RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.90 15.9501 0.472623
2 to 25 15.76 21.2728 0.785674
3 to 26 15.86 30.2449 0.975368
4 to 27 15.74 15.3500 0.429716
5 to 28 15.78 14.9776 0.402902
6 to 29 15.74 15.2524 0.422696
7 to 30 15.68 12.2389 0.214541
8 to 31 15.90 14.5665 0.373326
9 to 32 15.83 12.4023 0.224809
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.480565
Tough bday spacings test for dh-ranFile-2018-07-04_20:31: 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 43 78 104 92 67 48 28 17 12 6
(O-E)^2/E 1.9 1.1 0.3 0.4 0.3 1.6 0.3 0.1 0.3 4.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 11.661, p= 0.692
RESULTS OF GCD FOR dh-ranFile-2018-07-04_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.132444
p-value, dist. of gcd's: 0.889071
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.804 0.227 0.476 0.739 0.120 0.328 0.564 0.538
Bits 8 to 15---> 0.969 0.181 0.669 0.704 0.436 0.795 0.974 0.165
Bits 16 to 23---> 0.608 0.046 0.793 0.306 0.384 0.525 0.541 0.478
Bits 24 to 31---> 0.124 0.427 0.146 0.080 0.699 0.019 0.323 0.850
KS test for the above 32 p values: 0.110
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_20:31,
p-values for 5 runs: 0.6135, 0.5457, 0.0558, 0.6145, 0.4505
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5167 5134.0 0.212 0.267
r= 30 22958 23103.0 0.911 1.178
r= 31 11667 11551.5 1.154 2.332
chi-square = 2.332 with df = 3; p-value = 0.494
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 186 211.4 3.056 3.056
r= 30 5165 5134.0 0.187 3.243
r= 31 22997 23103.0 0.487 3.730
r= 32 11652 11551.5 0.874 4.604
chi-square = 4.604 with df = 3; p-value = 0.797
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_20:31
b-rank test for bits 1 to 8, p=0.97836
b-rank test for bits 2 to 9, p=0.86487
b-rank test for bits 3 to 10, p=0.16450
b-rank test for bits 4 to 11, p=0.73717
b-rank test for bits 5 to 12, p=0.66401
b-rank test for bits 6 to 13, p=0.74693
b-rank test for bits 7 to 14, p=0.00504
b-rank test for bits 8 to 15, p=0.98379
b-rank test for bits 9 to 16, p=0.70786
b-rank test for bits 10 to 17, p=0.90365
b-rank test for bits 11 to 18, p=0.78037
b-rank test for bits 12 to 19, p=0.27293
b-rank test for bits 13 to 20, p=0.48340
b-rank test for bits 14 to 21, p=0.73037
b-rank test for bits 15 to 22, p=0.36441
b-rank test for bits 16 to 23, p=0.51901
b-rank test for bits 17 to 24, p=0.83024
b-rank test for bits 18 to 25, p=0.47984
b-rank test for bits 19 to 26, p=0.22827
b-rank test for bits 20 to 27, p=0.14105
b-rank test for bits 21 to 28, p=0.15470
b-rank test for bits 22 to 29, p=0.34522
b-rank test for bits 23 to 30, p=0.61634
b-rank test for bits 24 to 31, p=0.64630
b-rank test for bits 25 to 32, p=0.00458
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 = 0.640846
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_20:31
(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 142906 2.33 0.990062
2 142336 1.00 0.840592
3 141798 -0.26 0.397387
4 141961 0.12 0.548045
5 142077 0.39 0.652379
6 141932 0.05 0.521121
7 141576 -0.78 0.218046
8 142098 0.44 0.670328
9 141296 -1.43 0.075927
10 141274 -1.48 0.068849
11 141935 0.06 0.523913
12 141961 0.12 0.548045
13 142298 0.91 0.818089
14 141588 -0.75 0.226395
15 142484 1.34 0.910313
16 142692 1.83 0.966275
