RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2020-01-29_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 15.68 14.6160 0.376881
2 to 25 15.68 30.8344 0.979081
3 to 26 15.75 23.4311 0.864265
4 to 27 15.97 21.9093 0.811767
5 to 28 16.16 17.3517 0.569206
6 to 29 15.82 17.5141 0.579905
7 to 30 15.49 15.4837 0.439315
8 to 31 15.69 11.4594 0.168291
9 to 32 15.79 15.8844 0.467958
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.586121
Tough bday spacings test for dh-ranFile-2020-01-29_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 7 33 95 92 100 65 51 32 16 3 6
(O-E)^2/E 0.5 0.4 6.4 0.3 0.1 2.2 0.0 0.2 0.1 2.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 13.085, p= 0.781
RESULTS OF GCD FOR dh-ranFile-2020-01-29_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.649859
p-value, dist. of gcd's: 0.821067
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2020-01-29_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.221 0.729 0.983 0.695 0.072 0.996 0.176 0.678
Bits 8 to 15---> 0.234 0.957 0.293 0.952 0.957 0.674 0.873 0.586
Bits 16 to 23---> 0.905 0.023 0.261 0.462 0.239 0.650 0.432 0.560
Bits 24 to 31---> 0.309 0.120 0.560 0.161 0.216 0.892 0.915 0.883
KS test for the above 32 p values: 0.779
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2020-01-29_14:31,
p-values for 5 runs: 0.9081, 0.6926, 0.6215, 0.3756, 0.3460
Rank test for binary matrices (31x31) for dh-ranFile-2020-01-29_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5133 5134.0 0.000 0.061
r= 30 22829 23103.0 3.251 3.312
r= 31 11823 11551.5 6.380 9.692
chi-square = 9.692 with df = 3; p-value = 0.979
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2020-01-29_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 4990 5134.0 4.040 4.311
r= 31 23209 23103.0 0.486 4.797
r= 32 11582 11551.5 0.080 4.878
chi-square = 4.878 with df = 3; p-value = 0.819
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2020-01-29_14:31
b-rank test for bits 1 to 8, p=0.32701
b-rank test for bits 2 to 9, p=0.19380
b-rank test for bits 3 to 10, p=0.15840
b-rank test for bits 4 to 11, p=0.32476
b-rank test for bits 5 to 12, p=0.91111
b-rank test for bits 6 to 13, p=0.99434
b-rank test for bits 7 to 14, p=0.98841
b-rank test for bits 8 to 15, p=0.92836
b-rank test for bits 9 to 16, p=0.74854
b-rank test for bits 10 to 17, p=0.91947
b-rank test for bits 11 to 18, p=0.49354
b-rank test for bits 12 to 19, p=0.09825
b-rank test for bits 13 to 20, p=0.30304
b-rank test for bits 14 to 21, p=0.31914
b-rank test for bits 15 to 22, p=0.68981
b-rank test for bits 16 to 23, p=0.31028
b-rank test for bits 17 to 24, p=0.90848
b-rank test for bits 18 to 25, p=0.99079
b-rank test for bits 19 to 26, p=0.02858
b-rank test for bits 20 to 27, p=0.08894
b-rank test for bits 21 to 28, p=0.74142
b-rank test for bits 22 to 29, p=0.05744
b-rank test for bits 23 to 30, p=0.71138
b-rank test for bits 24 to 31, p=0.08588
b-rank test for bits 25 to 32, p=0.24741
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 = 0.156910
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2020-01-29_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 141144 -1.79 0.036876
2 141608 -0.70 0.240703
3 141326 -1.36 0.086454
4 141692 -0.51 0.305804
5 141882 -0.06 0.474543
6 141754 -0.36 0.358332
7 142053 0.34 0.631443
8 141191 -1.68 0.046640
9 142410 1.17 0.878957
10 140912 -2.33 0.009898
11 141392 -1.21 0.113386
12 142254 0.81 0.789678
