RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_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 15.74 21.3313 0.788178
2 to 25 15.81 18.6654 0.651930
3 to 26 15.92 9.6253 0.081417
4 to 27 16.25 12.2804 0.217133
5 to 28 15.65 27.7077 0.951528
6 to 29 15.91 15.8162 0.463098
7 to 30 16.06 14.5804 0.374326
8 to 31 15.83 12.0890 0.205284
9 to 32 15.47 25.6672 0.919258
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.975365
Tough bday spacings test for dh-ranFile-2018-06-21_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 8 38 70 126 89 65 55 22 20 3 4
(O-E)^2/E 0.1 0.1 0.1 8.2 0.8 2.2 0.2 2.0 1.8 2.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 17.459, p= 0.935
RESULTS OF GCD FOR dh-ranFile-2018-06-21_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.167682
p-value, dist. of gcd's: 0.790673
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.961 0.275 0.594 0.809 0.804 0.278 0.925 0.943
Bits 8 to 15---> 0.974 0.249 0.226 0.099 0.750 0.904 0.638 0.734
Bits 16 to 23---> 0.574 0.133 0.277 0.368 0.048 0.981 0.381 0.230
Bits 24 to 31---> 0.734 0.525 0.365 0.176 0.124 0.247 0.912 0.653
KS test for the above 32 p values: 0.459
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_15:31,
p-values for 5 runs: 0.3775, 0.3830, 0.4070, 0.8454, 0.1199
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5047 5134.0 1.475 2.223
r= 30 23172 23103.0 0.206 2.429
r= 31 11557 11551.5 0.003 2.432
chi-square = 2.432 with df = 3; p-value = 0.512
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 5144 5134.0 0.019 1.003
r= 31 23246 23103.0 0.885 1.887
r= 32 11413 11551.5 1.661 3.548
chi-square = 3.548 with df = 3; p-value = 0.685
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_15:31
b-rank test for bits 1 to 8, p=0.22292
b-rank test for bits 2 to 9, p=0.03766
b-rank test for bits 3 to 10, p=0.02862
b-rank test for bits 4 to 11, p=0.05149
b-rank test for bits 5 to 12, p=0.86353
b-rank test for bits 6 to 13, p=0.37195
b-rank test for bits 7 to 14, p=0.60505
b-rank test for bits 8 to 15, p=0.61448
b-rank test for bits 9 to 16, p=0.95696
b-rank test for bits 10 to 17, p=0.24189
b-rank test for bits 11 to 18, p=0.09462
b-rank test for bits 12 to 19, p=0.75686
b-rank test for bits 13 to 20, p=0.29546
b-rank test for bits 14 to 21, p=0.61460
b-rank test for bits 15 to 22, p=0.76268
b-rank test for bits 16 to 23, p=0.88196
b-rank test for bits 17 to 24, p=0.40746
b-rank test for bits 18 to 25, p=0.15199
b-rank test for bits 19 to 26, p=0.71685
b-rank test for bits 20 to 27, p=0.43508
b-rank test for bits 21 to 28, p=0.51484
b-rank test for bits 22 to 29, p=0.38958
b-rank test for bits 23 to 30, p=0.15894
b-rank test for bits 24 to 31, p=0.69462
b-rank test for bits 25 to 32, p=0.07294
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 = 0.501694
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_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 142659 1.75 0.960076
2 141426 -1.13 0.129391
3 142221 0.73 0.766755
4 142120 0.49 0.688718
5 141591 -0.74 0.228510
6 141676 -0.55 0.292821
7 141270 -1.49 0.067619
8 141187 -1.69 0.045736
9 141259 -1.52 0.064323
10 142020 0.26 0.602018
11 141143 -1.79 0.036688
12 142031 0.28 0.611900
13 142436 1.23 0.890752
14 141618 -0.68 0.248038
15 141593 -0.74 0.229927
16 141944 0.08 0.532281
