RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.75 23.0753 0.853184
2 to 25 15.68 17.6935 0.591580
3 to 26 15.53 26.0600 0.926625
4 to 27 15.49 26.4049 0.932607
5 to 28 15.76 14.4252 0.363195
6 to 29 16.06 7.9089 0.031545
7 to 30 15.83 14.1036 0.340244
8 to 31 15.91 14.4030 0.361602
9 to 32 15.98 15.3369 0.428772
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.727350
Tough bday spacings test for dh-ranFile-2018-06-26_15:31: 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 5 47 63 103 97 85 55 24 15 5 1
(O-E)^2/E 1.9 2.9 1.4 0.3 0.0 0.6 0.2 1.1 0.0 0.4 2.3
Birthday Spacings: Sum(O-E)^2/E= 11.143, p= 0.654
RESULTS OF GCD FOR dh-ranFile-2018-06-26_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.606323
p-value, dist. of gcd's: 0.466449
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.469 0.176 0.308 0.514 0.549 0.523 0.257 0.304
Bits 8 to 15---> 0.313 0.122 0.864 0.749 0.992 0.613 0.731 0.031
Bits 16 to 23---> 0.092 0.972 0.943 0.821 0.236 0.472 0.926 0.866
Bits 24 to 31---> 0.203 0.044 0.188 0.372 0.405 0.530 0.796 0.122
KS test for the above 32 p values: 0.058
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_15:31,
p-values for 5 runs: 0.4603, 0.4066, 0.5999, 0.7542, 0.0547
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5097 5134.0 0.267 0.615
r= 30 23153 23103.0 0.108 0.723
r= 31 11530 11551.5 0.040 0.763
chi-square = 0.763 with df = 3; p-value = 0.142
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 233 211.4 2.203 2.203
r= 30 5177 5134.0 0.360 2.563
r= 31 23077 23103.0 0.029 2.592
r= 32 11513 11551.5 0.128 2.721
chi-square = 2.721 with df = 3; p-value = 0.563
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_15:31
b-rank test for bits 1 to 8, p=0.61544
b-rank test for bits 2 to 9, p=0.61312
b-rank test for bits 3 to 10, p=0.35862
b-rank test for bits 4 to 11, p=0.25690
b-rank test for bits 5 to 12, p=0.30699
b-rank test for bits 6 to 13, p=0.11412
b-rank test for bits 7 to 14, p=0.02404
b-rank test for bits 8 to 15, p=0.12990
b-rank test for bits 9 to 16, p=0.95986
b-rank test for bits 10 to 17, p=0.96215
b-rank test for bits 11 to 18, p=0.80916
b-rank test for bits 12 to 19, p=0.30094
b-rank test for bits 13 to 20, p=0.22908
b-rank test for bits 14 to 21, p=0.72759
b-rank test for bits 15 to 22, p=0.80880
b-rank test for bits 16 to 23, p=0.27365
b-rank test for bits 17 to 24, p=0.38723
b-rank test for bits 18 to 25, p=0.36037
b-rank test for bits 19 to 26, p=0.03661
b-rank test for bits 20 to 27, p=0.81877
b-rank test for bits 21 to 28, p=0.32276
b-rank test for bits 22 to 29, p=0.01923
b-rank test for bits 23 to 30, p=0.37128
b-rank test for bits 24 to 31, p=0.17342
b-rank test for bits 25 to 32, p=0.32175
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 = 0.147963
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_15:31
(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 141875 -0.08 0.468035
2 140985 -2.16 0.015400
3 141964 0.13 0.550820
4 142540 1.47 0.929696
5 142362 1.06 0.854890
6 141739 -0.40 0.345327
7 142045 0.32 0.624373
8 141470 -1.03 0.152335
9 141268 -1.50 0.067010
10 142353 1.04 0.850042
11 142396 1.14 0.872247
12 142156 0.58 0.717805
13 141117 -1.85 0.032068
14 141075 -1.95 0.025626
15 142768 2.01 0.977585
16 141473 -1.02 0.153992
17 141457 -1.06 0.145291