13 142045 0.32 0.624373
14 141686 -0.52 0.300905
15 141929 0.05 0.518328
16 141403 -1.18 0.118402
17 141948 0.09 0.535996
18 141704 -0.48 0.315705
19 142014 0.24 0.596600
20 141376 -1.25 0.106364
----------------------------------------------------------------
OPSO test for dh-ranFile-2020-01-29_14:31
Bits used No. missing words z-score p-value
23 to 32 142006 0.3333 0.630563
22 to 31 141904 -0.0184 0.492668
21 to 30 141660 -0.8598 0.194961
20 to 29 141860 -0.1701 0.432464
19 to 28 141971 0.2127 0.584202
18 to 27 141890 -0.0667 0.473428
17 to 26 141824 -0.2942 0.384287
16 to 25 141662 -0.8529 0.196868
15 to 24 141433 -1.6425 0.050241
14 to 23 141649 -0.8977 0.184676
13 to 22 142079 0.5851 0.720749
12 to 21 141668 -0.8322 0.202656
11 to 20 141912 0.0092 0.503673
10 to 19 141761 -0.5115 0.304507
9 to 18 141430 -1.6529 0.049179
8 to 17 141594 -1.0873 0.138442
7 to 16 141847 -0.2149 0.414911
6 to 15 142069 0.5506 0.709041
5 to 14 141030 -3.0322 0.001214
4 to 13 141787 -0.4218 0.336575
3 to 12 141796 -0.3908 0.347975
2 to 11 141824 -0.2942 0.384287
1 to 10 141886 -0.0804 0.467940
-----------------------------------------------------------------
OQSO test for dh-ranFile-2020-01-29_14:31
Bits used No. missing words z-score p-value
28 to 32 142060 0.5107 0.695236
27 to 31 141740 -0.5740 0.282984
26 to 30 142067 0.5345 0.703493
25 to 29 141956 0.1582 0.562852
24 to 28 141833 -0.2587 0.397916
23 to 27 142116 0.7006 0.758216
22 to 26 141609 -1.0181 0.154323
21 to 25 141655 -0.8621 0.194306
20 to 24 142087 0.6023 0.726503
19 to 23 142089 0.6091 0.728755
18 to 22 142342 1.4667 0.928768
17 to 21 142216 1.0396 0.850728
16 to 20 141819 -0.3062 0.379725
15 to 19 141644 -0.8994 0.184214
14 to 18 142160 0.8497 0.802262
13 to 17 141843 -0.2248 0.411049
12 to 16 141694 -0.7299 0.232716
11 to 15 142200 0.9853 0.837767
10 to 14 142227 1.0768 0.859226
9 to 13 142277 1.2463 0.893680
8 to 12 141747 -0.5503 0.291067
7 to 11 142029 0.4057 0.657504
6 to 10 142394 1.6429 0.949803
5 to 9 141954 0.1514 0.560179
4 to 8 141653 -0.8689 0.192447
3 to 7 142163 0.8599 0.805077
2 to 6 141298 -2.0723 0.019119
1 to 5 141589 -1.0859 0.138770
-----------------------------------------------------------------
DNA test for dh-ranFile-2020-01-29_14:31
Bits used No. missing words z-score p-value
31 to 32 141388 -1.5378 0.062043
30 to 31 141978 0.2026 0.580263
29 to 30 142786 2.5860 0.995146
28 to 29 142218 0.9105 0.818729
27 to 28 142154 0.7217 0.764773
26 to 27 141425 -1.4287 0.076545
25 to 26 142027 0.3471 0.635745
24 to 25 141634 -0.8122 0.208343
23 to 24 142205 0.8722 0.808446
22 to 23 142454 1.6067 0.945939
21 to 22 141290 -1.8269 0.033855
20 to 21 142531 1.8338 0.966661
19 to 20 142238 0.9695 0.833859
18 to 19 141795 -0.3373 0.367962
17 to 18 141658 -0.7414 0.229230
16 to 17 142193 0.8368 0.798643
15 to 16 142121 0.6244 0.733816
14 to 15 141552 -1.0541 0.145925
13 to 14 141288 -1.8328 0.033414
12 to 13 141253 -1.9361 0.026429
11 to 12 142045 0.4002 0.655498
10 to 11 141763 -0.4317 0.332997
9 to 10 142063 0.4533 0.674835
8 to 9 141630 -0.8240 0.204975
7 to 8 141767 -0.4199 0.337297
6 to 7 142244 0.9872 0.838234
5 to 6 141674 -0.6942 0.243782
4 to 5 141473 -1.2871 0.099028
3 to 4 141971 0.1819 0.572176
2 to 3 142141 0.6834 0.752821
1 to 2 141745 -0.4847 0.313927
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2020-01-29_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2706.45 2.920 0.998248
