RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.79 23.5703 0.868413
2 to 25 15.68 20.5695 0.753859
3 to 26 15.80 27.2115 0.944962
4 to 27 15.84 12.7334 0.246158
5 to 28 15.92 16.7126 0.526002
6 to 29 16.03 10.0865 0.100058
7 to 30 15.95 29.5030 0.969840
8 to 31 15.65 19.8909 0.720151
9 to 32 15.86 9.4627 0.075382
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.444134
Tough bday spacings test for dh-ranFile-2018-06-23_03:31: 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 6 42 68 101 90 92 53 29 13 3 3
(O-E)^2/E 1.1 0.8 0.4 0.1 0.6 2.5 0.0 0.0 0.2 2.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 7.956, p= 0.367
RESULTS OF GCD FOR dh-ranFile-2018-06-23_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.429526
p-value, dist. of gcd's: 0.395947
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.379 0.671 0.417 0.787 0.783 0.382 0.998 0.663
Bits 8 to 15---> 0.107 0.139 0.822 0.428 0.923 0.362 0.469 0.750
Bits 16 to 23---> 0.277 0.736 0.901 0.164 0.700 0.272 0.554 0.323
Bits 24 to 31---> 0.058 0.030 0.753 0.647 0.225 0.218 0.677 0.168
KS test for the above 32 p values: 0.053
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_03:31,
p-values for 5 runs: 0.4322, 0.0932, 0.4402, 0.8174, 0.0523
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5111 5134.0 0.103 1.378
r= 30 23272 23103.0 1.236 2.614
r= 31 11422 11551.5 1.452 4.066
chi-square = 4.066 with df = 3; p-value = 0.746
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 247 211.4 5.989 5.989
r= 30 5084 5134.0 0.487 6.476
r= 31 23083 23103.0 0.017 6.493
r= 32 11586 11551.5 0.103 6.596
chi-square = 6.596 with df = 3; p-value = 0.914
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_03:31
b-rank test for bits 1 to 8, p=0.01403
b-rank test for bits 2 to 9, p=0.30954
b-rank test for bits 3 to 10, p=0.78091
b-rank test for bits 4 to 11, p=0.01776
b-rank test for bits 5 to 12, p=0.12183
b-rank test for bits 6 to 13, p=0.62994
b-rank test for bits 7 to 14, p=0.01303
b-rank test for bits 8 to 15, p=0.36159
b-rank test for bits 9 to 16, p=0.01908
b-rank test for bits 10 to 17, p=0.37353
b-rank test for bits 11 to 18, p=0.75045
b-rank test for bits 12 to 19, p=0.33917
b-rank test for bits 13 to 20, p=0.32203
b-rank test for bits 14 to 21, p=0.48202
b-rank test for bits 15 to 22, p=0.52163
b-rank test for bits 16 to 23, p=0.60227
b-rank test for bits 17 to 24, p=0.84820
b-rank test for bits 18 to 25, p=0.67419
b-rank test for bits 19 to 26, p=0.11693
b-rank test for bits 20 to 27, p=0.76766
b-rank test for bits 21 to 28, p=0.68822
b-rank test for bits 22 to 29, p=0.95990
b-rank test for bits 23 to 30, p=0.94204
b-rank test for bits 24 to 31, p=0.45940
b-rank test for bits 25 to 32, p=0.45820
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 = 0.395570
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_03:31
(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 141913 0.01 0.503421
2 141723 -0.44 0.331654
3 142494 1.37 0.914039
4 142216 0.72 0.763164
5 141623 -0.67 0.251749
6 141658 -0.59 0.278528
7 142353 1.04 0.850042
8 141593 -0.74 0.229927
9 141439 -1.10 0.135905
10 142587 1.58 0.943328
11 141999 0.21 0.582975
12 142337 1.00 0.841158
13 141705 -0.48 0.316536
14 141897 -0.03 0.488509
15 141164 -1.74 0.040805
16 142743 1.95 0.974282
17 142132 0.52 0.698558
