RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2019-12-14_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.80 10.4641 0.116972
2 to 25 15.77 8.0921 0.035463
3 to 26 15.96 24.5891 0.895708
4 to 27 15.77 12.3911 0.224103
5 to 28 15.82 11.2135 0.154748
6 to 29 15.53 34.0628 0.991759
7 to 30 16.03 23.2473 0.858628
8 to 31 15.63 28.3766 0.959275
9 to 32 15.41 32.7626 0.987922
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.027496
Tough bday spacings test for dh-ranFile-2019-12-14_08:31: 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 12 35 79 108 107 67 46 25 12 5 4
(O-E)^2/E 0.9 0.1 0.4 1.1 0.9 1.6 0.7 0.8 0.6 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.405, p= 0.313
RESULTS OF GCD FOR dh-ranFile-2019-12-14_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.125565
p-value, dist. of gcd's: 0.899323
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2019-12-14_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.148 0.500 0.767 0.200 0.840 0.378 0.354 0.396
Bits 8 to 15---> 0.990 0.565 0.311 0.254 0.084 0.034 0.470 0.537
Bits 16 to 23---> 0.584 0.539 0.094 0.423 0.553 0.408 0.924 0.957
Bits 24 to 31---> 0.948 0.913 0.531 0.900 0.693 0.254 0.215 0.608
KS test for the above 32 p values: 0.175
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2019-12-14_08:31,
p-values for 5 runs: 0.3631, 0.9708, 0.2413, 0.4075, 0.4519
Rank test for binary matrices (31x31) for dh-ranFile-2019-12-14_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 205 211.4 0.195 0.195
r= 29 5060 5134.0 1.067 1.262
r= 30 23084 23103.0 0.016 1.277
r= 31 11651 11551.5 0.857 2.134
chi-square = 2.134 with df = 3; p-value = 0.455
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2019-12-14_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 207 211.4 0.092 0.092
r= 30 5214 5134.0 1.246 1.339
r= 31 23111 23103.0 0.003 1.341
r= 32 11468 11551.5 0.604 1.945
chi-square = 1.945 with df = 3; p-value = 0.416
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2019-12-14_08:31
b-rank test for bits 1 to 8, p=0.14836
b-rank test for bits 2 to 9, p=0.01518
b-rank test for bits 3 to 10, p=0.80491
b-rank test for bits 4 to 11, p=0.27610
b-rank test for bits 5 to 12, p=0.82410
b-rank test for bits 6 to 13, p=0.84723
b-rank test for bits 7 to 14, p=0.04430
b-rank test for bits 8 to 15, p=0.80486
b-rank test for bits 9 to 16, p=0.67578
b-rank test for bits 10 to 17, p=0.91415
b-rank test for bits 11 to 18, p=0.89298
b-rank test for bits 12 to 19, p=0.27212
b-rank test for bits 13 to 20, p=0.31252
b-rank test for bits 14 to 21, p=0.05535
b-rank test for bits 15 to 22, p=0.49107
b-rank test for bits 16 to 23, p=0.06629
b-rank test for bits 17 to 24, p=0.28757
b-rank test for bits 18 to 25, p=0.53142
b-rank test for bits 19 to 26, p=0.29662
b-rank test for bits 20 to 27, p=0.17448
b-rank test for bits 21 to 28, p=0.28964
b-rank test for bits 22 to 29, p=0.77870
b-rank test for bits 23 to 30, p=0.56871
b-rank test for bits 24 to 31, p=0.57849
b-rank test for bits 25 to 32, p=0.72347
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 = 0.701139
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2019-12-14_08:31
(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 142532 1.45 0.927143
2 142079 0.40 0.654104
3 141265 -1.51 0.066105
4 141936 0.06 0.524843
5 141985 0.18 0.570167
6 141590 -0.75 0.227804
7 142410 1.17 0.878957
8 142340 1.01 0.842850
9 142294 0.90 0.815610
10 142180 0.63 0.736439
11 141602 -0.72 0.236360
