RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_04:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.63 26.6874 0.937186
2 to 25 15.76 16.9810 0.544343
3 to 26 15.48 22.5012 0.833795
4 to 27 15.65 23.2395 0.858387
5 to 28 15.81 11.8640 0.191695
6 to 29 15.84 11.8800 0.192653
7 to 30 15.42 23.3057 0.860440
8 to 31 15.83 15.7442 0.457961
9 to 32 15.89 23.7063 0.872364
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.158017
Tough bday spacings test for dh-ranFile-2018-06-25_04:31: 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 40 70 114 111 74 41 27 8 7 0
(O-E)^2/E 0.1 0.3 0.1 2.7 1.8 0.2 2.4 0.3 3.2 0.0 4.1
Birthday Spacings: Sum(O-E)^2/E= 15.257, p= 0.877
RESULTS OF GCD FOR dh-ranFile-2018-06-25_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.499082
p-value, dist. of gcd's: 0.432077
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.079 0.645 0.266 0.950 0.533 0.548 0.213 0.403
Bits 8 to 15---> 0.904 0.077 0.624 0.334 0.992 0.434 0.991 0.146
Bits 16 to 23---> 0.031 0.131 0.539 0.552 0.735 0.388 0.146 0.102
Bits 24 to 31---> 0.092 0.726 0.957 0.205 0.227 0.918 0.701 0.636
KS test for the above 32 p values: 0.437
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_04:31,
p-values for 5 runs: 0.7608, 0.9548, 0.5258, 0.9413, 0.2430
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5004 5134.0 3.292 3.909
r= 30 23268 23103.0 1.178 5.087
r= 31 11528 11551.5 0.048 5.135
chi-square = 5.135 with df = 3; p-value = 0.838
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5054 5134.0 1.247 1.259
r= 31 23095 23103.0 0.003 1.262
r= 32 11638 11551.5 0.647 1.909
chi-square = 1.909 with df = 3; p-value = 0.408
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_04:31
b-rank test for bits 1 to 8, p=0.01838
b-rank test for bits 2 to 9, p=0.37780
b-rank test for bits 3 to 10, p=0.59798
b-rank test for bits 4 to 11, p=0.20948
b-rank test for bits 5 to 12, p=0.51139
b-rank test for bits 6 to 13, p=0.05880
b-rank test for bits 7 to 14, p=0.90631
b-rank test for bits 8 to 15, p=0.84448
b-rank test for bits 9 to 16, p=0.10177
b-rank test for bits 10 to 17, p=0.69738
b-rank test for bits 11 to 18, p=0.31236
b-rank test for bits 12 to 19, p=0.86330
b-rank test for bits 13 to 20, p=0.75534
b-rank test for bits 14 to 21, p=0.63134
b-rank test for bits 15 to 22, p=0.07787
b-rank test for bits 16 to 23, p=0.37912
b-rank test for bits 17 to 24, p=0.86327
b-rank test for bits 18 to 25, p=0.64494
b-rank test for bits 19 to 26, p=0.60288
b-rank test for bits 20 to 27, p=0.10069
b-rank test for bits 21 to 28, p=0.31618
b-rank test for bits 22 to 29, p=0.17657
b-rank test for bits 23 to 30, p=0.91105
b-rank test for bits 24 to 31, p=0.87041
b-rank test for bits 25 to 32, p=0.96343
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 = 0.835223
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_04:31
(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 142165 0.60 0.724866
2 142317 0.95 0.829578
3 141778 -0.31 0.379480
4 142117 0.49 0.686236
5 141735 -0.41 0.341889
6 142308 0.93 0.824195
7 142506 1.39 0.918355
8 141723 -0.44 0.331654
9 141592 -0.74 0.229218
10 142163 0.59 0.723305
11 142214 0.71 0.761720
12 141889 -0.05 0.481057
13 142196 0.67 0.748504
14 142628 1.68 0.953437
15 141750 -0.37 0.354847
16 141845 -0.15 0.440263