18 142480 1.33 0.908790
19 142009 0.23 0.592070
20 141777 -0.31 0.378591
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_03:31
Bits used No. missing words z-score p-value
23 to 32 142002 0.3196 0.625346
22 to 31 142150 0.8299 0.796701
21 to 30 142574 2.2920 0.989046
20 to 29 141908 -0.0046 0.498170
19 to 28 142201 1.0058 0.842734
18 to 27 141708 -0.6942 0.243765
17 to 26 141438 -1.6253 0.052052
16 to 25 141756 -0.5287 0.298498
15 to 24 141650 -0.8942 0.185596
14 to 23 141548 -1.2460 0.106389
13 to 22 141955 0.1575 0.562568
12 to 21 141581 -1.1322 0.128781
11 to 20 142311 1.3851 0.916984
10 to 19 141929 0.0678 0.527039
9 to 18 142059 0.5161 0.697109
8 to 17 142045 0.4678 0.680046
7 to 16 142603 2.3920 0.991621
6 to 15 141816 -0.3218 0.373792
5 to 14 141808 -0.3494 0.363389
4 to 13 142063 0.5299 0.701908
3 to 12 142136 0.7816 0.782781
2 to 11 141477 -1.4908 0.068008
1 to 10 141998 0.3058 0.620106
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_03:31
Bits used No. missing words z-score p-value
28 to 32 141851 -0.1977 0.421629
27 to 31 141660 -0.8452 0.199003
26 to 30 141799 -0.3740 0.354202
25 to 29 142524 2.0836 0.981403
24 to 28 142347 1.4836 0.931046
23 to 27 141745 -0.5571 0.288746
22 to 26 141948 0.1311 0.552146
21 to 25 141869 -0.1367 0.445629
20 to 24 142174 0.8972 0.815190
19 to 23 141896 -0.0452 0.481979
18 to 22 141780 -0.4384 0.330546
17 to 21 142288 1.2836 0.900364
16 to 20 141549 -1.2215 0.110956
15 to 19 141743 -0.5638 0.286435
14 to 18 141826 -0.2825 0.388790
13 to 17 141679 -0.7808 0.217466
12 to 16 142208 1.0124 0.844336
11 to 15 142052 0.4836 0.685675
10 to 14 141657 -0.8554 0.196177
9 to 13 142190 0.9514 0.829305
8 to 12 142119 0.7107 0.761379
7 to 11 142120 0.7141 0.762428
6 to 10 142153 0.8260 0.795598
5 to 9 142251 1.1582 0.876610
4 to 8 142080 0.5785 0.718551
3 to 7 141805 -0.3537 0.361797
2 to 6 141885 -0.0825 0.467135
1 to 5 141873 -0.1232 0.450993
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_03:31
Bits used No. missing words z-score p-value
31 to 32 141723 -0.5496 0.291281
30 to 31 141526 -1.1308 0.129077
29 to 30 141247 -1.9538 0.025364
28 to 29 141560 -1.0305 0.151394
27 to 28 141645 -0.7797 0.217774
26 to 27 141552 -1.0541 0.145925
25 to 26 142118 0.6155 0.730903
24 to 25 142467 1.6450 0.950020
23 to 24 141468 -1.3019 0.096482
22 to 23 141933 0.0698 0.527833
21 to 22 142092 0.5388 0.705005
20 to 21 141608 -0.8889 0.187034
19 to 20 141565 -1.0157 0.154881
18 to 19 141655 -0.7502 0.226556
17 to 18 141971 0.1819 0.572176
16 to 17 141532 -1.1131 0.132840
15 to 16 142303 1.1613 0.877234
14 to 15 141844 -0.1927 0.423592
13 to 14 142270 1.0639 0.856318
12 to 13 141441 -1.3815 0.083562
11 to 12 141897 -0.0364 0.485493
10 to 11 141530 -1.1190 0.131577
9 to 10 141517 -1.1573 0.123572
8 to 9 142272 1.0698 0.857651
7 to 8 141924 0.0433 0.517259
6 to 7 141659 -0.7384 0.230125
5 to 6 141875 -0.1013 0.459669
4 to 5 141482 -1.2606 0.103734
3 to 4 142378 1.3825 0.916592
2 to 3 141677 -0.6853 0.246565
1 to 2 141746 -0.4818 0.314974
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2554.34 0.768 0.778885
Test results for specific bytes for dh-ranFile-2018-06-23_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2556.55 0.800 0.788050
2 to 9 2444.90 -0.779 0.217927
3 to 10 2492.72 -0.103 0.459015