17 141633 -0.65 0.259259
18 141492 -0.98 0.164763
19 142264 0.83 0.796354
20 141774 -0.32 0.375929
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_15:31
Bits used No. missing words z-score p-value
23 to 32 141140 -2.6529 0.003991
22 to 31 142164 0.8782 0.810075
21 to 30 142000 0.3127 0.622729
20 to 29 141888 -0.0736 0.470684
19 to 28 141608 -1.0391 0.149386
18 to 27 141405 -1.7391 0.041011
17 to 26 141933 0.0816 0.532526
16 to 25 141838 -0.2460 0.402855
15 to 24 141381 -1.8218 0.034241
14 to 23 142067 0.5437 0.706673
13 to 22 141933 0.0816 0.532526
12 to 21 141848 -0.2115 0.416255
11 to 20 141779 -0.4494 0.326567
10 to 19 141473 -1.5046 0.066215
9 to 18 141594 -1.0873 0.138442
8 to 17 141633 -0.9529 0.170330
7 to 16 142275 1.2609 0.896333
6 to 15 141849 -0.2080 0.417601
5 to 14 141841 -0.2356 0.406864
4 to 13 141935 0.0885 0.535267
3 to 12 142281 1.2816 0.900012
2 to 11 142049 0.4816 0.684962
1 to 10 141847 -0.2149 0.414911
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_15:31
Bits used No. missing words z-score p-value
28 to 32 142266 1.2091 0.886678
27 to 31 141780 -0.4384 0.330546
26 to 30 142276 1.2429 0.893057
25 to 29 142132 0.7548 0.774820
24 to 28 141934 0.0836 0.533324
23 to 27 142183 0.9277 0.823217
22 to 26 141813 -0.3265 0.372007
21 to 25 141620 -0.9808 0.163351
20 to 24 142297 1.3141 0.905600
19 to 23 141605 -1.0316 0.151123
18 to 22 141916 0.0226 0.509019
17 to 21 142306 1.3446 0.910630
16 to 20 142222 1.0599 0.855405
15 to 19 141658 -0.8520 0.197116
14 to 18 141559 -1.1876 0.117504
13 to 17 141834 -0.2554 0.399224
12 to 16 141825 -0.2859 0.387491
11 to 15 141632 -0.9401 0.173583
10 to 14 141348 -1.9028 0.028532
9 to 13 142354 1.5074 0.934140
8 to 12 141968 0.1989 0.578822
7 to 11 141332 -1.9571 0.025171
6 to 10 142404 1.6768 0.953214
5 to 9 141828 -0.2757 0.391391
4 to 8 142182 0.9243 0.822336
3 to 7 142699 2.6768 0.996284
2 to 6 141632 -0.9401 0.173583
1 to 5 141842 -0.2282 0.409731
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_15:31
Bits used No. missing words z-score p-value
31 to 32 141758 -0.4464 0.327654
30 to 31 141759 -0.4435 0.328720
29 to 30 142144 0.6922 0.755607
28 to 29 141523 -1.1396 0.127223
27 to 28 141832 -0.2281 0.409780
26 to 27 142008 0.2911 0.614498
25 to 26 141869 -0.1190 0.452651
24 to 25 141247 -1.9538 0.025364
23 to 24 142040 0.3855 0.650051
22 to 23 141766 -0.4228 0.336220
21 to 22 141934 0.0728 0.529007
20 to 21 142027 0.3471 0.635745
19 to 20 141841 -0.2016 0.420129
18 to 19 141962 0.1554 0.561735
17 to 18 142574 1.9607 0.975042
16 to 17 141876 -0.0983 0.460840
15 to 16 141535 -1.1042 0.134749
14 to 15 141741 -0.4965 0.309754
13 to 14 142077 0.4946 0.689559
12 to 13 142029 0.3530 0.637959
11 to 12 141619 -0.8564 0.195880
10 to 11 141538 -1.0954 0.136678
9 to 10 141279 -1.8594 0.031487
8 to 9 141840 -0.2045 0.418976
7 to 8 142134 0.6627 0.746253
6 to 7 142291 1.1259 0.869890
5 to 6 141545 -1.0747 0.141250
4 to 5 142266 1.0521 0.853629
3 to 4 141908 -0.0039 0.498435
2 to 3 142024 0.3383 0.632416
1 to 2 142037 0.3766 0.646767
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2510.17 0.144 0.557185
Test results for specific bytes for dh-ranFile-2018-06-21_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2463.79 -0.512 0.304281
2 to 9 2525.84 0.365 0.642585
3 to 10 2597.71 1.382 0.916489
