RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_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 16.07 20.1432 0.733028
2 to 25 15.80 8.7565 0.052408
3 to 26 16.16 23.0115 0.851124
4 to 27 15.73 15.9056 0.469464
5 to 28 15.69 12.6215 0.238865
6 to 29 15.81 17.0410 0.548405
7 to 30 15.74 16.0456 0.479393
8 to 31 15.62 23.6139 0.869690
9 to 32 15.62 20.9850 0.773037
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.789136
Tough bday spacings test for dh-ranFile-2018-06-26_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 8 33 68 116 100 72 50 27 14 8 4
(O-E)^2/E 0.1 0.4 0.4 3.4 0.1 0.5 0.1 0.3 0.1 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.543, p= 0.148
RESULTS OF GCD FOR dh-ranFile-2018-06-26_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.363720
p-value, dist. of gcd's: 0.489839
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.623 0.096 0.010 0.056 0.775 0.451 0.525 0.539
Bits 8 to 15---> 0.951 0.820 0.482 0.634 0.640 0.456 0.926 0.380
Bits 16 to 23---> 0.883 0.233 0.009 0.994 0.182 0.423 0.593 0.643
Bits 24 to 31---> 0.386 0.431 0.443 0.092 0.921 0.118 0.768 0.980
KS test for the above 32 p values: 0.258
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_03:31,
p-values for 5 runs: 0.0909, 0.4795, 0.5444, 0.7077, 0.1065
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 194 211.4 1.435 1.435
r= 29 5123 5134.0 0.024 1.459
r= 30 23010 23103.0 0.375 1.833
r= 31 11673 11551.5 1.277 3.111
chi-square = 3.111 with df = 3; p-value = 0.625
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 204 211.4 0.260 0.260
r= 30 5076 5134.0 0.655 0.916
r= 31 23159 23103.0 0.136 1.051
r= 32 11561 11551.5 0.008 1.059
chi-square = 1.059 with df = 3; p-value = 0.213
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_03:31
b-rank test for bits 1 to 8, p=0.85782
b-rank test for bits 2 to 9, p=0.96680
b-rank test for bits 3 to 10, p=0.96341
b-rank test for bits 4 to 11, p=0.24295
b-rank test for bits 5 to 12, p=0.26549
b-rank test for bits 6 to 13, p=0.22205
b-rank test for bits 7 to 14, p=0.72459
b-rank test for bits 8 to 15, p=0.30179
b-rank test for bits 9 to 16, p=0.60386
b-rank test for bits 10 to 17, p=0.20792
b-rank test for bits 11 to 18, p=0.63618
b-rank test for bits 12 to 19, p=0.37100
b-rank test for bits 13 to 20, p=0.44893
b-rank test for bits 14 to 21, p=0.81964
b-rank test for bits 15 to 22, p=0.32213
b-rank test for bits 16 to 23, p=0.54867
b-rank test for bits 17 to 24, p=0.94633
b-rank test for bits 18 to 25, p=0.57169
b-rank test for bits 19 to 26, p=0.55411
b-rank test for bits 20 to 27, p=0.81127
b-rank test for bits 21 to 28, p=0.43549
b-rank test for bits 22 to 29, p=0.81000
b-rank test for bits 23 to 30, p=0.69983
b-rank test for bits 24 to 31, p=0.76902
b-rank test for bits 25 to 32, p=0.75840
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 = 0.135933
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_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 142289 0.89 0.812482
2 141901 -0.02 0.492236
3 142606 1.63 0.948209
4 142729 1.92 0.972261
5 142292 0.89 0.814363
6 141571 -0.79 0.214621
7 141537 -0.87 0.192169
8 141544 -0.85 0.196670
9 141615 -0.69 0.245825
10 141782 -0.30 0.383042
11 142118 0.49 0.687065
12 142024 0.27 0.605620
13 141828 -0.19 0.424645
14 142058 0.35 0.635840
15 142064 0.36 0.641092