Test results for specific bytes for dh-ranFile-2020-01-29_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2537.11 0.525 0.700168
2 to 9 2708.83 2.953 0.998428
3 to 10 2537.35 0.528 0.701318
4 to 11 2493.74 -0.089 0.464735
5 to 12 2453.94 -0.651 0.257416
6 to 13 2565.86 0.931 0.824165
7 to 14 2505.10 0.072 0.528771
8 to 15 2602.32 1.447 0.926046
9 to 16 2564.96 0.919 0.820873
10 to 17 2589.65 1.268 0.897564
11 to 18 2599.47 1.407 0.920249
12 to 19 2444.23 -0.789 0.215123
13 to 20 2550.94 0.720 0.764355
14 to 21 2516.53 0.234 0.592402
15 to 22 2539.07 0.553 0.709718
16 to 23 2389.94 -1.557 0.059790
17 to 24 2700.86 2.841 0.997749
18 to 25 2465.86 -0.483 0.314598
19 to 26 2411.88 -1.246 0.106342
20 to 27 2509.68 0.137 0.554458
21 to 28 2364.10 -1.922 0.027306
22 to 29 2512.35 0.175 0.569300
23 to 30 2478.06 -0.310 0.378150
24 to 31 2452.74 -0.668 0.251960
25 to 32 2395.60 -1.476 0.069917
CDPARK for dh-ranFile-2020-01-29_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
3544 0.9589 0.831196
3508 -0.6849 0.246694
3540 0.7763 0.781201
3541 0.8219 0.794438
3509 -0.6393 0.261324
3496 -1.2329 0.108811
3545 1.0046 0.842447
3498 -1.1416 0.126820
3546 1.0502 0.853193
3512 -0.5023 0.307734
Square side=100, avg. no. parked=3523.90 sample std.=19.89
p-value of the KSTEST for those 10 p-values: 0.506210
Results for the MINIMUM DISTANCE test for dh-ranFile-2020-01-29_14:31
0.7229,0.9060,0.6605,0.8095,0.6979,0.5696,0.0168,0.2573,0.8755,0.3669,
The KS test for those 10 p-values: 0.476253
The 3DSPHERES test for dh-ranFile-2020-01-29_14:31
sample no r^3 equiv. uni.
1 26.324 0.584162
2 25.170 0.567854
3 5.186 0.158756
4 19.268 0.473896
5 20.900 0.501762
6 104.032 0.968813
7 36.859 0.707304
8 65.738 0.888225
9 34.900 0.687561
10 82.941 0.937005
11 8.250 0.240419
12 22.669 0.530281
13 12.999 0.351642
14 23.345 0.540759
15 17.700 0.445673
16 103.776 0.968545
17 33.373 0.671237
18 24.136 0.552707
19 16.644 0.425818
20 11.812 0.325460
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.178405
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2020-01-29_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 2.7 0.2 -0.6 0.7
1.5 -0.1 0.8 -0.7 -3.0 1.1
-0.3 1.0 -0.5 0.9 0.1 -0.4
0.7 0.8 -2.3 0.1 0.9 0.1
-1.0 2.1 -1.0 0.0 0.2 -0.8
-0.7 0.6 0.2 -2.1 -0.6 -0.3
-1.2 0.5 -1.2 0.4 0.1 2.0
0.8
Chi-square with 42 degrees of freedom:53.877415
z-score=1.295932, p-value=0.896508
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2020-01-29_14:31
Test no p-value
1 0.058326
2 0.110309
3 0.695310
4 0.960534
5 0.082012
6 0.014298
7 0.443565
8 0.091669
9 0.926080
10 0.996807
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.052102
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2020-01-29_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 66463 0.62 66659 0.00
3 25000.00 25217 1.88 25039 0.06
4 6666.67 6662 0.00 6640 0.11
5 1388.89 1373 0.18 1367 0.35
6 238.10 231 0.21 256 1.35
7 34.72 42 1.53 33 0.09
8 4.96 11 7.36 5 0.00
p=0.93303 p=0.07535
Number of rngs required: 688298, p-value: 0.452
RESULTS OF CRAPS TEST for dh-ranFile-2020-01-29_14:31
No. of wins: Observed Expected
98840 98585.9
z-score= 1.137, pvalue=0.87216
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66449 66666.7 0.711 0.711
2 37671 37654.3 0.007 0.718
3 26900 26954.7 0.111 0.829
4 19463 19313.5 1.158 1.987
5 13688 13851.4 1.928 3.915
6 10009 9943.5 0.431 4.346
7 7194 7145.0 0.336 4.682
8 5137 5139.1 0.001 4.682
