RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.66 33.1168 0.989107
2 to 25 15.77 23.3427 0.861577
3 to 26 15.66 26.8528 0.939738
4 to 27 15.60 23.5824 0.868768
5 to 28 15.71 15.1363 0.414336
6 to 29 16.05 13.1986 0.277210
7 to 30 15.71 14.4461 0.364689
8 to 31 15.77 15.9247 0.470819
9 to 32 15.58 29.4949 0.969773
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.037052
Tough bday spacings test for dh-ranFile-2018-06-23_05:31: 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 7 34 73 97 97 97 40 30 13 10 2
(O-E)^2/E 0.5 0.2 0.0 0.0 0.0 4.5 2.8 0.0 0.2 1.7 1.0
Birthday Spacings: Sum(O-E)^2/E= 11.087, p= 0.649
RESULTS OF GCD FOR dh-ranFile-2018-06-23_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.773502
p-value, dist. of gcd's: 0.587124
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.750 0.545 0.385 0.081 0.231 0.356 0.000 0.110
Bits 8 to 15---> 0.104 0.357 0.597 0.177 0.362 0.888 0.162 0.225
Bits 16 to 23---> 0.399 0.273 0.841 0.906 0.538 0.322 0.884 0.273
Bits 24 to 31---> 0.782 0.695 0.948 0.978 0.335 0.152 0.299 0.017
KS test for the above 32 p values: 0.755
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_05:31,
p-values for 5 runs: 0.2423, 0.9904, 0.6532, 0.1659, 0.4458
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5080 5134.0 0.568 1.420
r= 30 23157 23103.0 0.126 1.546
r= 31 11565 11551.5 0.016 1.562
chi-square = 1.562 with df = 3; p-value = 0.332
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5167 5134.0 0.212 2.184
r= 31 23131 23103.0 0.034 2.218
r= 32 11511 11551.5 0.142 2.360
chi-square = 2.360 with df = 3; p-value = 0.499
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_05:31
b-rank test for bits 1 to 8, p=0.43875
b-rank test for bits 2 to 9, p=0.13615
b-rank test for bits 3 to 10, p=0.71552
b-rank test for bits 4 to 11, p=0.73760
b-rank test for bits 5 to 12, p=0.53415
b-rank test for bits 6 to 13, p=0.01168
b-rank test for bits 7 to 14, p=0.51601
b-rank test for bits 8 to 15, p=0.95853
b-rank test for bits 9 to 16, p=0.73607
b-rank test for bits 10 to 17, p=0.87779
b-rank test for bits 11 to 18, p=0.34983
b-rank test for bits 12 to 19, p=0.53716
b-rank test for bits 13 to 20, p=0.79605
b-rank test for bits 14 to 21, p=0.54041
b-rank test for bits 15 to 22, p=0.09844
b-rank test for bits 16 to 23, p=0.00389
b-rank test for bits 17 to 24, p=0.06148
b-rank test for bits 18 to 25, p=0.43435
b-rank test for bits 19 to 26, p=0.30416
b-rank test for bits 20 to 27, p=0.88460
b-rank test for bits 21 to 28, p=0.61005
b-rank test for bits 22 to 29, p=0.84045
b-rank test for bits 23 to 30, p=0.79725
b-rank test for bits 24 to 31, p=0.79814
b-rank test for bits 25 to 32, p=0.01679
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 = 0.437905
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_05:31
(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 141623 -0.67 0.251749
2 141903 -0.01 0.494100
3 142229 0.75 0.772436
4 142077 0.39 0.652379
5 142276 0.86 0.804196
6 141969 0.14 0.555439
7 141625 -0.66 0.253242
8 142824 2.14 0.983704
9 141600 -0.72 0.234922
10 141256 -1.53 0.063446
11 141804 -0.25 0.402803
12 142094 0.43 0.666937
13 141727 -0.43 0.335052
14 141814 -0.22 0.411871
15 141070 -1.96 0.024937
16 143024 2.60 0.995398
17 142647 1.72 0.957603
18 142130 0.52 0.696928