17 142135 0.53 0.700996
18 141511 -0.93 0.176010
19 142279 0.86 0.806128
20 142845 2.19 0.985597
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_04:31
Bits used No. missing words z-score p-value
23 to 32 141441 -1.6149 0.053163
22 to 31 142016 0.3678 0.643499
21 to 30 141448 -1.5908 0.055828
20 to 29 141548 -1.2460 0.106389
19 to 28 141774 -0.4667 0.320373
18 to 27 141909 -0.0011 0.499546
17 to 26 141827 -0.2839 0.388245
16 to 25 141924 0.0506 0.520172
15 to 24 141379 -1.8287 0.033720
14 to 23 141706 -0.7011 0.241609
13 to 22 142031 0.4196 0.662594
12 to 21 141708 -0.6942 0.243765
11 to 20 142027 0.4058 0.657540
10 to 19 142341 1.4885 0.931693
9 to 18 141833 -0.2632 0.396196
8 to 17 141978 0.2368 0.593591
7 to 16 141430 -1.6529 0.049179
6 to 15 141930 0.0713 0.528411
5 to 14 141689 -0.7598 0.223699
4 to 13 141523 -1.3322 0.091402
3 to 12 142048 0.4782 0.683736
2 to 11 142123 0.7368 0.769376
1 to 10 142477 1.9575 0.974855
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_04:31
Bits used No. missing words z-score p-value
28 to 32 141781 -0.4350 0.331775
27 to 31 142461 1.8701 0.969263
26 to 30 141667 -0.8215 0.205693
25 to 29 141549 -1.2215 0.110956
24 to 28 142062 0.5175 0.697605
23 to 27 142003 0.3175 0.624578
22 to 26 141657 -0.8554 0.196177
21 to 25 141861 -0.1638 0.434932
20 to 24 142119 0.7107 0.761379
19 to 23 141804 -0.3571 0.360527
18 to 22 141467 -1.4994 0.066882
17 to 21 141957 0.1616 0.564187
16 to 20 141864 -0.1537 0.438939
15 to 19 142194 0.9650 0.832723
14 to 18 141937 0.0938 0.537365
13 to 17 141677 -0.7876 0.215477
12 to 16 141525 -1.3028 0.096319
11 to 15 141626 -0.9604 0.168417
10 to 14 141975 0.2226 0.588081
9 to 13 142059 0.5074 0.694048
8 to 12 141959 0.1684 0.566855
7 to 11 141930 0.0701 0.527930
6 to 10 142455 1.8497 0.967824
5 to 9 141725 -0.6248 0.266036
4 to 8 142344 1.4735 0.929686
3 to 7 141758 -0.5130 0.303982
2 to 6 141814 -0.3232 0.373290
1 to 5 141369 -1.8316 0.033504
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_04:31
Bits used No. missing words z-score p-value
31 to 32 141674 -0.6942 0.243782
30 to 31 142601 2.0403 0.979341
29 to 30 142065 0.4592 0.676956
28 to 29 141887 -0.0659 0.473741
27 to 28 142101 0.5654 0.714099
26 to 27 142295 1.1377 0.872371
25 to 26 142278 1.0875 0.861597
24 to 25 142217 0.9076 0.817950
23 to 24 141885 -0.0718 0.471393
22 to 23 141435 -1.3992 0.080876
21 to 22 142199 0.8545 0.803582
20 to 21 141714 -0.5762 0.282242
19 to 20 141625 -0.8387 0.200810
18 to 19 141970 0.1790 0.571018
17 to 18 141751 -0.4671 0.320232
16 to 17 141422 -1.4376 0.075281
15 to 16 141902 -0.0216 0.491375
14 to 15 142287 1.1141 0.867376
13 to 14 141897 -0.0364 0.485493
12 to 13 141743 -0.4906 0.311837
11 to 12 141960 0.1495 0.559408
10 to 11 141715 -0.5732 0.283240
9 to 10 142031 0.3589 0.640168
8 to 9 141410 -1.4729 0.070382
7 to 8 141952 0.1259 0.550083
6 to 7 142322 1.2173 0.888258
5 to 6 142251 1.0079 0.843243
4 to 5 142341 1.2734 0.898555
3 to 4 141953 0.1288 0.551250
2 to 3 142203 0.8663 0.806833
1 to 2 141827 -0.2429 0.404056
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2548.65 0.688 0.754281
Test results for specific bytes for dh-ranFile-2018-06-25_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2460.89 -0.553 0.290084
2 to 9 2581.11 1.147 0.874316
3 to 10 2532.98 0.466 0.679534
