RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_02:31
(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 23.2870 0.859862
2 to 25 15.51 25.5172 0.916282
3 to 26 15.67 13.3835 0.289844
4 to 27 16.07 13.8868 0.324905
5 to 28 15.66 20.6403 0.757206
6 to 29 15.77 24.3317 0.889300
7 to 30 15.82 15.3717 0.431269
8 to 31 15.71 15.7560 0.458808
9 to 32 15.69 28.3423 0.958906
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.142765
Tough bday spacings test for dh-ranFile-2018-06-25_02:31: 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 10 37 66 94 104 81 55 29 12 9 3
(O-E)^2/E 0.1 0.0 0.7 0.1 0.4 0.1 0.2 0.0 0.6 0.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 3.332, p= 0.028
RESULTS OF GCD FOR dh-ranFile-2018-06-25_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.415846
p-value, dist. of gcd's: 0.973051
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.609 0.760 0.750 0.797 0.646 0.773 0.231 0.360
Bits 8 to 15---> 0.719 0.896 0.175 0.832 0.695 0.862 0.904 0.389
Bits 16 to 23---> 0.651 0.203 0.468 0.453 0.566 0.942 0.448 0.552
Bits 24 to 31---> 0.100 0.412 0.257 0.919 0.836 0.714 0.899 0.581
KS test for the above 32 p values: 0.954
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_02:31,
p-values for 5 runs: 0.7258, 0.5353, 0.8661, 0.5960, 0.5053
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5100 5134.0 0.225 0.257
r= 30 23204 23103.0 0.441 0.698
r= 31 11482 11551.5 0.418 1.116
chi-square = 1.116 with df = 3; p-value = 0.227
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5125 5134.0 0.016 0.077
r= 31 23094 23103.0 0.004 0.080
r= 32 11566 11551.5 0.018 0.098
chi-square = 0.098 with df = 3; p-value = 0.008
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_02:31
b-rank test for bits 1 to 8, p=0.22781
b-rank test for bits 2 to 9, p=0.79695
b-rank test for bits 3 to 10, p=0.37460
b-rank test for bits 4 to 11, p=0.63083
b-rank test for bits 5 to 12, p=0.59026
b-rank test for bits 6 to 13, p=0.42626
b-rank test for bits 7 to 14, p=0.63029
b-rank test for bits 8 to 15, p=0.37807
b-rank test for bits 9 to 16, p=0.65694
b-rank test for bits 10 to 17, p=0.51231
b-rank test for bits 11 to 18, p=0.02800
b-rank test for bits 12 to 19, p=0.75344
b-rank test for bits 13 to 20, p=0.72430
b-rank test for bits 14 to 21, p=0.52941
b-rank test for bits 15 to 22, p=0.63992
b-rank test for bits 16 to 23, p=0.85801
b-rank test for bits 17 to 24, p=0.04784
b-rank test for bits 18 to 25, p=0.67856
b-rank test for bits 19 to 26, p=0.61045
b-rank test for bits 20 to 27, p=0.62589
b-rank test for bits 21 to 28, p=0.13939
b-rank test for bits 22 to 29, p=0.47340
b-rank test for bits 23 to 30, p=0.91041
b-rank test for bits 24 to 31, p=0.24961
b-rank test for bits 25 to 32, p=0.67290
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 = 0.284362
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_02:31
(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 142404 1.16 0.876113
2 142001 0.21 0.584798
3 141876 -0.08 0.468964
4 142369 1.07 0.858588
5 142038 0.30 0.618152
6 142282 0.87 0.808048
7 141989 0.19 0.573834
8 142534 1.46 0.927788
9 142138 0.53 0.703425
10 141709 -0.47 0.319871
11 141923 0.03 0.512740
12 141367 -1.27 0.102555
13 142046 0.32 0.625259
14 142015 0.25 0.597504
15 142004 0.22 0.587528
16 141361 -1.28 0.100071