19 142530 1.45 0.926494
20 142182 0.64 0.737963
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_05:31
Bits used No. missing words z-score p-value
23 to 32 142152 0.8368 0.798646
22 to 31 142077 0.5782 0.718426
21 to 30 141429 -1.6563 0.048830
20 to 29 141895 -0.0494 0.480295
19 to 28 142093 0.6333 0.736746
18 to 27 141836 -0.2529 0.400187
17 to 26 141747 -0.5598 0.287822
16 to 25 142195 0.9851 0.837705
15 to 24 141368 -1.8667 0.030975
14 to 23 142111 0.6954 0.756602
13 to 22 142200 1.0023 0.841903
12 to 21 141506 -1.3908 0.082144
11 to 20 141611 -1.0287 0.151805
10 to 19 141435 -1.6356 0.050960
9 to 18 141831 -0.2701 0.393540
8 to 17 142283 1.2885 0.901217
7 to 16 142358 1.5471 0.939085
6 to 15 141871 -0.1322 0.447424
5 to 14 141897 -0.0425 0.483043
4 to 13 142404 1.7058 0.955973
3 to 12 142175 0.9161 0.820194
2 to 11 142043 0.4609 0.677576
1 to 10 142257 1.1989 0.884709
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_05:31
Bits used No. missing words z-score p-value
28 to 32 142202 0.9921 0.839426
27 to 31 141565 -1.1672 0.121561
26 to 30 141741 -0.5706 0.284132
25 to 29 141666 -0.8248 0.204729
24 to 28 141976 0.2260 0.589399
23 to 27 142112 0.6870 0.753964
22 to 26 141667 -0.8215 0.205693
21 to 25 141632 -0.9401 0.173583
20 to 24 141909 -0.0011 0.499554
19 to 23 141851 -0.1977 0.421629
18 to 22 141451 -1.5537 0.060133
17 to 21 142036 0.4294 0.666180
16 to 20 141460 -1.5232 0.063860
15 to 19 141869 -0.1367 0.445629
14 to 18 141819 -0.3062 0.379725
13 to 17 142394 1.6429 0.949803
12 to 16 142145 0.7989 0.787820
11 to 15 142231 1.0904 0.862233
10 to 14 141970 0.2057 0.581472
9 to 13 142399 1.6599 0.951533
8 to 12 141886 -0.0791 0.468483
7 to 11 141647 -0.8893 0.186933
6 to 10 141989 0.2701 0.606446
5 to 9 142429 1.7616 0.960931
4 to 8 141909 -0.0011 0.499554
3 to 7 141605 -1.0316 0.151123
2 to 6 141840 -0.2350 0.407098
1 to 5 141667 -0.8215 0.205693
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_05:31
Bits used No. missing words z-score p-value
31 to 32 141663 -0.7266 0.233724
30 to 31 142016 0.3147 0.623490
29 to 30 142411 1.4799 0.930544
28 to 29 142413 1.4858 0.931328
27 to 28 141418 -1.4494 0.073620
26 to 27 141611 -0.8800 0.189422
25 to 26 141690 -0.6470 0.258819
24 to 25 141539 -1.0924 0.137325
23 to 24 142362 1.3353 0.909113
22 to 23 141494 -1.2252 0.110257
21 to 22 141742 -0.4936 0.310795
20 to 21 141905 -0.0128 0.494905
19 to 20 142094 0.5447 0.707037
18 to 19 141831 -0.2311 0.408633
17 to 18 141768 -0.4169 0.338375
16 to 17 141213 -2.0541 0.019984
15 to 16 141937 0.0816 0.532527
14 to 15 141810 -0.2930 0.384758
13 to 14 141501 -1.2045 0.114196
12 to 13 141809 -0.2960 0.383631
11 to 12 141700 -0.6175 0.268455
10 to 11 141851 -0.1721 0.431693
9 to 10 141485 -1.2517 0.105338
8 to 9 141678 -0.6824 0.247496
7 to 8 141964 0.1613 0.564059
6 to 7 141946 0.1082 0.543070
5 to 6 142203 0.8663 0.806833
4 to 5 141968 0.1731 0.568701
3 to 4 142591 2.0108 0.977828
2 to 3 141596 -0.9243 0.177671
1 to 2 141360 -1.6204 0.052569
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2576.13 1.077 0.859165
Test results for specific bytes for dh-ranFile-2018-06-23_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2504.60 0.065 0.525911
2 to 9 2381.08 -1.682 0.046307
3 to 10 2515.83 0.224 0.588565
4 to 11 2433.46 -0.941 0.173349