4 to 11 2608.51 1.535 0.937551
5 to 12 2502.38 0.034 0.513409
6 to 13 2515.97 0.226 0.589337
7 to 14 2541.00 0.580 0.718965
8 to 15 2497.54 -0.035 0.486148
9 to 16 2569.87 0.988 0.838442
10 to 17 2697.60 2.795 0.997401
11 to 18 2489.06 -0.155 0.438531
12 to 19 2472.10 -0.395 0.346567
13 to 20 2693.98 2.743 0.996959
14 to 21 2655.20 2.195 0.985914
15 to 22 2543.46 0.615 0.730574
16 to 23 2460.66 -0.556 0.288971
17 to 24 2499.45 -0.008 0.496919
18 to 25 2325.08 -2.474 0.006684
19 to 26 2508.73 0.123 0.549140
20 to 27 2433.94 -0.934 0.175103
21 to 28 2450.45 -0.701 0.241728
22 to 29 2484.13 -0.224 0.411198
23 to 30 2308.16 -2.713 0.003334
24 to 31 2513.92 0.197 0.578009
25 to 32 2464.03 -0.509 0.305460
CDPARK for dh-ranFile-2018-06-25_04:31: 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
3492 -1.4155 0.078457
3497 -1.1872 0.117571
3499 -1.0959 0.136563
3533 0.4566 0.676028
3531 0.3653 0.642555
3527 0.1826 0.572463
3485 -1.7352 0.041356
3492 -1.4155 0.078457
3502 -0.9589 0.168804
Square side=100, avg. no. parked=3509.70 sample std.=19.30
p-value of the KSTEST for those 10 p-values: 0.044759
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_04:31
0.1294,0.0241,0.2445,0.1718,0.6287,0.8241,0.7424,0.2353,0.2668,0.3472,
The KS test for those 10 p-values: 0.196225
The 3DSPHERES test for dh-ranFile-2018-06-25_04:31
sample no r^3 equiv. uni.
1 14.080 0.374581
2 6.186 0.186318
3 47.320 0.793473
4 9.209 0.264335
5 0.442 0.014625
6 57.559 0.853191
7 3.051 0.096689
8 1.971 0.063603
9 40.999 0.745037
10 29.583 0.626974
11 3.280 0.103579
12 14.798 0.389371
13 34.107 0.679189
14 55.339 0.841918
15 42.961 0.761174
16 44.842 0.775693
17 9.698 0.276223
18 7.946 0.232692
19 4.014 0.125247
20 49.032 0.804928
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.425136
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.9 -0.1 0.6 -0.2 0.7
0.7 -0.9 0.5 2.6 -0.1 0.8
-1.1 -0.4 -1.1 -1.1 0.4 -0.4
1.8 0.4 -1.0 -0.9 0.1 0.5
0.0 2.0 0.7 -1.9 -2.1 0.8
1.9 -1.2 -0.4 0.0 0.1 0.4
-0.9 1.1 -0.8 -1.3 2.4 1.0
-0.1
Chi-square with 42 degrees of freedom:52.151084
z-score=1.107574, p-value=0.864464
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_04:31
Test no p-value
1 0.587961
2 0.017637
3 0.964377
4 0.159243
5 0.704873
6 0.829808
7 0.728888
8 0.841512
9 0.863916
10 0.067600
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.283514
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_04:31:
(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 66782 0.20 66598 0.07
3 25000.00 24962 0.06 25027 0.03
4 6666.67 6712 0.31 6685 0.05
5 1388.89 1297 6.08 1395 0.03
6 238.10 204 4.88 248 0.41
7 34.72 35 0.00 37 0.15
8 4.96 7 0.84 9 3.29
p=0.94577 p=0.32733
Number of rngs required: 688309, p-value: 0.457
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_04:31
No. of wins: Observed Expected
98585 98585.9
z-score=-0.004, pvalue=0.49847
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66873 66666.7 0.639 0.639
2 37557 37654.3 0.252 0.890
3 27029 26954.7 0.205 1.095
4 19438 19313.5 0.803 1.898
5 13845 13851.4 0.003 1.901
6 9985 9943.5 0.173 2.074
7 7175 7145.0 0.126 2.199
8 5029 5139.1 2.358 4.557
9 3632 3699.9 1.245 5.802
10 2607 2666.3 1.319 7.121
11 1933 1923.3 0.049 7.169
12 1332 1388.7 2.318 9.487
13 985 1003.7 0.349 9.836
14 729 726.1 0.011 9.848