18 142192 0.66 0.745516
19 141598 -0.73 0.233489
20 141699 -0.49 0.311563
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_15:31
Bits used No. missing words z-score p-value
23 to 32 141387 -1.8011 0.035841
22 to 31 141318 -2.0391 0.020722
21 to 30 142156 0.8506 0.802500
20 to 29 142373 1.5989 0.945074
19 to 28 141902 -0.0253 0.489918
18 to 27 141823 -0.2977 0.382970
17 to 26 141947 0.1299 0.551676
16 to 25 142043 0.4609 0.677576
15 to 24 141779 -0.4494 0.326567
14 to 23 141996 0.2989 0.617477
13 to 22 142390 1.6575 0.951289
12 to 21 141845 -0.2218 0.412224
11 to 20 141730 -0.6184 0.268163
10 to 19 142210 1.0368 0.850084
9 to 18 142055 0.5023 0.692275
8 to 17 141456 -1.5632 0.059002
7 to 16 142252 1.1816 0.881322
6 to 15 142380 1.6230 0.947705
5 to 14 141503 -1.4011 0.080586
4 to 13 141166 -2.5632 0.005186
3 to 12 142110 0.6920 0.755521
2 to 11 142130 0.7609 0.776651
1 to 10 142155 0.8471 0.801541
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_15:31
Bits used No. missing words z-score p-value
28 to 32 141997 0.2972 0.616838
27 to 31 141884 -0.0859 0.465787
26 to 30 142140 0.7819 0.782873
25 to 29 142349 1.4904 0.931941
24 to 28 141953 0.1480 0.558842
23 to 27 142002 0.3141 0.623291
22 to 26 142261 1.1921 0.883389
21 to 25 142003 0.3175 0.624578
20 to 24 141900 -0.0316 0.487385
19 to 23 141795 -0.3876 0.349171
18 to 22 141673 -0.8011 0.211532
17 to 21 142267 1.2124 0.887328
16 to 20 141796 -0.3842 0.350426
15 to 19 142134 0.7616 0.776849
14 to 18 141525 -1.3028 0.096319
13 to 17 141992 0.2802 0.610352
12 to 16 141922 0.0429 0.517129
11 to 15 141742 -0.5672 0.285282
10 to 14 141426 -1.6384 0.050668
9 to 13 141222 -2.3299 0.009905
8 to 12 141642 -0.9062 0.182414
7 to 11 141197 -2.4147 0.007875
6 to 10 141565 -1.1672 0.121561
5 to 9 141619 -0.9842 0.162516
4 to 8 142330 1.4260 0.923066
3 to 7 142460 1.8667 0.969027
2 to 6 141828 -0.2757 0.391391
1 to 5 141718 -0.6486 0.258306
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_15:31
Bits used No. missing words z-score p-value
31 to 32 141484 -1.2547 0.104801
30 to 31 142260 1.0344 0.849531
29 to 30 142040 0.3855 0.650051
28 to 29 141871 -0.1131 0.454988
27 to 28 142723 2.4002 0.991807
26 to 27 141667 -0.7148 0.237355
25 to 26 141402 -1.4965 0.067255
24 to 25 142607 2.0580 0.980206
23 to 24 142035 0.3707 0.644573
22 to 23 142315 1.1967 0.884282
21 to 22 141634 -0.8122 0.208343
20 to 21 141799 -0.3255 0.372418
19 to 20 141798 -0.3284 0.371302
18 to 19 141785 -0.3668 0.356901
17 to 18 142090 0.5329 0.702966
16 to 17 141396 -1.5142 0.064982
15 to 16 141632 -0.8181 0.206655
14 to 15 142367 1.3501 0.911501
13 to 14 141268 -1.8918 0.029257
12 to 13 142550 1.8899 0.970613
11 to 12 141872 -0.1101 0.456158
10 to 11 141657 -0.7443 0.228337
9 to 10 141732 -0.5231 0.300453
8 to 9 141761 -0.4376 0.330856
7 to 8 141708 -0.5939 0.276292
6 to 7 141859 -0.1485 0.440988
5 to 6 141501 -1.2045 0.114196
4 to 5 141959 0.1465 0.558244
3 to 4 141447 -1.3638 0.086314
2 to 3 142051 0.4179 0.661992
1 to 2 142037 0.3766 0.646767
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2506.70 0.095 0.537760
Test results for specific bytes for dh-ranFile-2018-06-26_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2497.78 -0.031 0.487494
2 to 9 2475.30 -0.349 0.363422
3 to 10 2535.39 0.500 0.691613