4 to 11 2429.24 -1.001 0.158498
5 to 12 2611.36 1.575 0.942349
6 to 13 2509.91 0.140 0.555740
7 to 14 2520.82 0.294 0.615783
8 to 15 2529.86 0.422 0.663608
9 to 16 2542.97 0.608 0.728326
10 to 17 2513.67 0.193 0.576665
11 to 18 2542.95 0.607 0.728186
12 to 19 2725.11 3.183 0.999272
13 to 20 2462.86 -0.525 0.299693
14 to 21 2593.93 1.328 0.907964
15 to 22 2474.37 -0.362 0.358497
16 to 23 2595.66 1.353 0.911954
17 to 24 2552.97 0.749 0.773102
18 to 25 2452.77 -0.668 0.252084
19 to 26 2594.52 1.337 0.909352
20 to 27 2496.11 -0.055 0.478037
21 to 28 2635.58 1.917 0.972406
22 to 29 2546.13 0.652 0.742904
23 to 30 2444.67 -0.782 0.216965
24 to 31 2568.35 0.967 0.833129
25 to 32 2501.70 0.024 0.509583
CDPARK for dh-ranFile-2018-06-23_03:31: 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
3534 0.5023 0.692266
3498 -1.1416 0.126820
3574 2.3288 0.990064
3541 0.8219 0.794438
3528 0.2283 0.590298
3503 -0.9132 0.180558
3511 -0.5479 0.291865
3526 0.1370 0.554479
3519 -0.1826 0.427537
3544 0.9589 0.831196
Square side=100, avg. no. parked=3527.80 sample std.=21.16
p-value of the KSTEST for those 10 p-values: 0.905332
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_03:31
0.3354,0.2027,0.4422,0.7894,0.6015,0.6934,0.1671,0.4262,0.9900,0.2318,
The KS test for those 10 p-values: 0.840004
The 3DSPHERES test for dh-ranFile-2018-06-23_03:31
sample no r^3 equiv. uni.
1 13.849 0.369755
2 10.407 0.293118
3 37.283 0.711414
4 5.585 0.169876
5 25.878 0.577940
6 42.416 0.756802
7 32.349 0.659827
8 57.547 0.853134
9 32.907 0.666097
10 1.296 0.042271
11 10.955 0.305925
12 16.698 0.426842
13 21.801 0.516498
14 25.426 0.571533
15 16.588 0.424744
16 36.769 0.706433
17 6.035 0.182235
18 118.203 0.980554
19 24.425 0.556991
20 4.316 0.133988
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.829634
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 1.3 1.8 1.2 0.1 -1.0
0.4 1.2 -0.3 0.2 0.4 -0.7
0.4 0.1 1.3 -1.5 -1.5 -0.9
2.1 -1.1 1.4 -0.7 1.1 -0.4
-0.1 -1.1 -0.6 2.6 0.2 -0.7
0.6 -2.4 -0.8 1.3 0.6 -1.7
-0.2 1.8 -0.8 -0.1 0.1 1.0
-1.1
Chi-square with 42 degrees of freedom:56.668426
z-score=1.600457, p-value=0.935203
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_03:31
Test no p-value
1 0.889184
2 0.340278
3 0.250412
4 0.814379
5 0.204909
6 0.038895
7 0.028146
8 0.383915
9 0.061204
10 0.414634
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.098261
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_03:31:
(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 66578 0.12 66529 0.28
3 25000.00 25039 0.06 25162 1.05
4 6666.67 6619 0.34 6673 0.01
5 1388.89 1501 9.05 1353 0.93
6 238.10 222 1.09 239 0.00
7 34.72 32 0.21 38 0.31
8 4.96 8 1.86 5 0.00
p=0.95253 p=0.14072
Number of rngs required: 687980, p-value: 0.313
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_03:31
No. of wins: Observed Expected
98372 98585.9
z-score=-0.957, pvalue=0.16941
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66356 66666.7 1.448 1.448
2 38104 37654.3 5.370 6.818
3 26842 26954.7 0.471 7.289
4 19137 19313.5 1.612 8.902
5 13923 13851.4 0.370 9.272
6 9956 9943.5 0.016 9.287
7 7196 7145.0 0.364 9.651
8 5133 5139.1 0.007 9.658
9 3705 3699.9 0.007 9.665
10 2650 2666.3 0.100 9.765
11 1908 1923.3 0.122 9.887
12 1369 1388.7 0.281 10.168
13 1043 1003.7 1.538 11.705