16 142082 0.40 0.656686
17 142334 0.99 0.839455
18 141962 0.12 0.548971
19 141431 -1.12 0.131870
20 142108 0.46 0.678741
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_03:31
Bits used No. missing words z-score p-value
23 to 32 141740 -0.5839 0.279645
22 to 31 142504 2.0506 0.979846
21 to 30 141906 -0.0115 0.495419
20 to 29 142327 1.4402 0.925100
19 to 28 142017 0.3713 0.644784
18 to 27 141934 0.0851 0.533897
17 to 26 141923 0.0471 0.518798
16 to 25 141994 0.2920 0.614844
15 to 24 142304 1.3609 0.913232
14 to 23 142580 2.3127 0.989629
13 to 22 141935 0.0885 0.535267
12 to 21 141328 -2.0046 0.022504
11 to 20 141443 -1.6080 0.053914
10 to 19 142019 0.3782 0.647349
9 to 18 141525 -1.3253 0.092540
8 to 17 141549 -1.2425 0.107023
7 to 16 141693 -0.7460 0.227844
6 to 15 141818 -0.3149 0.376407
5 to 14 141822 -0.3011 0.381655
4 to 13 141990 0.2782 0.609560
3 to 12 142007 0.3368 0.631864
2 to 11 141980 0.2437 0.596264
1 to 10 142160 0.8644 0.806310
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_03:31
Bits used No. missing words z-score p-value
28 to 32 142145 0.7989 0.787820
27 to 31 141991 0.2768 0.609051
26 to 30 141978 0.2328 0.592034
25 to 29 142117 0.7040 0.759273
24 to 28 141700 -0.7096 0.238978
23 to 27 141906 -0.0113 0.495497
22 to 26 141819 -0.3062 0.379725
21 to 25 141643 -0.9028 0.183312
20 to 24 142203 0.9955 0.840251
19 to 23 141664 -0.8316 0.202810
18 to 22 141501 -1.3842 0.083153
17 to 21 141858 -0.1740 0.430933
16 to 20 141927 0.0599 0.523882
15 to 19 142321 1.3955 0.918566
14 to 18 141450 -1.5571 0.059729
13 to 17 141629 -0.9503 0.170987
12 to 16 141836 -0.2486 0.401844
11 to 15 141755 -0.5232 0.300434
10 to 14 141925 0.0531 0.521181
9 to 13 141569 -1.1537 0.124320
8 to 12 141877 -0.1096 0.456366
7 to 11 142119 0.7107 0.761379
6 to 10 141705 -0.6926 0.244267
5 to 9 142000 0.3074 0.620714
4 to 8 142049 0.4735 0.682057
3 to 7 141941 0.1074 0.542747
2 to 6 141702 -0.7028 0.241086
1 to 5 141845 -0.2181 0.413688
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_03:31
Bits used No. missing words z-score p-value
31 to 32 141270 -1.8859 0.029652
30 to 31 141319 -1.7414 0.040808
29 to 30 142165 0.7542 0.774632
28 to 29 142473 1.6627 0.951818
27 to 28 141748 -0.4759 0.317073
26 to 27 141890 -0.0570 0.477264
25 to 26 141895 -0.0423 0.483141
24 to 25 141914 0.0138 0.505496
23 to 24 141372 -1.5850 0.056478
22 to 23 141847 -0.1839 0.427060
21 to 22 142121 0.6244 0.733816
20 to 21 141864 -0.1337 0.446813
19 to 20 142146 0.6981 0.757456
18 to 19 142268 1.0580 0.854978
17 to 18 142013 0.3058 0.620126
16 to 17 142159 0.7365 0.769284
15 to 16 142014 0.3088 0.621248
14 to 15 141863 -0.1367 0.445647
13 to 14 141866 -0.1278 0.449147
12 to 13 141532 -1.1131 0.132840
11 to 12 141927 0.0521 0.520785
10 to 11 141241 -1.9715 0.024335
9 to 10 141955 0.1347 0.553583
8 to 9 142022 0.3324 0.630191
7 to 8 142461 1.6273 0.948168
6 to 7 141884 -0.0747 0.470219
5 to 6 141908 -0.0039 0.498435
4 to 5 141625 -0.8387 0.200810
3 to 4 141760 -0.4405 0.329787
2 to 3 142445 1.5801 0.942963
1 to 2 141344 -1.6676 0.047694
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2491.94 -0.114 0.454613
Test results for specific bytes for dh-ranFile-2018-06-26_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2605.40 1.491 0.931962
2 to 9 2623.64 1.749 0.959816