4 to 11 2425.35 -1.056 0.145564
5 to 12 2420.92 -1.118 0.131719
6 to 13 2470.81 -0.413 0.339885
7 to 14 2517.37 0.246 0.597016
8 to 15 2608.34 1.532 0.937258
9 to 16 2531.52 0.446 0.672132
10 to 17 2489.65 -0.146 0.441796
11 to 18 2583.00 1.174 0.879772
12 to 19 2418.09 -1.158 0.123350
13 to 20 2495.56 -0.063 0.474989
14 to 21 2456.15 -0.620 0.267596
15 to 22 2526.07 0.369 0.643842
16 to 23 2489.67 -0.146 0.441943
17 to 24 2670.40 2.410 0.992021
18 to 25 2598.53 1.393 0.918252
19 to 26 2512.95 0.183 0.572653
20 to 27 2489.23 -0.152 0.439451
21 to 28 2493.91 -0.086 0.465707
22 to 29 2427.90 -1.020 0.153935
23 to 30 2548.89 0.691 0.755365
24 to 31 2729.53 3.246 0.999415
25 to 32 2490.37 -0.136 0.445845
CDPARK for dh-ranFile-2018-06-26_15:31: 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
3501 -1.0046 0.157553
3530 0.3196 0.625377
3538 0.6849 0.753306
3518 -0.2283 0.409702
3519 -0.1826 0.427537
3517 -0.2740 0.392053
3514 -0.4110 0.340551
3520 -0.1370 0.445521
3548 1.1416 0.873180
3539 0.7306 0.767486
Square side=100, avg. no. parked=3524.40 sample std.=13.37
p-value of the KSTEST for those 10 p-values: 0.612352
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_15:31
0.8400,0.2406,0.5691,0.8481,0.9029,0.9609,0.0203,0.3858,0.4018,0.2566,
The KS test for those 10 p-values: 0.762333
The 3DSPHERES test for dh-ranFile-2018-06-26_15:31
sample no r^3 equiv. uni.
1 8.568 0.248448
2 14.532 0.383933
3 18.712 0.464052
4 12.470 0.340111
5 15.365 0.400813
6 14.485 0.382973
7 31.026 0.644485
8 31.693 0.652307
9 20.297 0.491641
10 75.758 0.919964
11 18.291 0.456486
12 0.888 0.029165
13 96.555 0.959984
14 14.896 0.391371
15 79.965 0.930434
16 19.098 0.470915
17 63.855 0.880986
18 2.573 0.082200
19 38.516 0.723036
20 10.917 0.305042
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.654222
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 0.1 1.8 0.4 0.1
0.3 0.1 1.1 1.2 -1.0 -0.6
-0.9 -0.6 0.2 0.2 -0.7 1.1
-0.6 -0.7 0.8 -0.5 -0.2 1.2
0.9 0.2 -0.3 -0.0 -0.2 -0.4
0.6 0.1 0.3 -0.3 -0.1 0.8
1.7 -0.1 -1.2 1.5 -1.3 0.0
0.8
Chi-square with 42 degrees of freedom:25.993664
z-score=-1.746434, p-value=0.024956
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_15:31
Test no p-value
1 0.097264
2 0.665963
3 0.364790
4 0.844957
5 0.162657
6 0.910495
7 0.180238
8 0.120082
9 0.320048
10 0.096081
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.184731
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_15:31:
(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 66628 0.02 66876 0.66
3 25000.00 25038 0.06 24753 2.44
4 6666.67 6685 0.05 6667 0.00
5 1388.89 1399 0.07 1411 0.35
6 238.10 220 1.38 259 1.84
7 34.72 26 2.19 29 0.94
8 4.96 3 0.77 4 0.19
p=0.39652 p=0.62148
Number of rngs required: 687412, p-value: 0.125
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_15:31
No. of wins: Observed Expected
98373 98585.9
z-score=-0.952, pvalue=0.17054
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66708 66666.7 0.026 0.026
2 37528 37654.3 0.424 0.449
3 27147 26954.7 1.371 1.821
4 19121 19313.5 1.918 3.739
5 13942 13851.4 0.592 4.331
6 9904 9943.5 0.157 4.488
7 7325 7145.0 4.533 9.022
8 5104 5139.1 0.239 9.261
9 3681 3699.9 0.096 9.357
10 2674 2666.3 0.022 9.379
11 1887 1923.3 0.686 10.066
12 1370 1388.7 0.253 10.319
13 1017 1003.7 0.176 10.494
14 648 726.1 8.409 18.903