17 141941 0.07 0.529493
18 141793 -0.27 0.392888
19 142052 0.33 0.630562
20 142250 0.80 0.786972
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_20:31
Bits used No. missing words z-score p-value
23 to 32 142315 1.3989 0.919073
22 to 31 141757 -0.5253 0.299696
21 to 30 141962 0.1816 0.572060
20 to 29 142580 2.3127 0.989629
19 to 28 141782 -0.4391 0.330306
18 to 27 141406 -1.7356 0.041315
17 to 26 141670 -0.8253 0.204608
16 to 25 141873 -0.1253 0.450153
15 to 24 141848 -0.2115 0.416255
14 to 23 141649 -0.8977 0.184676
13 to 22 141342 -1.9563 0.025214
12 to 21 141522 -1.3356 0.090837
11 to 20 141748 -0.5563 0.288999
10 to 19 142115 0.7092 0.760902
9 to 18 141886 -0.0804 0.467940
8 to 17 141768 -0.4873 0.313007
7 to 16 141836 -0.2529 0.400187
6 to 15 141944 0.1196 0.547581
5 to 14 141966 0.1954 0.577466
4 to 13 141628 -0.9701 0.165998
3 to 12 141702 -0.7149 0.237326
2 to 11 141544 -1.2598 0.103878
1 to 10 142022 0.3885 0.651183
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_20:31
Bits used No. missing words z-score p-value
28 to 32 142249 1.1514 0.875221
27 to 31 141759 -0.5096 0.305168
26 to 30 141596 -1.0621 0.144087
25 to 29 141996 0.2938 0.615543
24 to 28 142082 0.5853 0.720834
23 to 27 141663 -0.8350 0.201854
22 to 26 141799 -0.3740 0.354202
21 to 25 141694 -0.7299 0.232716
20 to 24 142179 0.9141 0.819677
19 to 23 141691 -0.7401 0.229619
18 to 22 142042 0.4497 0.673547
17 to 21 141783 -0.4282 0.334239
16 to 20 141885 -0.0825 0.467135
15 to 19 141768 -0.4791 0.315939
14 to 18 141770 -0.4723 0.318355
13 to 17 141997 0.2972 0.616838
12 to 16 142187 0.9413 0.826713
11 to 15 142039 0.4396 0.669872
10 to 14 142408 1.6904 0.954525
9 to 13 141446 -1.5706 0.058137
8 to 12 142029 0.4057 0.657504
7 to 11 141970 0.2057 0.581472
6 to 10 141971 0.2091 0.582796
5 to 9 141656 -0.8587 0.195240
4 to 8 141915 0.0192 0.507667
3 to 7 141538 -1.2587 0.104061
2 to 6 141996 0.2938 0.615543
1 to 5 142673 2.5887 0.995183
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_20:31
Bits used No. missing words z-score p-value
31 to 32 142309 1.1790 0.880794
30 to 31 141702 -0.6116 0.270404
29 to 30 142207 0.8781 0.810051
28 to 29 142106 0.5801 0.719092
27 to 28 141655 -0.7502 0.226556
26 to 27 141696 -0.6293 0.264579
25 to 26 141512 -1.1721 0.120586
24 to 25 142116 0.6096 0.728952
23 to 24 141966 0.1672 0.566381
22 to 23 142541 1.8633 0.968792
21 to 22 141848 -0.1809 0.428217
20 to 21 141426 -1.4258 0.076970
19 to 20 142116 0.6096 0.728952
18 to 19 142090 0.5329 0.702966
17 to 18 142329 1.2380 0.892135
16 to 17 142166 0.7571 0.775517
15 to 16 141754 -0.4582 0.323404
14 to 15 141954 0.1318 0.552417
13 to 14 142586 1.9961 0.977037
12 to 13 141843 -0.1957 0.422437
11 to 12 141935 0.0757 0.530180
10 to 11 141802 -0.3166 0.375771
9 to 10 142236 0.9636 0.832384
8 to 9 142083 0.5123 0.695780
7 to 8 141989 0.2350 0.592901
6 to 7 141996 0.2557 0.600895
5 to 6 142220 0.9164 0.820280
4 to 5 141599 -0.9154 0.179984
3 to 4 142052 0.4209 0.663070
2 to 3 141737 -0.5083 0.305605
1 to 2 141981 0.2114 0.583719
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2610.49 1.563 0.940927
Test results for specific bytes for dh-ranFile-2018-07-04_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2481.65 -0.260 0.397608
2 to 9 2484.51 -0.219 0.413308
3 to 10 2560.00 0.849 0.801930