4 to 11 2546.77 0.661 0.745815
5 to 12 2439.05 -0.862 0.194343
6 to 13 2513.51 0.191 0.575753
7 to 14 2505.33 0.075 0.530069
8 to 15 2511.35 0.160 0.563736
9 to 16 2437.86 -0.879 0.189770
10 to 17 2470.33 -0.420 0.337376
11 to 18 2403.69 -1.362 0.086600
12 to 19 2631.37 1.858 0.968405
13 to 20 2530.26 0.428 0.665660
14 to 21 2520.40 0.288 0.613502
15 to 22 2476.43 -0.333 0.369432
16 to 23 2632.18 1.869 0.969211
17 to 24 2522.20 0.314 0.623198
18 to 25 2493.54 -0.091 0.463609
19 to 26 2376.45 -1.747 0.040292
20 to 27 2538.90 0.550 0.708908
21 to 28 2602.63 1.451 0.926663
22 to 29 2531.31 0.443 0.671047
23 to 30 2535.82 0.507 0.693757
24 to 31 2560.36 0.854 0.803335
25 to 32 2602.41 1.448 0.926238
CDPARK for dh-ranFile-2018-06-21_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
3522 -0.0457 0.481790
3502 -0.9589 0.168804
3520 -0.1370 0.445521
3501 -1.0046 0.157553
3488 -1.5982 0.055002
3529 0.2740 0.607947
3523 0.0000 0.500000
3510 -0.5936 0.276387
3516 -0.3196 0.374623
3483 -1.8265 0.033889
Square side=100, avg. no. parked=3509.40 sample std.=14.71
p-value of the KSTEST for those 10 p-values: 0.058292
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_15:31
0.6543,0.2859,0.5863,0.2589,0.8881,0.4097,0.2688,0.7707,0.6120,0.7141,
The KS test for those 10 p-values: 0.583794
The 3DSPHERES test for dh-ranFile-2018-06-21_15:31
sample no r^3 equiv. uni.
1 35.315 0.691845
2 6.905 0.205609
3 6.913 0.205815
4 77.521 0.924532
5 38.116 0.719316
6 44.891 0.776054
7 5.276 0.161273
8 15.227 0.398046
9 58.711 0.858724
10 7.985 0.233692
11 21.676 0.514484
12 7.468 0.220357
13 18.586 0.461800
14 10.362 0.292061
15 2.223 0.071433
16 6.550 0.196132
17 83.733 0.938647
18 15.204 0.397580
19 1.972 0.063613
20 67.352 0.894078
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.656440
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 0.3 -1.3 -1.1 -1.4
0.7 -0.7 0.8 0.3 0.8 -1.5
-0.3 0.5 -1.2 0.5 0.2 0.9
0.7 -2.0 0.1 1.0 0.6 -0.8
0.2 0.3 -0.3 -0.6 0.6 -0.7
1.8 -1.1 1.9 -1.6 -0.4 1.3
0.5 -1.7 0.1 -0.7 0.1 0.0
1.8
Chi-square with 42 degrees of freedom:40.700745
z-score=-0.141760, p-value=0.472001
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_15:31
Test no p-value
1 0.017790
2 0.250871
3 0.711491
4 0.117750
5 0.230977
6 0.556497
7 0.013540
8 0.906727
9 0.054961
10 0.722038
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.080589
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_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 66497 0.43 66575 0.13
3 25000.00 25085 0.29 24965 0.05
4 6666.67 6737 0.74 6775 1.76
5 1388.89 1408 0.26 1420 0.70
6 238.10 233 0.11 218 1.70
7 34.72 36 0.05 42 1.53
8 4.96 3 0.77 4 0.19
p=0.14944 p=0.58133
Number of rngs required: 687957, p-value: 0.304
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_15:31
No. of wins: Observed Expected
98520 98585.9
z-score=-0.295, pvalue=0.38417
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66818 66666.7 0.344 0.344
2 37626 37654.3 0.021 0.365
3 26777 26954.7 1.172 1.537
4 19500 19313.5 1.802 3.338
5 13843 13851.4 0.005 3.344
6 9865 9943.5 0.620 3.964
7 7102 7145.0 0.259 4.223
8 5104 5139.1 0.239 4.462
9 3830 3699.9 4.577 9.040
10 2614 2666.3 1.026 10.065
11 1833 1923.3 4.242 14.308
12 1388 1388.7 0.000 14.308
13 990 1003.7 0.187 14.495
14 723 726.1 0.014 14.509