17 141865 -0.10 0.458753
18 141367 -1.27 0.102555
19 142559 1.52 0.935483
20 142034 0.29 0.614583
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_02:31
Bits used No. missing words z-score p-value
23 to 32 141937 0.0954 0.538007
22 to 31 142231 1.1092 0.866330
21 to 30 141734 -0.6046 0.272727
20 to 29 141980 0.2437 0.596264
19 to 28 141549 -1.2425 0.107023
18 to 27 142095 0.6402 0.738992
17 to 26 142002 0.3196 0.625346
16 to 25 142145 0.8127 0.791792
15 to 24 142327 1.4402 0.925100
14 to 23 142148 0.8230 0.794746
13 to 22 141819 -0.3115 0.377717
12 to 21 141850 -0.2046 0.418948
11 to 20 141657 -0.8701 0.192122
10 to 19 141546 -1.2529 0.105128
9 to 18 141545 -1.2563 0.104502
8 to 17 142106 0.6782 0.751169
7 to 16 142143 0.8058 0.789809
6 to 15 141899 -0.0356 0.485792
5 to 14 141611 -1.0287 0.151805
4 to 13 141701 -0.7184 0.236262
3 to 12 141562 -1.1977 0.115519
2 to 11 142103 0.6678 0.747878
1 to 10 142462 1.9058 0.971659
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_02:31
Bits used No. missing words z-score p-value
28 to 32 141761 -0.5028 0.307548
27 to 31 142154 0.8294 0.796558
26 to 30 142019 0.3718 0.644965
25 to 29 141708 -0.6825 0.247470
24 to 28 142090 0.6124 0.729877
23 to 27 142465 1.8836 0.970192
22 to 26 141888 -0.0723 0.471180
21 to 25 141753 -0.5299 0.298080
20 to 24 141944 0.1175 0.546778
19 to 23 141945 0.1209 0.548121
18 to 22 141766 -0.4859 0.313532
17 to 21 142088 0.6057 0.727630
16 to 20 142155 0.8328 0.797516
15 to 19 141784 -0.4248 0.335474
14 to 18 141805 -0.3537 0.361797
13 to 17 141759 -0.5096 0.305168
12 to 16 141886 -0.0791 0.468483
11 to 15 141771 -0.4689 0.319565
10 to 14 141723 -0.6316 0.263815
9 to 13 141473 -1.4791 0.069559
8 to 12 142102 0.6531 0.743160
7 to 11 141196 -2.4181 0.007802
6 to 10 142016 0.3616 0.641172
5 to 9 141710 -0.6757 0.249617
4 to 8 142232 1.0938 0.862978
3 to 7 141370 -1.8282 0.033757
2 to 6 141753 -0.5299 0.298080
1 to 5 141707 -0.6859 0.246399
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_02:31
Bits used No. missing words z-score p-value
31 to 32 142278 1.0875 0.861597
30 to 31 141607 -0.8918 0.186242
29 to 30 142291 1.1259 0.869890
28 to 29 142228 0.9400 0.826399
27 to 28 141842 -0.1986 0.421283
26 to 27 141405 -1.4877 0.068415
25 to 26 141578 -0.9774 0.164192
24 to 25 142128 0.6450 0.740551
23 to 24 141635 -0.8092 0.209191
22 to 23 141277 -1.8653 0.031071
21 to 22 142271 1.0669 0.856985
20 to 21 141879 -0.0895 0.464355
19 to 20 141661 -0.7325 0.231921
18 to 19 141567 -1.0098 0.156290
17 to 18 142352 1.3058 0.904192
16 to 17 141910 0.0020 0.500789
15 to 16 141427 -1.4228 0.077397
14 to 15 141540 -1.0895 0.137974
13 to 14 141980 0.2085 0.582568
12 to 13 142218 0.9105 0.818729
11 to 12 141755 -0.4553 0.324464
10 to 11 142235 0.9607 0.831643
9 to 10 141728 -0.5349 0.296361
8 to 9 141380 -1.5614 0.059209
7 to 8 142787 2.5890 0.995187
6 to 7 141732 -0.5231 0.300453
5 to 6 142037 0.3766 0.646767
4 to 5 141760 -0.4405 0.329787
3 to 4 142286 1.1111 0.866742
2 to 3 141500 -1.2075 0.113627
1 to 2 141917 0.0226 0.509025
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2529.65 0.419 0.662529
Test results for specific bytes for dh-ranFile-2018-06-25_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2639.06 1.967 0.975384
2 to 9 2602.17 1.445 0.925765