3 to 10 2448.25 -0.732 0.232133
4 to 11 2491.83 -0.116 0.454007
5 to 12 2565.15 0.921 0.821582
6 to 13 2424.02 -1.075 0.141284
7 to 14 2379.88 -1.699 0.044689
8 to 15 2391.18 -1.539 0.061909
9 to 16 2464.82 -0.498 0.309409
10 to 17 2520.49 0.290 0.613997
11 to 18 2496.80 -0.045 0.481969
12 to 19 2479.66 -0.288 0.386819
13 to 20 2572.52 1.026 0.847444
14 to 21 2542.67 0.603 0.726908
15 to 22 2545.03 0.637 0.737883
16 to 23 2403.56 -1.364 0.086306
17 to 24 2611.69 1.580 0.942893
18 to 25 2522.47 0.318 0.624654
19 to 26 2465.19 -0.492 0.311280
20 to 27 2468.26 -0.449 0.326768
21 to 28 2471.10 -0.409 0.341391
22 to 29 2646.86 2.077 0.981094
23 to 30 2554.73 0.774 0.780544
24 to 31 2463.91 -0.510 0.304888
25 to 32 2355.88 -2.038 0.020766
CDPARK for dh-ranFile-2018-06-26_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
3516 -0.3196 0.374623
3535 0.5479 0.708135
3545 1.0046 0.842447
3516 -0.3196 0.374623
3491 -1.4612 0.071982
3525 0.0913 0.536383
3553 1.3699 0.914635
3533 0.4566 0.676028
3541 0.8219 0.794438
3527 0.1826 0.572463
Square side=100, avg. no. parked=3528.20 sample std.=16.80
p-value of the KSTEST for those 10 p-values: 0.543845
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_03:31
0.4581,0.6093,0.2673,0.3251,0.3167,0.6832,0.7251,0.1117,0.1998,0.1465,
The KS test for those 10 p-values: 0.271352
The 3DSPHERES test for dh-ranFile-2018-06-26_03:31
sample no r^3 equiv. uni.
1 27.961 0.606253
2 180.201 0.997538
3 36.160 0.700406
4 2.648 0.084497
5 2.675 0.085318
6 0.278 0.009239
7 4.592 0.141934
8 4.451 0.137874
9 13.362 0.359441
10 8.938 0.257642
11 52.743 0.827630
12 25.543 0.573203
13 7.150 0.212065
14 3.371 0.106292
15 6.963 0.207127
16 32.549 0.662084
17 5.182 0.158646
18 7.935 0.232421
19 114.182 0.977765
20 56.144 0.846102
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.107523
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 -1.1 -0.7 0.2 0.3
0.4 -0.5 -0.3 0.9 -0.8 1.1
0.2 -0.2 -1.3 1.2 0.3 0.6
-0.1 0.6 -0.1 -0.3 -0.2 -0.6
0.5 -1.6 0.9 -0.7 -1.5 0.0
-0.2 -0.3 0.5 -0.3 -0.9 1.7
-0.7 -0.4 0.5 -1.3 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:26.393252
z-score=-1.702836, p-value=0.028671
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_03:31
Test no p-value
1 0.175530
2 0.703527
3 0.277579
4 0.267240
5 0.450450
6 0.203172
7 0.841336
8 0.169319
9 0.160500
10 0.169072
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.064919
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_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 66380 1.23 66763 0.14
3 25000.00 25198 1.57 25038 0.06
4 6666.67 6684 0.05 6536 2.56
5 1388.89 1447 2.43 1389 0.00
6 238.10 251 0.70 237 0.01
7 34.72 31 0.40 30 0.64
8 4.96 8 1.86 6 0.22
p=0.77885 p=0.27245
Number of rngs required: 689056, p-value: 0.775
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_03:31
No. of wins: Observed Expected
98556 98585.9
z-score=-0.134, pvalue=0.44688
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66935 66666.7 1.080 1.080
2 37168 37654.3 6.281 7.361
3 27232 26954.7 2.852 10.213
4 19290 19313.5 0.029 10.242
5 13861 13851.4 0.007 10.248
6 10076 9943.5 1.764 12.013
7 6976 7145.0 3.999 16.011
8 5138 5139.1 0.000 16.012
9 3836 3699.9 5.009 21.021
10 2628 2666.3 0.550 21.571
11 1851 1923.3 2.720 24.291
12 1387 1388.7 0.002 24.293
13 995 1003.7 0.076 24.368
