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_14:31:
(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 66721 0.04 66656 0.00
3 25000.00 24962 0.06 24999 0.00
4 6666.67 6619 0.34 6690 0.08
5 1388.89 1418 0.61 1372 0.21
6 238.10 238 0.00 248 0.41
7 34.72 38 0.31 29 0.94
8 4.96 3 0.77 5 0.00
p=0.09337 p=0.05060
Number of rngs required: 687618, p-value: 0.182
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_14:31
No. of wins: Observed Expected
98610 98585.9
z-score= 0.108, pvalue=0.54299
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66731 66666.7 0.062 0.062
2 37595 37654.3 0.093 0.156
3 26952 26954.7 0.000 0.156
4 19285 19313.5 0.042 0.198
5 13966 13851.4 0.948 1.146
6 10025 9943.5 0.667 1.813
7 7170 7145.0 0.087 1.900
8 4996 5139.1 3.983 5.883
9 3785 3699.9 1.959 7.842
10 2548 2666.3 5.249 13.091
11 1923 1923.3 0.000 13.091
12 1442 1388.7 2.043 15.133
13 1012 1003.7 0.068 15.202
14 707 726.1 0.505 15.706
15 515 525.8 0.223 15.930
16 348 381.2 2.883 18.813
17 271 276.5 0.111 18.924
18 198 200.8 0.040 18.964
19 164 146.0 2.223 21.187
20 90 106.2 2.475 23.663
21 277 287.1 0.356 24.019
Chisq= 24.02 for 20 degrees of freedom, p= 0.75843
SUMMARY of craptest
p-value for no. of wins: 0.542992
p-value for throws/game: 0.758430
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_14:31
No. of wins: Observed Expected
98604 98585.9
z-score= 0.081, pvalue=0.53233
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66717 66666.7 0.038 0.038
2 37647 37654.3 0.001 0.039
3 26692 26954.7 2.561 2.600
4 19299 19313.5 0.011 2.611
5 13928 13851.4 0.423 3.035
6 9961 9943.5 0.031 3.065
7 7122 7145.0 0.074 3.139
8 5243 5139.1 2.102 5.241
9 3687 3699.9 0.045 5.286
10 2688 2666.3 0.177 5.463
11 1923 1923.3 0.000 5.463
12 1337 1388.7 1.928 7.390
13 1034 1003.7 0.914 8.304
14 766 726.1 2.188 10.492
15 548 525.8 0.934 11.426
16 390 381.2 0.205 11.632
17 276 276.5 0.001 11.633
18 199 200.8 0.017 11.649
19 149 146.0 0.062 11.712
20 107 106.2 0.006 11.718
21 287 287.1 0.000 11.718
Chisq= 11.72 for 20 degrees of freedom, p= 0.07455
SUMMARY of craptest
p-value for no. of wins: 0.532334
p-value for throws/game: 0.074546
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0037,0.0037,0.0045,0.0066,0.0088,0.0099,0.0108,0.0141,0.0178,0.0186,
0.0212,0.0247,0.0307,0.0343,0.0351,0.0357,0.0375,0.0422,0.0423,0.0506,
0.0598,0.0606,0.0657,0.0684,0.0693,0.0704,0.0724,0.0745,0.0760,0.0775,
0.0828,0.0840,0.0840,0.0848,0.0870,0.0874,0.0887,0.0927,0.0934,0.0970,
0.0990,0.1028,0.1037,0.1041,0.1059,0.1077,0.1146,0.1173,0.1236,0.1255,
0.1269,0.1332,0.1469,0.1470,0.1478,0.1576,0.1605,0.1605,0.1650,0.1676,
0.1736,0.1818,0.1819,0.1827,0.1842,0.1846,0.1977,0.1982,0.2000,0.2004,
0.2056,0.2076,0.2092,0.2125,0.2172,0.2179,0.2203,0.2255,0.2296,0.2304,
0.2314,0.2361,0.2363,0.2383,0.2449,0.2499,0.2597,0.2685,0.2685,0.2723,
0.2752,0.2766,0.2863,0.2878,0.2994,0.3004,0.3042,0.3144,0.3165,0.3299,
0.3336,0.3406,0.3427,0.3462,0.3517,0.3535,0.3612,0.3643,0.3686,0.3692,
0.3803,0.3849,0.3849,0.3867,0.3966,0.4003,0.4026,0.4034,0.4089,0.4124,
0.4162,0.4236,0.4256,0.4281,0.4294,0.4364,0.4406,0.4510,0.4515,0.4597,
0.4597,0.4630,0.4654,0.4702,0.4702,0.4739,0.4769,0.4799,0.4818,0.4899,
0.4961,0.4995,0.4998,0.5033,0.5078,0.5090,0.5127,0.5131,0.5182,0.5197,
0.5220,0.5265,0.5279,0.5323,0.5430,0.5430,0.5447,0.5536,0.5536,0.5547,
0.5560,0.5585,0.5623,0.5624,0.5639,0.5651,0.5675,0.5699,0.5729,0.5751,
0.5756,0.5765,0.5815,0.5822,0.5882,0.6035,0.6036,0.6043,0.6074,0.6079,
0.6148,0.6181,0.6201,0.6201,0.6241,0.6265,0.6278,0.6295,0.6365,0.6446,
0.6471,0.6479,0.6496,0.6618,0.6637,0.6652,0.6692,0.6699,0.6711,0.6723,
0.6757,0.6792,0.6871,0.6874,0.6881,0.6938,0.6952,0.6959,0.7005,0.7086,
0.7107,0.7150,0.7154,0.7199,0.7311,0.7367,0.7387,0.7425,0.7565,0.7584,
0.7718,0.7762,0.7849,0.7908,0.7997,0.8015,0.8028,0.8056,0.8082,0.8108,
0.8196,0.8206,0.8226,0.8244,0.8300,0.8414,0.8525,0.8738,0.8761,0.8772,
0.8790,0.8834,0.8850,0.8942,0.9004,0.9025,0.9143,0.9153,0.9157,0.9216,
0.9269,0.9340,0.9344,0.9366,0.9391,0.9400,0.9532,0.9582,0.9646,0.9646,
0.9678,0.9686,0.9794,0.9817,0.9841,0.9846,0.9857,0.9936,0.9977,
Overall p-value after applying KStest on 269 p-values = 0.020725
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.