14 729 726.1 0.011 11.716
15 549 525.8 1.020 12.737
16 358 381.2 1.406 14.143
17 287 276.5 0.396 14.539
18 188 200.8 0.820 15.358
19 142 146.0 0.109 15.467
20 127 106.2 4.067 19.534
21 298 287.1 0.413 19.947
Chisq= 19.95 for 20 degrees of freedom, p= 0.53875
SUMMARY of craptest
p-value for no. of wins: 0.169410
p-value for throws/game: 0.538753
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_03:31
No. of wins: Observed Expected
98587 98585.9
z-score= 0.005, pvalue=0.50204
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66726 66666.7 0.053 0.053
2 37882 37654.3 1.377 1.429
3 27000 26954.7 0.076 1.506
4 19280 19313.5 0.058 1.563
5 13716 13851.4 1.324 2.887
6 9693 9943.5 6.313 9.200
7 7166 7145.0 0.062 9.262
8 5287 5139.1 4.258 13.520
9 3703 3699.9 0.003 13.523
10 2621 2666.3 0.770 14.292
11 1880 1923.3 0.976 15.268
12 1368 1388.7 0.310 15.578
13 969 1003.7 1.201 16.779
14 753 726.1 0.994 17.772
15 530 525.8 0.033 17.805
16 385 381.2 0.039 17.844
17 284 276.5 0.201 18.045
18 203 200.8 0.023 18.069
19 155 146.0 0.557 18.626
20 112 106.2 0.315 18.941
21 287 287.1 0.000 18.941
Chisq= 18.94 for 20 degrees of freedom, p= 0.47431
SUMMARY of craptest
p-value for no. of wins: 0.502037
p-value for throws/game: 0.474312
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0130,0.0140,0.0178,0.0191,0.0254,0.0281,0.0300,0.0389,0.0408,0.0423,
0.0521,0.0523,0.0531,0.0583,0.0612,0.0680,0.0754,0.0836,0.0932,0.0965,
0.0983,0.1001,0.1037,0.1064,0.1074,0.1110,0.1169,0.1218,0.1236,0.1268,
0.1288,0.1291,0.1316,0.1328,0.1340,0.1359,0.1393,0.1407,0.1459,0.1514,
0.1549,0.1585,0.1641,0.1671,0.1684,0.1694,0.1699,0.1806,0.1822,0.1856,
0.1870,0.1962,0.1990,0.2027,0.2049,0.2170,0.2175,0.2175,0.2178,0.2179,
0.2253,0.2266,0.2299,0.2301,0.2318,0.2438,0.2462,0.2466,0.2504,0.2517,
0.2521,0.2716,0.2769,0.2785,0.2864,0.2887,0.2913,0.2919,0.2931,0.2985,
0.2997,0.3059,0.3095,0.3130,0.3150,0.3165,0.3220,0.3230,0.3305,0.3317,
0.3354,0.3392,0.3403,0.3542,0.3585,0.3616,0.3618,0.3622,0.3634,0.3669,
0.3698,0.3735,0.3738,0.3786,0.3788,0.3824,0.3839,0.3888,0.3956,0.3959,
0.4146,0.4166,0.4216,0.4236,0.4247,0.4262,0.4268,0.4275,0.4283,0.4295,
0.4322,0.4402,0.4422,0.4441,0.4456,0.4510,0.4582,0.4590,0.4594,0.4597,
0.4671,0.4686,0.4743,0.4780,0.4820,0.4820,0.4855,0.4885,0.4982,0.5020,
0.5034,0.5096,0.5165,0.5173,0.5216,0.5260,0.5270,0.5278,0.5388,0.5521,
0.5539,0.5545,0.5557,0.5570,0.5626,0.5715,0.5722,0.5767,0.5779,0.5830,
0.5903,0.5921,0.6015,0.6023,0.6158,0.6201,0.6253,0.6299,0.6470,0.6598,
0.6632,0.6636,0.6661,0.6713,0.6742,0.6770,0.6800,0.6857,0.6882,0.6923,
0.6934,0.6971,0.6986,0.7003,0.7019,0.7050,0.7064,0.7114,0.7186,0.7202,
0.7282,0.7283,0.7309,0.7356,0.7429,0.7456,0.7502,0.7504,0.7529,0.7539,
0.7568,0.7614,0.7624,0.7632,0.7677,0.7731,0.7789,0.7809,0.7828,0.7830,
0.7870,0.7880,0.7894,0.7944,0.7956,0.7967,0.8144,0.8152,0.8174,0.8215,
0.8293,0.8296,0.8312,0.8331,0.8400,0.8412,0.8427,0.8443,0.8482,0.8500,
0.8531,0.8563,0.8577,0.8684,0.8766,0.8772,0.8892,0.9004,0.9015,0.9053,
0.9080,0.9088,0.9094,0.9120,0.9140,0.9140,0.9166,0.9170,0.9227,0.9310,
0.9352,0.9420,0.9423,0.9433,0.9450,0.9500,0.9525,0.9599,0.9698,0.9724,
0.9743,0.9806,0.9814,0.9890,0.9900,0.9901,0.9916,0.9977,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.942034
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.