15 527 525.8 0.003 14.512
16 439 381.2 8.780 23.292
17 255 276.5 1.678 24.969
18 201 200.8 0.000 24.970
19 160 146.0 1.346 26.315
20 109 106.2 0.073 26.388
21 296 287.1 0.275 26.663
Chisq= 26.66 for 20 degrees of freedom, p= 0.85499
SUMMARY of craptest
p-value for no. of wins: 0.384166
p-value for throws/game: 0.854993
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_15:31
No. of wins: Observed Expected
98631 98585.9
z-score= 0.202, pvalue=0.58000
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66409 66666.7 0.996 0.996
2 37883 37654.3 1.389 2.385
3 27088 26954.7 0.659 3.044
4 19303 19313.5 0.006 3.049
5 13792 13851.4 0.255 3.304
6 9968 9943.5 0.060 3.364
7 7176 7145.0 0.134 3.499
8 5186 5139.1 0.429 3.927
9 3622 3699.9 1.639 5.566
10 2571 2666.3 3.406 8.972
11 1889 1923.3 0.613 9.585
12 1402 1388.7 0.127 9.711
13 1050 1003.7 2.134 11.846
14 747 726.1 0.599 12.445
15 509 525.8 0.539 12.984
16 356 381.2 1.660 14.643
17 295 276.5 1.232 15.876
18 208 200.8 0.256 16.132
19 161 146.0 1.544 17.676
20 100 106.2 0.364 18.040
21 285 287.1 0.016 18.055
Chisq= 18.06 for 20 degrees of freedom, p= 0.41624
SUMMARY of craptest
p-value for no. of wins: 0.580002
p-value for throws/game: 0.416245
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0040,0.0135,0.0178,0.0252,0.0254,0.0285,0.0286,0.0315,0.0339,0.0342,
0.0367,0.0377,0.0403,0.0410,0.0457,0.0483,0.0515,0.0550,0.0550,0.0583,
0.0636,0.0643,0.0662,0.0676,0.0714,0.0729,0.0806,0.0814,0.0866,0.0946,
0.0994,0.1175,0.1177,0.1199,0.1239,0.1272,0.1294,0.1326,0.1347,0.1367,
0.1384,0.1413,0.1494,0.1494,0.1511,0.1520,0.1576,0.1589,0.1613,0.1634,
0.1648,0.1677,0.1688,0.1703,0.1736,0.1736,0.1764,0.1898,0.1943,0.1959,
0.1961,0.1971,0.2053,0.2056,0.2058,0.2171,0.2204,0.2229,0.2258,0.2285,
0.2299,0.2304,0.2310,0.2337,0.2419,0.2468,0.2480,0.2486,0.2509,0.2589,
0.2593,0.2688,0.2751,0.2764,0.2773,0.2775,0.2859,0.2921,0.2928,0.2955,
0.3036,0.3043,0.3098,0.3266,0.3277,0.3287,0.3305,0.3362,0.3374,0.3646,
0.3675,0.3694,0.3720,0.3720,0.3743,0.3746,0.3759,0.3775,0.3811,0.3830,
0.3842,0.3875,0.3896,0.3914,0.3976,0.3980,0.3992,0.4029,0.4069,0.4070,
0.4075,0.4097,0.4097,0.4098,0.4149,0.4162,0.4163,0.4176,0.4190,0.4201,
0.4351,0.4455,0.4527,0.4589,0.4608,0.4618,0.4631,0.4636,0.4707,0.4720,
0.4818,0.4984,0.5000,0.5017,0.5090,0.5123,0.5145,0.5148,0.5250,0.5290,
0.5301,0.5323,0.5325,0.5325,0.5333,0.5353,0.5565,0.5572,0.5617,0.5637,
0.5736,0.5758,0.5788,0.5800,0.5813,0.5838,0.5863,0.5945,0.6020,0.6050,
0.6079,0.6119,0.6120,0.6135,0.6145,0.6145,0.6146,0.6227,0.6232,0.6324,
0.6357,0.6379,0.6380,0.6426,0.6468,0.6501,0.6519,0.6534,0.6543,0.6564,
0.6657,0.6710,0.6850,0.6855,0.6887,0.6896,0.6918,0.6938,0.6946,0.7067,
0.7089,0.7115,0.7141,0.7169,0.7193,0.7220,0.7337,0.7341,0.7458,0.7463,
0.7499,0.7556,0.7569,0.7627,0.7668,0.7707,0.7748,0.7761,0.7882,0.7907,
0.7964,0.8033,0.8044,0.8089,0.8101,0.8223,0.8232,0.8454,0.8536,0.8550,
0.8554,0.8587,0.8635,0.8699,0.8820,0.8867,0.8881,0.8908,0.8931,0.8941,
0.8963,0.9000,0.9041,0.9056,0.9067,0.9106,0.9123,0.9165,0.9193,0.9245,
0.9248,0.9262,0.9267,0.9341,0.9352,0.9386,0.9432,0.9515,0.9532,0.9570,
0.9601,0.9608,0.9684,0.9692,0.9742,0.9750,0.9754,0.9810,0.9963,
Overall p-value after applying KStest on 269 p-values = 0.290038
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.