12 141429 -1.12 0.130875
13 141499 -0.96 0.168851
14 141743 -0.39 0.348778
15 142603 1.62 0.947462
16 141063 -1.98 0.023998
17 141466 -1.04 0.150144
18 141784 -0.29 0.384827
19 141446 -1.08 0.139505
20 142192 0.66 0.745516
----------------------------------------------------------------
OPSO test for dh-ranFile-2019-12-14_08:31
Bits used No. missing words z-score p-value
23 to 32 141432 -1.6460 0.049885
22 to 31 141593 -1.0908 0.137682
21 to 30 142245 1.1575 0.876462
20 to 29 142323 1.4264 0.923131
19 to 28 142173 0.9092 0.818380
18 to 27 141970 0.2092 0.582857
17 to 26 142100 0.6575 0.744565
16 to 25 141600 -1.0667 0.143064
15 to 24 142142 0.8023 0.788813
14 to 23 141446 -1.5977 0.055056
13 to 22 141770 -0.4804 0.315454
12 to 21 142150 0.8299 0.796701
11 to 20 141603 -1.0563 0.145413
10 to 19 141738 -0.5908 0.277330
9 to 18 141498 -1.4184 0.078040
8 to 17 141554 -1.2253 0.110236
7 to 16 141851 -0.2011 0.420295
6 to 15 141808 -0.3494 0.363389
5 to 14 141573 -1.1598 0.123074
4 to 13 141716 -0.6667 0.252496
3 to 12 141947 0.1299 0.551676
2 to 11 141545 -1.2563 0.104502
1 to 10 141714 -0.6736 0.250298
-----------------------------------------------------------------
OQSO test for dh-ranFile-2019-12-14_08:31
Bits used No. missing words z-score p-value
28 to 32 141803 -0.3604 0.359259
27 to 31 141887 -0.0757 0.469831
26 to 30 142183 0.9277 0.823217
25 to 29 141901 -0.0282 0.488737
24 to 28 141672 -0.8045 0.210552
23 to 27 141888 -0.0723 0.471180
22 to 26 141840 -0.2350 0.407098
21 to 25 141630 -0.9469 0.171850
20 to 24 141709 -0.6791 0.248542
19 to 23 141743 -0.5638 0.286435
18 to 22 141891 -0.0621 0.475227
17 to 21 141838 -0.2418 0.404469
16 to 20 142535 2.1209 0.983036
15 to 19 141731 -0.6045 0.272753
14 to 18 141787 -0.4147 0.339189
13 to 17 141825 -0.2859 0.387491
12 to 16 141983 0.2497 0.598602
11 to 15 141704 -0.6960 0.243204
10 to 14 142513 2.0463 0.979638
9 to 13 142160 0.8497 0.802262
8 to 12 141490 -1.4215 0.077592
7 to 11 142071 0.5480 0.708166
6 to 10 142190 0.9514 0.829305
5 to 9 142070 0.5446 0.707001
4 to 8 142266 1.2091 0.886678
3 to 7 142152 0.8226 0.794635
2 to 6 142220 1.0531 0.853857
1 to 5 142010 0.3413 0.633544
-----------------------------------------------------------------
DNA test for dh-ranFile-2019-12-14_08:31
Bits used No. missing words z-score p-value
31 to 32 141746 -0.4818 0.314974
30 to 31 142403 1.4563 0.927339
29 to 30 142480 1.6834 0.953850
28 to 29 141251 -1.9420 0.026070
27 to 28 142287 1.1141 0.867376
26 to 27 142290 1.1229 0.869264
25 to 26 142524 1.8132 0.965098
24 to 25 142213 0.8958 0.814815
23 to 24 142369 1.3560 0.912444
22 to 23 142378 1.3825 0.916592
21 to 22 141720 -0.5585 0.288253
20 to 21 141699 -0.6204 0.267483
19 to 20 142109 0.5890 0.722068
18 to 19 142133 0.6598 0.745307
17 to 18 141681 -0.6735 0.250302
16 to 17 141652 -0.7591 0.223901
15 to 16 141917 0.0226 0.509025
14 to 15 142191 0.8309 0.796981
13 to 14 142216 0.9046 0.817170
12 to 13 142469 1.6509 0.950625
11 to 12 142225 0.9312 0.824120
10 to 11 142476 1.6716 0.952698
9 to 10 141906 -0.0098 0.496081
8 to 9 141429 -1.4169 0.078256
7 to 8 141910 0.0020 0.500789
6 to 7 141794 -0.3402 0.366851
5 to 6 141915 0.0167 0.506672
4 to 5 141909 -0.0010 0.499612
3 to 4 142003 0.2763 0.608846
2 to 3 141978 0.2026 0.580263
1 to 2 141803 -0.3137 0.376891
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2019-12-14_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2416.62 -1.179 0.119159