15 536 525.8 0.196 19.100
16 414 381.2 2.831 21.931
17 303 276.5 2.532 24.463
18 209 200.8 0.332 24.795
19 124 146.0 3.311 28.106
20 109 106.2 0.073 28.179
21 249 287.1 5.060 33.238
Chisq= 33.24 for 20 degrees of freedom, p= 0.96824
SUMMARY of craptest
p-value for no. of wins: 0.170541
p-value for throws/game: 0.968237
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_15:31
No. of wins: Observed Expected
98357 98585.9
z-score=-1.024, pvalue=0.15301
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66522 66666.7 0.314 0.314
2 38114 37654.3 5.612 5.926
3 26642 26954.7 3.628 9.554
4 19410 19313.5 0.483 10.037
5 13969 13851.4 0.998 11.035
6 9967 9943.5 0.055 11.090
7 6999 7145.0 2.984 14.074
8 5166 5139.1 0.141 14.215
9 3651 3699.9 0.645 14.861
10 2650 2666.3 0.100 14.960
11 1886 1923.3 0.725 15.685
12 1390 1388.7 0.001 15.686
13 1008 1003.7 0.018 15.704
14 722 726.1 0.024 15.728
15 513 525.8 0.313 16.041
16 366 381.2 0.602 16.644
17 289 276.5 0.561 17.205
18 195 200.8 0.169 17.374
19 154 146.0 0.440 17.814
20 101 106.2 0.256 18.070
21 286 287.1 0.004 18.075
Chisq= 18.07 for 20 degrees of freedom, p= 0.41752
SUMMARY of craptest
p-value for no. of wins: 0.153015
p-value for throws/game: 0.417516
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0052,0.0079,0.0099,0.0154,0.0192,0.0203,0.0207,0.0240,0.0250,0.0256,
0.0292,0.0293,0.0312,0.0315,0.0321,0.0358,0.0366,0.0443,0.0507,0.0547,
0.0575,0.0590,0.0650,0.0670,0.0673,0.0806,0.0822,0.0863,0.0920,0.0961,
0.0963,0.0973,0.1048,0.1141,0.1142,0.1201,0.1216,0.1217,0.1221,0.1234,
0.1249,0.1299,0.1317,0.1418,0.1453,0.1456,0.1480,0.1523,0.1530,0.1539,
0.1540,0.1576,0.1625,0.1627,0.1705,0.1734,0.1764,0.1802,0.1824,0.1847,
0.1884,0.2027,0.2067,0.2083,0.2115,0.2283,0.2291,0.2335,0.2365,0.2374,
0.2406,0.2484,0.2566,0.2569,0.2574,0.2583,0.2676,0.2682,0.2736,0.2763,
0.2853,0.3005,0.3009,0.3041,0.3050,0.3070,0.3076,0.3116,0.3130,0.3200,
0.3218,0.3228,0.3266,0.3309,0.3399,0.3401,0.3402,0.3406,0.3453,0.3492,
0.3504,0.3569,0.3586,0.3604,0.3616,0.3632,0.3634,0.3648,0.3713,0.3713,
0.3719,0.3724,0.3830,0.3830,0.3839,0.3858,0.3872,0.3914,0.3914,0.3921,
0.3965,0.4008,0.4018,0.4049,0.4066,0.4097,0.4122,0.4175,0.4275,0.4288,
0.4395,0.4410,0.4418,0.4419,0.4455,0.4458,0.4550,0.4562,0.4565,0.4603,
0.4641,0.4657,0.4658,0.4664,0.4680,0.4686,0.4709,0.4720,0.4750,0.4874,
0.4875,0.4899,0.4916,0.5137,0.5171,0.5231,0.5300,0.5378,0.5493,0.5508,
0.5517,0.5582,0.5588,0.5633,0.5691,0.5727,0.5916,0.5970,0.5999,0.6063,
0.6104,0.6124,0.6126,0.6131,0.6154,0.6168,0.6175,0.6215,0.6233,0.6244,
0.6246,0.6254,0.6438,0.6445,0.6446,0.6468,0.6501,0.6523,0.6535,0.6542,
0.6620,0.6660,0.6721,0.6776,0.6916,0.6923,0.7030,0.7178,0.7230,0.7274,
0.7276,0.7313,0.7455,0.7490,0.7533,0.7542,0.7554,0.7555,0.7623,0.7675,
0.7767,0.7768,0.7829,0.7958,0.8015,0.8025,0.8088,0.8092,0.8188,0.8205,
0.8400,0.8450,0.8481,0.8495,0.8500,0.8501,0.8532,0.8549,0.8635,0.8660,
0.8722,0.8732,0.8798,0.8810,0.8813,0.8834,0.8843,0.8873,0.9029,0.9105,
0.9115,0.9183,0.9200,0.9231,0.9259,0.9266,0.9297,0.9304,0.9319,0.9326,
0.9373,0.9430,0.9451,0.9477,0.9513,0.9599,0.9600,0.9609,0.9621,0.9682,
0.9690,0.9706,0.9722,0.9776,0.9802,0.9918,0.9918,0.9920,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.205248
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.