14 710 726.1 0.359 24.727
15 525 525.8 0.001 24.729
16 372 381.2 0.220 24.948
17 295 276.5 1.232 26.181
18 184 200.8 1.410 27.591
19 152 146.0 0.248 27.839
20 112 106.2 0.315 28.154
21 277 287.1 0.356 28.510
Chisq= 28.51 for 20 degrees of freedom, p= 0.90214
SUMMARY of craptest
p-value for no. of wins: 0.446881
p-value for throws/game: 0.902139
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_03:31
No. of wins: Observed Expected
98497 98585.9
z-score=-0.397, pvalue=0.34553
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66903 66666.7 0.838 0.838
2 37410 37654.3 1.585 2.423
3 26792 26954.7 0.982 3.406
4 19342 19313.5 0.042 3.448
5 14015 13851.4 1.932 5.380
6 9882 9943.5 0.381 5.760
7 7072 7145.0 0.746 6.507
8 5187 5139.1 0.447 6.954
9 3741 3699.9 0.457 7.411
10 2653 2666.3 0.066 7.477
11 1898 1923.3 0.334 7.811
12 1364 1388.7 0.441 8.252
13 1025 1003.7 0.451 8.703
14 729 726.1 0.011 8.714
15 573 525.8 4.230 12.945
16 377 381.2 0.045 12.990
17 289 276.5 0.561 13.551
18 223 200.8 2.447 15.999
19 149 146.0 0.062 16.061
20 94 106.2 1.405 17.466
21 282 287.1 0.091 17.557
Chisq= 17.56 for 20 degrees of freedom, p= 0.38343
SUMMARY of craptest
p-value for no. of wins: 0.345526
p-value for throws/game: 0.383432
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0090,0.0092,0.0102,0.0208,0.0225,0.0243,0.0287,0.0297,0.0408,0.0447,
0.0477,0.0524,0.0539,0.0555,0.0565,0.0597,0.0619,0.0649,0.0720,0.0832,
0.0845,0.0853,0.0863,0.0909,0.0917,0.0925,0.0958,0.1063,0.1065,0.1070,
0.1075,0.1117,0.1179,0.1243,0.1319,0.1328,0.1359,0.1379,0.1413,0.1419,
0.1465,0.1479,0.1586,0.1605,0.1691,0.1693,0.1710,0.1755,0.1823,0.1833,
0.1922,0.1967,0.1998,0.2008,0.2028,0.2032,0.2071,0.2079,0.2121,0.2130,
0.2146,0.2221,0.2278,0.2321,0.2324,0.2331,0.2389,0.2390,0.2411,0.2430,
0.2443,0.2458,0.2576,0.2580,0.2655,0.2672,0.2673,0.2714,0.2724,0.2776,
0.2796,0.3004,0.3018,0.3049,0.3094,0.3113,0.3167,0.3171,0.3221,0.3251,
0.3268,0.3298,0.3414,0.3455,0.3594,0.3637,0.3710,0.3746,0.3746,0.3764,
0.3797,0.3799,0.3817,0.3830,0.3834,0.3865,0.3868,0.4018,0.4137,0.4233,
0.4246,0.4271,0.4309,0.4312,0.4355,0.4432,0.4456,0.4468,0.4469,0.4489,
0.4491,0.4505,0.4507,0.4540,0.4546,0.4558,0.4564,0.4581,0.4695,0.4702,
0.4773,0.4794,0.4795,0.4818,0.4820,0.4831,0.4898,0.4922,0.4954,0.4955,
0.4984,0.5055,0.5188,0.5208,0.5212,0.5239,0.5248,0.5339,0.5353,0.5364,
0.5387,0.5427,0.5438,0.5444,0.5484,0.5487,0.5490,0.5536,0.5541,0.5717,
0.5725,0.5732,0.5920,0.5933,0.5963,0.6039,0.6056,0.6063,0.6091,0.6093,
0.6096,0.6140,0.6148,0.6201,0.6207,0.6212,0.6228,0.6247,0.6251,0.6302,
0.6319,0.6336,0.6358,0.6362,0.6401,0.6411,0.6431,0.6448,0.6473,0.6567,
0.6621,0.6760,0.6787,0.6821,0.6832,0.6871,0.6998,0.7004,0.7035,0.7077,
0.7081,0.7246,0.7251,0.7269,0.7330,0.7338,0.7379,0.7575,0.7584,0.7593,
0.7614,0.7685,0.7690,0.7693,0.7730,0.7746,0.7747,0.7753,0.7788,0.7805,
0.7878,0.7891,0.7944,0.8063,0.8100,0.8113,0.8125,0.8144,0.8196,0.8197,
0.8216,0.8276,0.8395,0.8403,0.8413,0.8424,0.8461,0.8474,0.8511,0.8550,
0.8578,0.8697,0.8828,0.9021,0.9132,0.9146,0.9186,0.9205,0.9251,0.9256,
0.9320,0.9429,0.9430,0.9463,0.9482,0.9482,0.9510,0.9518,0.9598,0.9634,
0.9668,0.9723,0.9778,0.9798,0.9802,0.9811,0.9896,0.9937,0.9975,
Overall p-value after applying KStest on 269 p-values = 0.646658
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.