Test results for specific bytes for dh-ranFile-2019-12-14_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2540.28 0.570 0.715560
2 to 9 2577.06 1.090 0.862084
3 to 10 2592.16 1.303 0.903764
4 to 11 2611.00 1.570 0.941768
5 to 12 2574.48 1.053 0.853905
6 to 13 2479.27 -0.293 0.384715
7 to 14 2466.73 -0.471 0.318999
8 to 15 2466.15 -0.479 0.316087
9 to 16 2437.29 -0.887 0.187575
10 to 17 2558.47 0.827 0.795834
11 to 18 2404.11 -1.356 0.087540
12 to 19 2410.47 -1.266 0.102719
13 to 20 2445.27 -0.774 0.219470
14 to 21 2369.51 -1.845 0.032489
15 to 22 2549.10 0.694 0.756294
16 to 23 2485.91 -0.199 0.421016
17 to 24 2520.70 0.293 0.615166
18 to 25 2523.74 0.336 0.631465
19 to 26 2499.70 -0.004 0.498301
20 to 27 2474.83 -0.356 0.360940
21 to 28 2482.90 -0.242 0.404451
22 to 29 2530.62 0.433 0.667489
23 to 30 2527.92 0.395 0.653507
24 to 31 2491.27 -0.123 0.450867
25 to 32 2662.35 2.296 0.989163
CDPARK for dh-ranFile-2019-12-14_08:31: 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
3506 -0.7763 0.218799
3505 -0.8219 0.205562
3575 2.3744 0.991212
3506 -0.7763 0.218799
3528 0.2283 0.590298
3507 -0.7306 0.232514
3523 0.0000 0.500000
3511 -0.5479 0.291865
3552 1.3242 0.907282
3556 1.5068 0.934075
Square side=100, avg. no. parked=3526.90 sample std.=24.10
p-value of the KSTEST for those 10 p-values: 0.409522
Results for the MINIMUM DISTANCE test for dh-ranFile-2019-12-14_08:31
0.0217,0.0037,0.2030,0.5238,0.3648,0.4928,0.6749,0.0927,0.9413,0.3651,
The KS test for those 10 p-values: 0.161635
The 3DSPHERES test for dh-ranFile-2019-12-14_08:31
sample no r^3 equiv. uni.
1 31.532 0.650430
2 41.519 0.749421
3 12.681 0.344730
4 24.536 0.558627
5 179.252 0.997459
6 13.792 0.368548
7 36.231 0.701120
8 19.474 0.477498
9 6.279 0.188844
10 76.135 0.920963
11 47.042 0.791550
12 1.702 0.055150
13 4.438 0.137503
14 9.073 0.260971
15 15.830 0.410017
16 2.602 0.083083
17 4.006 0.125007
18 45.589 0.781210
19 56.521 0.848025
20 10.729 0.300681
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.981224
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2019-12-14_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -2.0 1.5 0.9 -0.8 -0.1
0.0 -2.0 1.2 -0.1 -0.7 0.9
-0.3 -0.7 0.5 0.3 -1.5 1.0
-0.6 0.3 1.8 -1.9 1.4 0.4
0.9 2.4 -1.6 0.6 -3.6 -1.3
-0.4 -0.9 0.4 -0.3 -0.4 -0.7
0.5 -0.7 -0.4 2.1 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:62.104405
z-score=2.193570, p-value=0.976574
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2019-12-14_08:31
Test no p-value
1 0.859811
2 0.465807
3 0.602289
4 0.367748
5 0.564169
6 0.482133
7 0.382021
8 0.666660
9 0.049698
10 0.579254
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.462058
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2019-12-14_08:31:
(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 66996 1.63 66485 0.50
3 25000.00 24702 3.55 25127 0.65
4 6666.67 6682 0.04 6745 0.92
5 1388.89 1349 1.15 1378 0.09
6 238.10 228 0.43 219 1.53
7 34.72 38 0.31 39 0.53
8 4.96 4 0.19 6 0.22
p=0.70459 p=0.38037
Number of rngs required: 687703, p-value: 0.209
RESULTS OF CRAPS TEST for dh-ranFile-2019-12-14_08:31
No. of wins: Observed Expected
98593 98585.9
z-score= 0.032, pvalue=0.51274
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66887 66666.7 0.728 0.728
2 37574 37654.3 0.171 0.900
3 26789 26954.7 1.019 1.919
4 19123 19313.5 1.878 3.797
5 13926 13851.4 0.402 4.198
6 10144 9943.5 4.041 8.239
7 7245 7145.0 1.399 9.638
8 5114 5139.1 0.122 9.761