15 517 525.8 0.148 9.996
16 341 381.2 4.229 14.226
17 249 276.5 2.743 16.968
18 210 200.8 0.419 17.387
19 146 146.0 0.000 17.387
20 112 106.2 0.315 17.702
21 276 287.1 0.430 18.132
Chisq= 18.13 for 20 degrees of freedom, p= 0.42130
SUMMARY of craptest
p-value for no. of wins: 0.498468
p-value for throws/game: 0.421297
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_04:31
No. of wins: Observed Expected
98644 98585.9
z-score= 0.260, pvalue=0.60258
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66337 66666.7 1.630 1.630
2 38006 37654.3 3.285 4.915
3 26885 26954.7 0.180 5.095
4 19305 19313.5 0.004 5.099
5 13699 13851.4 1.677 6.776
6 10038 9943.5 0.897 7.673
7 7057 7145.0 1.084 8.758
8 5185 5139.1 0.410 9.168
9 3778 3699.9 1.650 10.818
10 2638 2666.3 0.300 11.119
11 1991 1923.3 2.381 13.500
12 1401 1388.7 0.108 13.608
13 1033 1003.7 0.854 14.462
14 744 726.1 0.439 14.902
15 511 525.8 0.419 15.320
16 375 381.2 0.099 15.419
17 282 276.5 0.108 15.527
18 198 200.8 0.040 15.567
19 139 146.0 0.334 15.901
20 113 106.2 0.433 16.335
21 285 287.1 0.016 16.350
Chisq= 16.35 for 20 degrees of freedom, p= 0.30533
SUMMARY of craptest
p-value for no. of wins: 0.602584
p-value for throws/game: 0.305325
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0033,0.0067,0.0146,0.0176,0.0184,0.0241,0.0310,0.0335,0.0337,0.0414,
0.0448,0.0492,0.0532,0.0558,0.0588,0.0636,0.0669,0.0676,0.0704,0.0753,
0.0774,0.0779,0.0785,0.0785,0.0795,0.0809,0.0914,0.0923,0.0963,0.0967,
0.1007,0.1018,0.1022,0.1036,0.1064,0.1110,0.1176,0.1252,0.1294,0.1308,
0.1366,0.1459,0.1461,0.1580,0.1592,0.1684,0.1688,0.1718,0.1751,0.1760,
0.1766,0.1863,0.1917,0.1927,0.1962,0.1962,0.2008,0.2054,0.2057,0.2095,
0.2133,0.2155,0.2237,0.2268,0.2292,0.2327,0.2353,0.2416,0.2417,0.2430,
0.2438,0.2438,0.2445,0.2643,0.2660,0.2664,0.2668,0.2762,0.2822,0.2832,
0.2835,0.2890,0.2901,0.3040,0.3053,0.3055,0.3118,0.3124,0.3162,0.3202,
0.3204,0.3273,0.3317,0.3318,0.3341,0.3419,0.3466,0.3472,0.3548,0.3605,
0.3733,0.3746,0.3778,0.3791,0.3795,0.3882,0.3882,0.3894,0.3962,0.4026,
0.4041,0.4085,0.4112,0.4213,0.4251,0.4321,0.4343,0.4349,0.4367,0.4385,
0.4389,0.4403,0.4569,0.4580,0.4714,0.4737,0.4811,0.4855,0.4861,0.4914,
0.4969,0.4985,0.4991,0.4995,0.5114,0.5134,0.5202,0.5258,0.5279,0.5284,
0.5325,0.5374,0.5388,0.5443,0.5481,0.5491,0.5501,0.5513,0.5517,0.5594,
0.5642,0.5669,0.5710,0.5725,0.5780,0.5880,0.5881,0.5893,0.5936,0.5980,
0.6026,0.6029,0.6243,0.6246,0.6270,0.6287,0.6313,0.6359,0.6402,0.6426,
0.6435,0.6449,0.6454,0.6575,0.6626,0.6760,0.6770,0.6792,0.6795,0.6837,
0.6862,0.6940,0.6974,0.6976,0.7010,0.7011,0.7049,0.7141,0.7190,0.7233,
0.7249,0.7258,0.7289,0.7306,0.7354,0.7424,0.7450,0.7485,0.7543,0.7553,
0.7608,0.7612,0.7614,0.7617,0.7675,0.7694,0.7757,0.7935,0.8036,0.8049,
0.8061,0.8068,0.8180,0.8241,0.8242,0.8296,0.8298,0.8327,0.8338,0.8352,
0.8378,0.8384,0.8415,0.8419,0.8432,0.8445,0.8532,0.8584,0.8604,0.8616,
0.8633,0.8633,0.8639,0.8645,0.8674,0.8704,0.8724,0.8724,0.8743,0.8770,
0.8883,0.8986,0.9035,0.9063,0.9110,0.9177,0.9184,0.9297,0.9317,0.9372,
0.9376,0.9413,0.9458,0.9503,0.9534,0.9548,0.9567,0.9634,0.9644,0.9678,
0.9693,0.9749,0.9793,0.9856,0.9859,0.9911,0.9923,0.9970,0.9974,
Overall p-value after applying KStest on 269 p-values = 0.968154
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.