3 to 10 2571.08 1.005 0.842601
4 to 11 2428.22 -1.015 0.155020
5 to 12 2519.59 0.277 0.609117
6 to 13 2491.87 -0.115 0.454257
7 to 14 2569.22 0.979 0.836198
8 to 15 2591.75 1.297 0.902767
9 to 16 2368.08 -1.866 0.031047
10 to 17 2617.64 1.664 0.951918
11 to 18 2590.41 1.279 0.899485
12 to 19 2537.79 0.534 0.703497
13 to 20 2627.45 1.802 0.964261
14 to 21 2462.09 -0.536 0.295925
15 to 22 2443.58 -0.798 0.212444
16 to 23 2465.22 -0.492 0.311415
17 to 24 2501.19 0.017 0.506696
18 to 25 2534.63 0.490 0.687854
19 to 26 2499.69 -0.004 0.498253
20 to 27 2694.01 2.744 0.996962
21 to 28 2542.70 0.604 0.727024
22 to 29 2576.15 1.077 0.859239
23 to 30 2517.94 0.254 0.600115
24 to 31 2600.12 1.416 0.921596
25 to 32 2565.20 0.922 0.821735
CDPARK for dh-ranFile-2018-06-25_02:31: 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
3495 -1.2785 0.100530
3510 -0.5936 0.276387
3515 -0.3653 0.357445
3553 1.3699 0.914635
3523 0.0000 0.500000
3468 -2.5114 0.006012
3539 0.7306 0.767486
3520 -0.1370 0.445521
3578 2.5114 0.993988
3492 -1.4155 0.078457
Square side=100, avg. no. parked=3519.30 sample std.=30.09
p-value of the KSTEST for those 10 p-values: 0.472671
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_02:31
0.8263,0.4191,0.4910,0.2850,0.3624,0.0555,0.2811,0.2940,0.3299,0.7753,
The KS test for those 10 p-values: 0.321058
The 3DSPHERES test for dh-ranFile-2018-06-25_02:31
sample no r^3 equiv. uni.
1 23.647 0.545356
2 22.434 0.526591
3 14.116 0.375339
4 5.121 0.156927
5 13.772 0.368136
6 23.819 0.547952
7 1.707 0.055306
8 51.126 0.818082
9 122.160 0.982957
10 35.192 0.690583
11 39.940 0.735874
12 74.109 0.915441
13 4.284 0.133060
14 7.264 0.215039
15 69.909 0.902735
16 20.868 0.501223
17 60.672 0.867664
18 4.922 0.151306
19 26.841 0.591266
20 28.016 0.606972
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.914468
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.2 0.8 -0.1 -1.1 0.9
1.2 -0.6 -1.7 1.0 0.3 -0.2
-0.6 1.3 -1.4 0.4 -0.4 -0.2
-1.3 -1.0 -0.3 0.3 0.2 1.6
2.0 -0.5 1.1 0.8 0.0 -0.7
0.8 1.0 1.1 -1.5 0.8 -0.7
0.5 -1.0 -0.4 1.0 -1.3 0.0
-0.1
Chi-square with 42 degrees of freedom:38.702259
z-score=-0.359813, p-value=0.383470
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_02:31
Test no p-value
1 0.836218
2 0.180927
3 0.998926
4 0.052826
5 0.531363
6 0.153189
7 0.269297
8 0.086587
9 0.828473
10 0.094669
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.139543
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_02:31:
(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 66430 0.84 66514 0.35
3 25000.00 25146 0.85 25299 3.58
4 6666.67 6692 0.10 6492 4.58
5 1388.89 1442 2.03 1425 0.94
6 238.10 251 0.70 233 0.11
7 34.72 33 0.09 33 0.09
8 4.96 5 0.00 3 0.77
p=0.40461 p=0.89157
Number of rngs required: 688269, p-value: 0.439
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_02:31
No. of wins: Observed Expected
98725 98585.9
z-score= 0.622, pvalue=0.73313
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67053 66666.7 2.239 2.239
2 37391 37654.3 1.841 4.080
3 26930 26954.7 0.023 4.103
4 19278 19313.5 0.065 4.168
5 13933 13851.4 0.480 4.649
6 9968 9943.5 0.060 4.709
7 7089 7145.0 0.439 5.148
8 5137 5139.1 0.001 5.149
9 3702 3699.9 0.001 5.150
10 2644 2666.3 0.186 5.337
11 1877 1923.3 1.116 6.452
12 1392 1388.7 0.008 6.460
13 1012 1003.7 0.068 6.529