9 3649 3699.9 0.699 10.460
10 2687 2666.3 0.161 10.621
11 1961 1923.3 0.738 11.359
12 1392 1388.7 0.008 11.366
13 914 1003.7 8.019 19.385
14 691 726.1 1.701 21.086
15 555 525.8 1.618 22.703
16 372 381.2 0.220 22.923
17 291 276.5 0.756 23.679
18 170 200.8 4.733 28.412
19 131 146.0 1.538 29.950
20 111 106.2 0.216 30.165
21 274 287.1 0.599 30.764
Chisq= 30.76 for 20 degrees of freedom, p= 0.94162
SUMMARY of craptest
p-value for no. of wins: 0.512740
p-value for throws/game: 0.941623
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2019-12-14_08:31
No. of wins: Observed Expected
98719 98585.9
z-score= 0.595, pvalue=0.72424
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66219 66666.7 3.006 3.006
2 37875 37654.3 1.293 4.299
3 26887 26954.7 0.170 4.470
4 19633 19313.5 5.287 9.756
5 13917 13851.4 0.310 10.067
6 9953 9943.5 0.009 10.076
7 7155 7145.0 0.014 10.090
8 5141 5139.1 0.001 10.090
9 3665 3699.9 0.329 10.419
10 2681 2666.3 0.081 10.500
11 1939 1923.3 0.128 10.628
12 1387 1388.7 0.002 10.630
13 957 1003.7 2.174 12.804
14 693 726.1 1.513 14.317
15 519 525.8 0.089 14.406
16 393 381.2 0.368 14.774
17 254 276.5 1.837 16.611
18 199 200.8 0.017 16.628
19 144 146.0 0.027 16.655
20 94 106.2 1.405 18.059
21 295 287.1 0.217 18.276
Chisq= 18.28 for 20 degrees of freedom, p= 0.43077
SUMMARY of craptest
p-value for no. of wins: 0.724241
p-value for throws/game: 0.430771
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0037,0.0152,0.0217,0.0240,0.0261,0.0275,0.0325,0.0342,0.0355,0.0443,
0.0497,0.0499,0.0551,0.0552,0.0553,0.0661,0.0663,0.0776,0.0780,0.0783,
0.0831,0.0836,0.0875,0.0927,0.0941,0.1027,0.1045,0.1102,0.1170,0.1192,
0.1231,0.1250,0.1256,0.1309,0.1375,0.1377,0.1395,0.1431,0.1454,0.1475,
0.1484,0.1501,0.1547,0.1616,0.1689,0.1718,0.1745,0.1749,0.1876,0.1888,
0.1996,0.2030,0.2056,0.2092,0.2106,0.2153,0.2188,0.2188,0.2195,0.2239,
0.2241,0.2278,0.2325,0.2364,0.2413,0.2432,0.2485,0.2503,0.2503,0.2525,
0.2537,0.2540,0.2610,0.2675,0.2721,0.2728,0.2761,0.2773,0.2864,0.2876,
0.2883,0.2896,0.2919,0.2966,0.3007,0.3112,0.3125,0.3133,0.3150,0.3155,
0.3161,0.3190,0.3392,0.3447,0.3488,0.3543,0.3593,0.3609,0.3631,0.3634,
0.3648,0.3651,0.3669,0.3677,0.3685,0.3769,0.3780,0.3804,0.3820,0.3847,
0.3848,0.3875,0.3955,0.4045,0.4045,0.4071,0.4075,0.4078,0.4095,0.4100,
0.4162,0.4203,0.4210,0.4233,0.4308,0.4509,0.4519,0.4550,0.4621,0.4658,
0.4698,0.4705,0.4712,0.4752,0.4775,0.4821,0.4887,0.4911,0.4928,0.4961,
0.4983,0.4995,0.4996,0.5000,0.5008,0.5067,0.5090,0.5127,0.5238,0.5248,
0.5308,0.5314,0.5372,0.5390,0.5517,0.5526,0.5586,0.5642,0.5646,0.5687,
0.5702,0.5785,0.5793,0.5803,0.5829,0.5843,0.5903,0.5986,0.6023,0.6077,
0.6088,0.6152,0.6315,0.6335,0.6504,0.6535,0.6541,0.6667,0.6675,0.6749,
0.6758,0.6933,0.7011,0.7011,0.7046,0.7070,0.7082,0.7156,0.7221,0.7235,
0.7242,0.7364,0.7446,0.7453,0.7455,0.7494,0.7563,0.7673,0.7787,0.7812,
0.7888,0.7916,0.7946,0.7958,0.7967,0.7970,0.8023,0.8049,0.8049,0.8148,
0.8156,0.8172,0.8184,0.8232,0.8241,0.8241,0.8293,0.8401,0.8428,0.8472,
0.8480,0.8539,0.8539,0.8586,0.8598,0.8621,0.8674,0.8693,0.8765,0.8790,
0.8867,0.8930,0.8957,0.8993,0.8998,0.9038,0.9073,0.9124,0.9130,0.9141,
0.9166,0.9210,0.9231,0.9241,0.9271,0.9273,0.9341,0.9413,0.9416,0.9418,
0.9475,0.9483,0.9506,0.9527,0.9539,0.9567,0.9593,0.9651,0.9708,0.9766,
0.9796,0.9812,0.9830,0.9879,0.9892,0.9903,0.9912,0.9918,0.9975,
Overall p-value after applying KStest on 269 p-values = 0.543447
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.