5 to 12 2485.17 -0.210 0.416937
6 to 13 2437.05 -0.890 0.186652
7 to 14 2670.47 2.411 0.992041
8 to 15 2579.64 1.126 0.869987
9 to 16 2387.20 -1.595 0.055323
10 to 17 2466.55 -0.473 0.318094
11 to 18 2566.37 0.939 0.826052
12 to 19 2442.30 -0.816 0.207240
13 to 20 2462.95 -0.524 0.300146
14 to 21 2507.63 0.108 0.542988
15 to 22 2588.41 1.250 0.894410
16 to 23 2313.87 -2.632 0.004240
17 to 24 2434.94 -0.920 0.178761
18 to 25 2502.48 0.035 0.513973
19 to 26 2601.08 1.430 0.923576
20 to 27 2539.17 0.554 0.710203
21 to 28 2515.32 0.217 0.585787
22 to 29 2536.77 0.520 0.698469
23 to 30 2496.59 -0.048 0.480779
24 to 31 2522.16 0.313 0.622989
25 to 32 2465.70 -0.485 0.313827
CDPARK for dh-ranFile-2018-06-23_05:31: 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
3539 0.7306 0.767486
3568 2.0548 0.980051
3477 -2.1005 0.017844
3519 -0.1826 0.427537
3551 1.2785 0.899470
3542 0.8676 0.807188
3468 -2.5114 0.006012
3537 0.6393 0.738676
3524 0.0457 0.518210
3539 0.7306 0.767486
Square side=100, avg. no. parked=3526.40 sample std.=29.87
p-value of the KSTEST for those 10 p-values: 0.155462
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_05:31
0.4040,0.5431,0.9446,0.2817,0.4141,0.1179,0.9863,0.3676,0.8322,0.6418,
The KS test for those 10 p-values: 0.715393
The 3DSPHERES test for dh-ranFile-2018-06-23_05:31
sample no r^3 equiv. uni.
1 4.032 0.125772
2 15.403 0.401557
3 10.639 0.298573
4 44.556 0.773544
5 22.534 0.528167
6 61.356 0.870645
7 10.613 0.297971
8 93.170 0.955205
9 16.800 0.428798
10 61.939 0.873137
11 3.023 0.095845
12 35.453 0.693264
13 8.969 0.258408
14 9.494 0.271292
15 21.897 0.518038
16 5.883 0.178081
17 11.580 0.320230
18 33.054 0.667732
19 23.008 0.535562
20 10.957 0.305974
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.654900
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.3 -0.4 1.5 1.5 -2.3
-0.8 0.1 0.1 1.6 1.2 -0.2
-0.8 -0.7 0.5 -0.6 0.4 1.3
-2.3 1.2 -0.6 2.1 -0.9 -0.4
-0.9 -0.3 -0.8 -1.3 2.8 1.2
-0.7 -1.8 0.5 1.5 0.1 -0.1
-0.5 0.5 1.3 1.0 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:55.362109
z-score=1.457926, p-value=0.918937
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_05:31
Test no p-value
1 0.122501
2 0.577214
3 0.921116
4 0.575527
5 0.175046
6 0.427400
7 0.247013
8 0.031100
9 0.454222
10 0.038965
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.180961
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_05:31:
(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 66573 0.13 66893 0.77
3 25000.00 24958 0.07 24736 2.79
4 6666.67 6775 1.76 6685 0.05
5 1388.89 1382 0.03 1410 0.32
6 238.10 258 1.66 238 0.00
7 34.72 45 3.04 30 0.64
8 4.96 8 1.86 7 0.84
p=0.80061 p=0.50738
Number of rngs required: 687659, p-value: 0.195
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_05:31
No. of wins: Observed Expected
98215 98585.9
z-score=-1.659, pvalue=0.04859
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66647 66666.7 0.006 0.006
2 37669 37654.3 0.006 0.012
3 26898 26954.7 0.119 0.131
4 19259 19313.5 0.154 0.285
5 13708 13851.4 1.485 1.770
6 9980 9943.5 0.134 1.903
7 7128 7145.0 0.041 1.944
8 5291 5139.1 4.491 6.435
9 3683 3699.9 0.077 6.512
10 2743 2666.3 2.207 8.719
11 1889 1923.3 0.613 9.331
12 1366 1388.7 0.372 9.704
13 1082 1003.7 6.106 15.810
14 758 726.1 1.398 17.207