4 to 11 2413.14 -1.228 0.109650
5 to 12 2424.86 -1.063 0.143961
6 to 13 2601.64 1.437 0.924704
7 to 14 2452.63 -0.670 0.251454
8 to 15 2703.00 2.871 0.997953
9 to 16 2675.37 2.480 0.993432
10 to 17 2587.93 1.244 0.893170
11 to 18 2408.32 -1.297 0.097381
12 to 19 2510.84 0.153 0.560930
13 to 20 2503.98 0.056 0.522417
14 to 21 2505.08 0.072 0.528648
15 to 22 2525.12 0.355 0.638825
16 to 23 2422.52 -1.096 0.136601
17 to 24 2377.33 -1.735 0.041388
18 to 25 2537.31 0.528 0.701116
19 to 26 2637.52 1.945 0.974103
20 to 27 2512.93 0.183 0.572549
21 to 28 2558.86 0.832 0.797395
22 to 29 2294.88 -2.901 0.001861
23 to 30 2408.99 -1.287 0.099035
24 to 31 2600.24 1.418 0.921851
25 to 32 2455.95 -0.623 0.266666
CDPARK for dh-ranFile-2018-07-04_20:31: 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
3535 0.5479 0.708135
3518 -0.2283 0.409702
3542 0.8676 0.807188
3534 0.5023 0.692266
3544 0.9589 0.831196
3530 0.3196 0.625377
3569 2.1005 0.982156
3503 -0.9132 0.180558
3543 0.9132 0.819442
Square side=100, avg. no. parked=3535.70 sample std.=16.43
p-value of the KSTEST for those 10 p-values: 0.059486
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_20:31
0.5642,0.9108,0.1918,0.9867,0.3388,0.0816,0.9453,0.9586,0.0502,0.1330,
The KS test for those 10 p-values: 0.156131
The 3DSPHERES test for dh-ranFile-2018-07-04_20:31
sample no r^3 equiv. uni.
1 48.787 0.803331
2 23.900 0.549169
3 14.638 0.386097
4 51.293 0.819091
5 44.546 0.773466
6 35.252 0.691206
7 66.704 0.891766
8 82.272 0.935584
9 6.978 0.207524
10 23.866 0.548663
11 26.503 0.586637
12 22.540 0.528263
13 64.206 0.882369
14 48.321 0.800252
15 124.155 0.984053
16 1.796 0.058118
17 28.812 0.617259
18 7.311 0.216276
19 40.449 0.740321
20 97.632 0.961396
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.033593
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 -0.4 0.8 -0.4 2.2
0.1 0.9 -0.7 -1.7 -0.6 -1.8
1.1 0.0 1.3 -0.3 -0.9 -1.7
-0.1 -0.6 0.9 -0.7 1.5 0.2
-1.7 2.4 2.3 0.1 0.2 0.9
0.8 0.1 -0.0 1.8 2.7 0.6
0.3 -0.7 -0.8 1.0 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:56.325813
z-score=1.563074, p-value=0.931227
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_20:31
Test no p-value
1 0.004556
2 0.167508
3 0.194120
4 0.180503
5 0.390151
6 0.074570
7 0.098449
8 0.693639
9 0.816917
10 0.284673
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.025015
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_20:31:
(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 66788 0.22 66777 0.18
3 25000.00 24934 0.17 25001 0.00
4 6666.67 6584 1.03 6562 1.64
5 1388.89 1425 0.94 1370 0.26
6 238.10 225 0.72 250 0.60
7 34.72 37 0.15 36 0.05
8 4.96 6 0.22 3 0.77
p=0.24900 p=0.25601
Number of rngs required: 687893, p-value: 0.278
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_20:31
No. of wins: Observed Expected
98941 98585.9
z-score= 1.588, pvalue=0.94390
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66410 66666.7 0.988 0.988
2 37832 37654.3 0.838 1.827
3 26886 26954.7 0.175 2.002
4 19284 19313.5 0.045 2.047
5 13812 13851.4 0.112 2.159
6 10033 9943.5 0.805 2.964
7 7259 7145.0 1.818 4.782
8 5133 5139.1 0.007 4.789
9 3691 3699.9 0.021 4.810
10 2649 2666.3 0.112 4.922
11 1897 1923.3 0.360 5.283
12 1339 1388.7 1.782 7.064
13 993 1003.7 0.114 7.179
14 733 726.1 0.065 7.244
