RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 23.6109 0.869601
2 to 25 15.49 22.7756 0.843302
3 to 26 15.51 25.3673 0.913214
4 to 27 15.82 16.8447 0.535068
5 to 28 15.79 25.0007 0.905307
6 to 29 15.59 23.6889 0.871864
7 to 30 15.85 14.9458 0.400613
8 to 31 16.01 10.5326 0.120195
9 to 32 15.72 25.7932 0.921689
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.019642
Tough bday spacings test for dh-ranFile-2018-06-23_19:31: 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 7 33 64 84 90 97 53 35 20 7 10
(O-E)^2/E 0.5 0.4 1.2 1.9 0.6 4.5 0.0 0.9 1.8 0.0 8.7
Birthday Spacings: Sum(O-E)^2/E= 20.483, p= 0.975
RESULTS OF GCD FOR dh-ranFile-2018-06-23_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.565011
p-value, dist. of gcd's: 0.556495
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.090 0.461 0.274 0.308 0.258 0.964 0.909 0.669
Bits 8 to 15---> 0.609 0.886 0.096 0.146 0.387 0.742 0.523 0.906
Bits 16 to 23---> 0.363 0.434 0.842 0.264 0.149 0.884 0.569 0.707
Bits 24 to 31---> 0.902 0.265 0.498 0.814 0.683 0.977 0.505 0.209
KS test for the above 32 p values: 0.346
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_19:31,
p-values for 5 runs: 0.4948, 0.1391, 0.5047, 0.4851, 0.2928
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 210 211.4 0.010 0.010
r= 29 5160 5134.0 0.132 0.141
r= 30 23121 23103.0 0.014 0.155
r= 31 11509 11551.5 0.157 0.312
chi-square = 0.312 with df = 3; p-value = 0.042
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 196 211.4 1.124 1.124
r= 30 5090 5134.0 0.377 1.502
r= 31 23135 23103.0 0.044 1.546
r= 32 11579 11551.5 0.065 1.611
chi-square = 1.611 with df = 3; p-value = 0.343
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_19:31
b-rank test for bits 1 to 8, p=0.87938
b-rank test for bits 2 to 9, p=0.98096
b-rank test for bits 3 to 10, p=0.79258
b-rank test for bits 4 to 11, p=0.88563
b-rank test for bits 5 to 12, p=0.67663
b-rank test for bits 6 to 13, p=0.97918
b-rank test for bits 7 to 14, p=0.42798
b-rank test for bits 8 to 15, p=0.73326
b-rank test for bits 9 to 16, p=0.21684
b-rank test for bits 10 to 17, p=0.98928
b-rank test for bits 11 to 18, p=0.90369
b-rank test for bits 12 to 19, p=0.12343
b-rank test for bits 13 to 20, p=0.46943
b-rank test for bits 14 to 21, p=0.27631
b-rank test for bits 15 to 22, p=0.41342
b-rank test for bits 16 to 23, p=0.86408
b-rank test for bits 17 to 24, p=0.16860
b-rank test for bits 18 to 25, p=0.19238
b-rank test for bits 19 to 26, p=0.43428
b-rank test for bits 20 to 27, p=0.98720
b-rank test for bits 21 to 28, p=0.89498
b-rank test for bits 22 to 29, p=0.83498
b-rank test for bits 23 to 30, p=0.72560
b-rank test for bits 24 to 31, p=0.90486
b-rank test for bits 25 to 32, p=0.04146
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 = 0.010228
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_19:31
(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 141040 -2.03 0.021120
2 141487 -0.99 0.161882
3 142022 0.26 0.603820
4 142702 1.85 0.967989
5 141717 -0.45 0.326583
6 141558 -0.82 0.205862
7 141813 -0.23 0.410962
8 142190 0.66 0.744014
9 142168 0.60 0.727201
10 142579 1.56 0.941167
11 141891 -0.04 0.482920
12 141830 -0.19 0.426477
13 142194 0.67 0.747012
14 141703 -0.48 0.314875
15 142602 1.62 0.947210
16 142190 0.66 0.744014
17 142472 1.31 0.905686
18 141779 -0.30 0.380370
19 142507 1.40 0.918707
20 141743 -0.39 0.348778
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_19:31
Bits used No. missing words z-score p-value
23 to 32 141838 -0.2460 0.402855
22 to 31 141613 -1.0218 0.153431
21 to 30 141863 -0.1598 0.436536
20 to 29 141709 -0.6908 0.244848
19 to 28 142073 0.5644 0.713752
18 to 27 142188 0.9609 0.831707
17 to 26 142156 0.8506 0.802500
16 to 25 141646 -0.9080 0.181930
15 to 24 141468 -1.5218 0.064026
14 to 23 141945 0.1230 0.548947
13 to 22 141579 -1.1391 0.127337
12 to 21 141824 -0.2942 0.384287
11 to 20 141609 -1.0356 0.150190
10 to 19 142055 0.5023 0.692275
9 to 18 141790 -0.4115 0.340359