14 705 726.1 0.615 7.144
15 525 525.8 0.001 7.145
16 335 381.2 5.588 12.733
17 269 276.5 0.206 12.939
18 202 200.8 0.007 12.946
19 153 146.0 0.337 13.283
20 111 106.2 0.216 13.498
21 294 287.1 0.165 13.664
Chisq= 13.66 for 20 degrees of freedom, p= 0.15286
SUMMARY of craptest
p-value for no. of wins: 0.733135
p-value for throws/game: 0.152864
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_02:31
No. of wins: Observed Expected
98464 98585.9
z-score=-0.545, pvalue=0.29287
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66671 66666.7 0.000 0.000
2 37429 37654.3 1.348 1.349
3 27077 26954.7 0.555 1.903
4 19461 19313.5 1.127 3.030
5 13776 13851.4 0.411 3.441
6 10062 9943.5 1.411 4.852
7 7143 7145.0 0.001 4.853
8 5135 5139.1 0.003 4.856
9 3717 3699.9 0.079 4.935
10 2675 2666.3 0.028 4.964
11 1961 1923.3 0.738 5.701
12 1365 1388.7 0.406 6.107
13 971 1003.7 1.066 7.174
14 746 726.1 0.543 7.717
15 499 525.8 1.370 9.086
16 355 381.2 1.794 10.881
17 239 276.5 5.096 15.976
18 199 200.8 0.017 15.993
19 151 146.0 0.172 16.165
20 94 106.2 1.405 17.570
21 274 287.1 0.599 18.169
Chisq= 18.17 for 20 degrees of freedom, p= 0.42374
SUMMARY of craptest
p-value for no. of wins: 0.292869
p-value for throws/game: 0.423736
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0060,0.0078,0.0079,0.0275,0.0280,0.0310,0.0311,0.0338,0.0478,0.0528,
0.0553,0.0555,0.0592,0.0684,0.0696,0.0774,0.0785,0.0866,0.0947,0.1001,
0.1005,0.1005,0.1026,0.1026,0.1045,0.1051,0.1070,0.1136,0.1155,0.1331,
0.1380,0.1394,0.1395,0.1428,0.1513,0.1518,0.1529,0.1532,0.1550,0.1563,
0.1569,0.1642,0.1746,0.1809,0.1862,0.1921,0.2029,0.2092,0.2124,0.2150,
0.2269,0.2278,0.2312,0.2319,0.2363,0.2464,0.2475,0.2496,0.2496,0.2574,
0.2638,0.2693,0.2727,0.2764,0.2811,0.2844,0.2850,0.2898,0.2929,0.2940,
0.2959,0.2964,0.2981,0.2981,0.3005,0.3052,0.3075,0.3114,0.3135,0.3196,
0.3199,0.3211,0.3245,0.3249,0.3298,0.3299,0.3355,0.3574,0.3595,0.3618,
0.3624,0.3681,0.3746,0.3753,0.3777,0.3781,0.3835,0.3891,0.4046,0.4120,
0.4158,0.4189,0.4191,0.4213,0.4237,0.4263,0.4313,0.4387,0.4455,0.4480,
0.4527,0.4543,0.4588,0.4588,0.4644,0.4683,0.4685,0.4690,0.4712,0.4727,
0.4734,0.4858,0.4910,0.4983,0.5000,0.5008,0.5012,0.5053,0.5067,0.5090,
0.5123,0.5127,0.5266,0.5294,0.5314,0.5353,0.5380,0.5454,0.5468,0.5480,
0.5481,0.5520,0.5655,0.5738,0.5811,0.5826,0.5848,0.5875,0.5903,0.5913,
0.5960,0.5963,0.5975,0.6001,0.6070,0.6091,0.6093,0.6105,0.6146,0.6182,
0.6253,0.6253,0.6259,0.6303,0.6308,0.6399,0.6412,0.6450,0.6464,0.6468,
0.6509,0.6569,0.6625,0.6729,0.6786,0.6879,0.6906,0.6952,0.7034,0.7035,
0.7144,0.7195,0.7243,0.7258,0.7270,0.7276,0.7299,0.7331,0.7359,0.7390,
0.7406,0.7432,0.7479,0.7496,0.7512,0.7534,0.7572,0.7597,0.7675,0.7731,
0.7753,0.7898,0.7918,0.7947,0.7966,0.7969,0.7972,0.7975,0.8080,0.8181,
0.8187,0.8217,0.8263,0.8264,0.8285,0.8316,0.8317,0.8360,0.8362,0.8362,
0.8426,0.8570,0.8580,0.8586,0.8592,0.8599,0.8616,0.8617,0.8630,0.8661,
0.8663,0.8667,0.8677,0.8699,0.8761,0.8893,0.8916,0.8957,0.8991,0.8995,
0.9027,0.9028,0.9036,0.9042,0.9104,0.9145,0.9146,0.9154,0.9163,0.9193,
0.9216,0.9251,0.9258,0.9278,0.9355,0.9424,0.9519,0.9541,0.9589,0.9643,
0.9702,0.9717,0.9731,0.9754,0.9830,0.9940,0.9952,0.9970,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.292869
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.