15 545 525.8 0.698 17.906
16 373 381.2 0.174 18.080
17 274 276.5 0.023 18.103
18 208 200.8 0.256 18.359
19 145 146.0 0.007 18.366
20 88 106.2 3.124 21.490
21 266 287.1 1.553 23.043
Chisq= 23.04 for 20 degrees of freedom, p= 0.71329
SUMMARY of craptest
p-value for no. of wins: 0.048589
p-value for throws/game: 0.713292
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_05:31
No. of wins: Observed Expected
98703 98585.9
z-score= 0.524, pvalue=0.69983
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66567 66666.7 0.149 0.149
2 37625 37654.3 0.023 0.172
3 26974 26954.7 0.014 0.186
4 19592 19313.5 4.017 4.203
5 13853 13851.4 0.000 4.203
6 9932 9943.5 0.013 4.216
7 7131 7145.0 0.028 4.244
8 5043 5139.1 1.796 6.040
9 3683 3699.9 0.077 6.117
10 2604 2666.3 1.456 7.572
11 1982 1923.3 1.790 9.362
12 1379 1388.7 0.068 9.430
13 993 1003.7 0.114 9.545
14 701 726.1 0.870 10.415
15 542 525.8 0.497 10.912
16 415 381.2 3.006 13.918
17 256 276.5 1.526 15.444
18 194 200.8 0.232 15.676
19 159 146.0 1.160 16.836
20 109 106.2 0.073 16.909
21 266 287.1 1.553 18.462
Chisq= 18.46 for 20 degrees of freedom, p= 0.44300
SUMMARY of craptest
p-value for no. of wins: 0.699835
p-value for throws/game: 0.443002
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0039,0.0042,0.0060,0.0117,0.0168,0.0171,0.0178,0.0200,0.0249,
0.0310,0.0311,0.0371,0.0390,0.0463,0.0486,0.0488,0.0510,0.0526,0.0553,
0.0601,0.0615,0.0634,0.0639,0.0736,0.0810,0.0821,0.0958,0.0984,0.1038,
0.1053,0.1101,0.1103,0.1142,0.1179,0.1216,0.1225,0.1258,0.1361,0.1373,
0.1511,0.1516,0.1518,0.1555,0.1617,0.1659,0.1733,0.1736,0.1750,0.1769,
0.1777,0.1781,0.1788,0.1810,0.1867,0.1869,0.1894,0.1948,0.2047,0.2057,
0.2057,0.2072,0.2250,0.2308,0.2337,0.2349,0.2423,0.2470,0.2475,0.2517,
0.2532,0.2584,0.2588,0.2685,0.2713,0.2727,0.2728,0.2772,0.2817,0.2841,
0.2878,0.2980,0.2986,0.2986,0.3001,0.3042,0.3060,0.3108,0.3138,0.3181,
0.3202,0.3218,0.3319,0.3351,0.3354,0.3384,0.3498,0.3565,0.3571,0.3620,
0.3647,0.3676,0.3797,0.3836,0.3848,0.3850,0.3935,0.3995,0.4002,0.4016,
0.4028,0.4040,0.4071,0.4086,0.4119,0.4141,0.4143,0.4169,0.4216,0.4274,
0.4275,0.4288,0.4317,0.4343,0.4379,0.4387,0.4430,0.4456,0.4458,0.4474,
0.4542,0.4685,0.4708,0.4803,0.4808,0.4830,0.4941,0.4949,0.4988,0.4996,
0.4996,0.5074,0.5140,0.5160,0.5180,0.5182,0.5259,0.5282,0.5325,0.5342,
0.5356,0.5372,0.5381,0.5404,0.5430,0.5431,0.5431,0.5447,0.5554,0.5641,
0.5687,0.5755,0.5772,0.5815,0.5858,0.5871,0.5886,0.5894,0.5974,0.6064,
0.6100,0.6230,0.6235,0.6418,0.6493,0.6524,0.6532,0.6549,0.6662,0.6669,
0.6677,0.6776,0.6933,0.6950,0.6969,0.6985,0.6998,0.7070,0.7102,0.7133,
0.7154,0.7155,0.7184,0.7361,0.7367,0.7376,0.7380,0.7387,0.7499,0.7540,
0.7550,0.7566,0.7675,0.7675,0.7724,0.7735,0.7735,0.7816,0.7878,0.7960,
0.7973,0.7981,0.7986,0.8006,0.8042,0.8068,0.8072,0.8202,0.8261,0.8322,
0.8377,0.8394,0.8405,0.8410,0.8419,0.8592,0.8616,0.8622,0.8688,0.8700,
0.8706,0.8731,0.8778,0.8837,0.8846,0.8847,0.8882,0.8944,0.8995,0.9012,
0.9060,0.9091,0.9189,0.9211,0.9236,0.9265,0.9305,0.9313,0.9391,0.9397,
0.9446,0.9482,0.9498,0.9515,0.9552,0.9560,0.9576,0.9585,0.9609,0.9698,
0.9778,0.9780,0.9801,0.9837,0.9863,0.9891,0.9904,0.9920,0.9954,
Overall p-value after applying KStest on 269 p-values = 0.824201
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.