8 to 17 141899 -0.0356 0.485792
7 to 16 141338 -1.9701 0.024413
6 to 15 141914 0.0161 0.506424
5 to 14 141637 -0.9391 0.173848
4 to 13 141910 0.0023 0.500922
3 to 12 142072 0.5609 0.712578
2 to 11 141655 -0.8770 0.190243
1 to 10 141902 -0.0253 0.489918
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_19:31
Bits used No. missing words z-score p-value
28 to 32 141589 -1.0859 0.138770
27 to 31 142163 0.8599 0.805077
26 to 30 142145 0.7989 0.787820
25 to 29 142112 0.6870 0.753964
24 to 28 141827 -0.2791 0.390090
23 to 27 141339 -1.9333 0.026598
22 to 26 142040 0.4429 0.671099
21 to 25 141849 -0.2045 0.418978
20 to 24 141720 -0.6418 0.260503
19 to 23 142081 0.5819 0.719694
18 to 22 141767 -0.4825 0.314734
17 to 21 141653 -0.8689 0.192447
16 to 20 142153 0.8260 0.795598
15 to 19 141779 -0.4418 0.329318
14 to 18 141787 -0.4147 0.339189
13 to 17 141805 -0.3537 0.361797
12 to 16 142133 0.7582 0.775835
11 to 15 141811 -0.3333 0.369446
10 to 14 141875 -0.1164 0.453679
9 to 13 141534 -1.2723 0.101632
8 to 12 142002 0.3141 0.623291
7 to 11 142180 0.9175 0.820566
6 to 10 141719 -0.6452 0.259403
5 to 9 142203 0.9955 0.840251
4 to 8 141796 -0.3842 0.350426
3 to 7 141787 -0.4147 0.339189
2 to 6 142087 0.6023 0.726503
1 to 5 141992 0.2802 0.610352
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_19:31
Bits used No. missing words z-score p-value
31 to 32 141794 -0.3402 0.366851
30 to 31 141752 -0.4641 0.321288
29 to 30 141602 -0.9066 0.182315
28 to 29 142179 0.7955 0.786835
27 to 28 142048 0.4091 0.658751
26 to 27 141824 -0.2517 0.400632
25 to 26 142159 0.7365 0.769284
24 to 25 142890 2.8928 0.998091
23 to 24 142321 1.2144 0.887696
22 to 23 141435 -1.3992 0.080876
21 to 22 141827 -0.2429 0.404056
20 to 21 141950 0.1200 0.547747
19 to 20 142120 0.6214 0.732847
18 to 19 142498 1.7365 0.958761
17 to 18 141985 0.2232 0.588316
16 to 17 142301 1.1554 0.876030
15 to 16 142515 1.7866 0.963002
14 to 15 141629 -0.8269 0.204138
13 to 14 141864 -0.1337 0.446813
12 to 13 141971 0.1819 0.572176
11 to 12 142368 1.3530 0.911974
10 to 11 142090 0.5329 0.702966
9 to 10 141585 -0.9567 0.169353
8 to 9 142181 0.8014 0.788546
7 to 8 142040 0.3855 0.650051
6 to 7 142136 0.6686 0.748138
5 to 6 141590 -0.9420 0.173102
4 to 5 141575 -0.9862 0.162012
3 to 4 142133 0.6598 0.745307
2 to 3 141906 -0.0098 0.496081
1 to 2 141378 -1.5673 0.058517
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2503.08 0.043 0.517346
Test results for specific bytes for dh-ranFile-2018-06-23_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2596.23 1.361 0.913231
2 to 9 2532.41 0.458 0.676658
3 to 10 2457.27 -0.604 0.272828
4 to 11 2459.49 -0.573 0.283353
5 to 12 2382.84 -1.657 0.048764
6 to 13 2360.20 -1.977 0.024018
7 to 14 2577.14 1.091 0.862332
8 to 15 2532.32 0.457 0.676209
9 to 16 2560.62 0.857 0.804375
10 to 17 2480.09 -0.282 0.389142
11 to 18 2513.55 0.192 0.576010
12 to 19 2497.16 -0.040 0.483991
13 to 20 2540.05 0.566 0.714456
14 to 21 2536.75 0.520 0.698357
15 to 22 2449.58 -0.713 0.237887
16 to 23 2487.22 -0.181 0.428293
17 to 24 2437.65 -0.882 0.188942
18 to 25 2504.45 0.063 0.525107
19 to 26 2490.85 -0.129 0.448524
20 to 27 2494.71 -0.075 0.470210
21 to 28 2580.89 1.144 0.873686
22 to 29 2453.32 -0.660 0.254581
23 to 30 2317.15 -2.586 0.004856
24 to 31 2468.11 -0.451 0.325997
25 to 32 2441.90 -0.822 0.205617
CDPARK for dh-ranFile-2018-06-23_19:31: 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
3512 -0.5023 0.307734
3554 1.4155 0.921543
3506 -0.7763 0.218799
3484 -1.7808 0.037471
3502 -0.9589 0.168804
3476 -2.1461 0.015932
3544 0.9589 0.831196
3512 -0.5023 0.307734
3478 -2.0548 0.019949
3523 0.0000 0.500000
Square side=100, avg. no. parked=3509.10 sample std.=24.89
p-value of the KSTEST for those 10 p-values: 0.047308
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_19:31
0.8556,0.2430,0.6609,0.6064,0.8834,0.4319,0.8266,0.7855,0.8891,0.4808,
The KS test for those 10 p-values: 0.093601
The 3DSPHERES test for dh-ranFile-2018-06-23_19:31
sample no r^3 equiv. uni.