15 568 525.8 3.381 10.625
16 394 381.2 0.433 11.058
17 297 276.5 1.514 12.572
18 203 200.8 0.023 12.595
19 164 146.0 2.223 14.818
20 102 106.2 0.167 14.986
21 321 287.1 3.999 18.985
Chisq= 18.98 for 20 degrees of freedom, p= 0.47719
SUMMARY of craptest
p-value for no. of wins: 0.943902
p-value for throws/game: 0.477191
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_20:31
No. of wins: Observed Expected
98414 98585.9
z-score=-0.769, pvalue=0.22105
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66478 66666.7 0.534 0.534
2 37596 37654.3 0.090 0.624
3 27079 26954.7 0.573 1.197
4 19380 19313.5 0.229 1.426
5 13777 13851.4 0.400 1.826
6 9962 9943.5 0.034 1.860
7 7166 7145.0 0.062 1.922
8 5138 5139.1 0.000 1.922
9 3717 3699.9 0.079 2.002
10 2664 2666.3 0.002 2.004
11 1963 1923.3 0.818 2.822
12 1387 1388.7 0.002 2.824
13 1009 1003.7 0.028 2.852
14 717 726.1 0.115 2.967
15 538 525.8 0.281 3.248
16 425 381.2 5.045 8.293
17 291 276.5 0.756 9.049
18 203 200.8 0.023 9.073
19 142 146.0 0.109 9.181
20 119 106.2 1.539 10.720
21 249 287.1 5.060 15.780
Chisq= 15.78 for 20 degrees of freedom, p= 0.26981
SUMMARY of craptest
p-value for no. of wins: 0.221050
p-value for throws/game: 0.269811
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0019,0.0046,0.0046,0.0050,0.0191,0.0250,0.0252,0.0336,0.0413,0.0414,
0.0462,0.0502,0.0558,0.0581,0.0581,0.0595,0.0688,0.0746,0.0759,0.0770,
0.0799,0.0816,0.0908,0.0974,0.0984,0.0990,0.1039,0.1041,0.1097,0.1104,
0.1203,0.1206,0.1244,0.1324,0.1330,0.1366,0.1411,0.1440,0.1441,0.1457,
0.1547,0.1561,0.1645,0.1654,0.1660,0.1675,0.1800,0.1805,0.1806,0.1806,
0.1847,0.1918,0.1941,0.1952,0.2019,0.2046,0.2075,0.2145,0.2163,0.2180,
0.2211,0.2248,0.2264,0.2266,0.2267,0.2283,0.2296,0.2327,0.2373,0.2490,
0.2515,0.2560,0.2646,0.2667,0.2698,0.2704,0.2729,0.2782,0.2847,0.2890,
0.2997,0.3052,0.3055,0.3056,0.3130,0.3159,0.3184,0.3227,0.3234,0.3278,
0.3303,0.3342,0.3388,0.3452,0.3542,0.3644,0.3733,0.3758,0.3840,0.3861,
0.3902,0.3929,0.3974,0.3976,0.4002,0.4029,0.4097,0.4133,0.4163,0.4224,
0.4227,0.4274,0.4282,0.4297,0.4362,0.4502,0.4505,0.4671,0.4679,0.4726,
0.4759,0.4772,0.4784,0.4798,0.4806,0.4834,0.4936,0.5077,0.5190,0.5211,
0.5224,0.5239,0.5252,0.5283,0.5286,0.5295,0.5302,0.5376,0.5409,0.5457,
0.5476,0.5480,0.5480,0.5487,0.5492,0.5524,0.5609,0.5642,0.5644,0.5664,
0.5721,0.5725,0.5775,0.5815,0.5828,0.5837,0.5866,0.5929,0.6009,0.6081,
0.6135,0.6145,0.6155,0.6155,0.6163,0.6168,0.6173,0.6254,0.6306,0.6388,
0.6408,0.6463,0.6512,0.6524,0.6575,0.6631,0.6640,0.6688,0.6699,0.6703,
0.6735,0.6912,0.6916,0.6923,0.6936,0.6958,0.6993,0.7011,0.7030,0.7041,
0.7079,0.7081,0.7191,0.7208,0.7290,0.7290,0.7304,0.7372,0.7389,0.7403,
0.7469,0.7609,0.7675,0.7735,0.7755,0.7804,0.7857,0.7870,0.7930,0.7950,
0.7968,0.7974,0.8003,0.8019,0.8033,0.8039,0.8072,0.8101,0.8169,0.8181,
0.8191,0.8194,0.8197,0.8203,0.8267,0.8302,0.8312,0.8324,0.8406,0.8501,
0.8649,0.8752,0.8808,0.8824,0.8891,0.8918,0.8921,0.8932,0.9036,0.9103,
0.9108,0.9191,0.9219,0.9247,0.9312,0.9356,0.9409,0.9439,0.9453,0.9545,
0.9586,0.9614,0.9663,0.9688,0.9689,0.9735,0.9741,0.9754,0.9770,0.9784,
0.9822,0.9838,0.9841,0.9867,0.9896,0.9901,0.9934,0.9952,0.9980,
Overall p-value after applying KStest on 269 p-values = 0.782388
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.