9 3794 3699.9 2.395 7.078
10 2671 2666.3 0.008 7.086
11 1941 1923.3 0.162 7.248
12 1381 1388.7 0.043 7.291
13 1003 1003.7 0.001 7.292
14 764 726.1 1.974 9.266
15 525 525.8 0.001 9.267
16 397 381.2 0.659 9.926
17 299 276.5 1.824 11.750
18 189 200.8 0.697 12.447
19 140 146.0 0.245 12.693
20 125 106.2 3.322 16.015
21 260 287.1 2.561 18.575
Chisq= 18.58 for 20 degrees of freedom, p= 0.45043
SUMMARY of craptest
p-value for no. of wins: 0.872162
p-value for throws/game: 0.450434
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2020-01-29_14:31
No. of wins: Observed Expected
98713 98585.9
z-score= 0.569, pvalue=0.71520
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66789 66666.7 0.224 0.224
2 37754 37654.3 0.264 0.488
3 26944 26954.7 0.004 0.493
4 19313 19313.5 0.000 0.493
5 13743 13851.4 0.849 1.341
6 9996 9943.5 0.277 1.618
7 7195 7145.0 0.350 1.968
8 5052 5139.1 1.475 3.443
9 3784 3699.9 1.913 5.356
10 2621 2666.3 0.770 6.126
11 1886 1923.3 0.725 6.850
12 1373 1388.7 0.178 7.029
13 976 1003.7 0.765 7.794
14 695 726.1 1.335 9.129
15 544 525.8 0.627 9.757
16 358 381.2 1.406 11.163
17 269 276.5 0.206 11.368
18 198 200.8 0.040 11.408
19 131 146.0 1.538 12.946
20 99 106.2 0.490 13.436
21 280 287.1 0.176 13.613
Chisq= 13.61 for 20 degrees of freedom, p= 0.15042
SUMMARY of craptest
p-value for no. of wins: 0.715203
p-value for throws/game: 0.150425
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0099,0.0143,0.0168,0.0191,0.0235,0.0264,0.0273,0.0286,0.0334,
0.0339,0.0369,0.0466,0.0492,0.0502,0.0521,0.0574,0.0583,0.0598,0.0620,
0.0699,0.0718,0.0753,0.0765,0.0820,0.0859,0.0865,0.0889,0.0917,0.0983,
0.0990,0.1063,0.1064,0.1088,0.1103,0.1134,0.1184,0.1203,0.1268,0.1384,
0.1388,0.1459,0.1504,0.1543,0.1569,0.1584,0.1588,0.1606,0.1683,0.1764,
0.1784,0.1842,0.1847,0.1924,0.1938,0.1943,0.1950,0.1969,0.2027,0.2050,
0.2083,0.2151,0.2162,0.2211,0.2292,0.2327,0.2344,0.2388,0.2404,0.2407,
0.2438,0.2467,0.2474,0.2520,0.2573,0.2574,0.2613,0.2614,0.2830,0.2911,
0.2927,0.3009,0.3030,0.3045,0.3058,0.3077,0.3089,0.3103,0.3139,0.3146,
0.3157,0.3191,0.3248,0.3255,0.3270,0.3330,0.3366,0.3373,0.3460,0.3480,
0.3516,0.3583,0.3669,0.3680,0.3756,0.3769,0.3782,0.3797,0.3843,0.3843,
0.3979,0.4110,0.4149,0.4258,0.4319,0.4325,0.4393,0.4436,0.4457,0.4504,
0.4519,0.4617,0.4647,0.4679,0.4680,0.4734,0.4739,0.4745,0.4763,0.4927,
0.4935,0.5018,0.5037,0.5062,0.5183,0.5288,0.5303,0.5360,0.5408,0.5527,
0.5545,0.5599,0.5602,0.5602,0.5629,0.5679,0.5692,0.5693,0.5696,0.5722,
0.5799,0.5803,0.5842,0.5842,0.5861,0.5863,0.5924,0.5966,0.6215,0.6244,
0.6306,0.6314,0.6357,0.6497,0.6499,0.6555,0.6575,0.6605,0.6712,0.6741,
0.6748,0.6776,0.6876,0.6898,0.6926,0.6947,0.6952,0.6953,0.6979,0.7002,
0.7013,0.7035,0.7073,0.7090,0.7097,0.7114,0.7152,0.7207,0.7229,0.7265,
0.7288,0.7291,0.7338,0.7414,0.7485,0.7528,0.7582,0.7644,0.7648,0.7792,
0.7810,0.7812,0.7897,0.7944,0.7986,0.8023,0.8051,0.8084,0.8095,0.8118,
0.8187,0.8190,0.8209,0.8211,0.8242,0.8312,0.8339,0.8378,0.8382,0.8424,
0.8507,0.8532,0.8592,0.8643,0.8722,0.8734,0.8755,0.8790,0.8833,0.8882,
0.8921,0.8937,0.8965,0.8976,0.9047,0.9060,0.9081,0.9085,0.9111,0.9146,
0.9195,0.9202,0.9260,0.9261,0.9284,0.9288,0.9330,0.9370,0.9459,0.9498,
0.9516,0.9569,0.9572,0.9605,0.9667,0.9685,0.9688,0.9786,0.9791,0.9827,
0.9884,0.9908,0.9943,0.9951,0.9964,0.9968,0.9977,0.9982,0.9984,
Overall p-value after applying KStest on 269 p-values = 0.318360
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.