1 21.617 0.513521
2 19.010 0.469352
3 4.334 0.134530
4 32.110 0.657104
5 123.514 0.983709
6 22.243 0.523569
7 10.489 0.295056
8 54.745 0.838753
9 2.037 0.065635
10 10.061 0.284922
11 0.920 0.030204
12 32.682 0.663578
13 19.552 0.478855
14 27.250 0.596802
15 10.598 0.297618
16 56.263 0.846710
17 44.204 0.770873
18 60.079 0.865023
19 62.234 0.874375
20 0.040 0.001333
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.837822
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.8 1.1 0.8 -0.4 -0.6
-0.7 0.2 0.9 -0.8 -0.1 -0.6
-0.4 1.5 -0.9 0.8 -0.8 -0.2
-0.3 -0.7 -0.1 1.6 0.6 2.0
-1.6 0.9 0.3 -0.5 -0.7 -0.7
-0.4 0.1 -1.1 -1.2 -0.2 1.1
-0.5 -0.7 -0.4 0.4 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:31.562744
z-score=-1.138798, p-value=0.119942
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_19:31
Test no p-value
1 0.539708
2 0.291829
3 0.056140
4 0.772028
5 0.104957
6 0.627508
7 0.711675
8 0.009631
9 0.243338
10 0.192737
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.166733
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_19:31:
(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 66805 0.29 66732 0.06
3 25000.00 24899 0.41 24923 0.24
4 6666.67 6645 0.07 6691 0.09
5 1388.89 1364 0.45 1402 0.12
6 238.10 242 0.06 218 1.70
7 34.72 33 0.09 32 0.21
8 4.96 11 7.36 1 3.16
p=0.80981 p=0.52869
Number of rngs required: 687985, p-value: 0.315
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_19:31
No. of wins: Observed Expected
98909 98585.9
z-score= 1.445, pvalue=0.92581
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66758 66666.7 0.125 0.125
2 37757 37654.3 0.280 0.405
3 26940 26954.7 0.008 0.413
4 19249 19313.5 0.215 0.628
5 13840 13851.4 0.009 0.638
6 9862 9943.5 0.669 1.306
7 7224 7145.0 0.873 2.179
8 5074 5139.1 0.824 3.003
9 3635 3699.9 1.137 4.141
10 2682 2666.3 0.092 4.233
11 1954 1923.3 0.489 4.722
12 1376 1388.7 0.117 4.839
13 1034 1003.7 0.914 5.753
14 679 726.1 3.060 8.813
15 551 525.8 1.204 10.017
16 376 381.2 0.070 10.087
17 259 276.5 1.112 11.199
18 193 200.8 0.305 11.505
19 139 146.0 0.334 11.839
20 100 106.2 0.364 12.202
21 318 287.1 3.323 15.525
Chisq= 15.53 for 20 degrees of freedom, p= 0.25438
SUMMARY of craptest
p-value for no. of wins: 0.925810
p-value for throws/game: 0.254380
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_19:31
No. of wins: Observed Expected
98465 98585.9
z-score=-0.541, pvalue=0.29441
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66246 66666.7 2.654 2.654
2 37657 37654.3 0.000 2.655
3 27057 26954.7 0.388 3.043
4 19300 19313.5 0.009 3.052
5 13880 13851.4 0.059 3.111
6 10010 9943.5 0.444 3.555
7 7232 7145.0 1.059 4.614
8 5174 5139.1 0.237 4.851
9 3804 3699.9 2.931 7.782
10 2712 2666.3 0.783 8.566
11 1938 1923.3 0.112 8.677
12 1365 1388.7 0.406 9.083
13 1071 1003.7 4.511 13.594
14 707 726.1 0.505 14.098
15 523 525.8 0.015 14.114
16 381 381.2 0.000 14.114
17 249 276.5 2.743 16.856
18 188 200.8 0.820 17.676
19 144 146.0 0.027 17.703
20 79 106.2 6.973 24.676
21 283 287.1 0.059 24.735
Chisq= 24.74 for 20 degrees of freedom, p= 0.78824
SUMMARY of craptest
p-value for no. of wins: 0.294409
p-value for throws/game: 0.788245
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0013,0.0049,0.0096,0.0102,0.0159,0.0196,0.0199,0.0211,0.0240,0.0244,
0.0266,0.0302,0.0375,0.0415,0.0422,0.0473,0.0488,0.0561,0.0585,0.0640,
0.0656,0.0809,0.0899,0.0936,0.0962,0.1016,0.1050,0.1199,0.1202,0.1234,
0.1273,0.1345,0.1388,0.1391,0.1461,0.1492,0.1502,0.1534,0.1619,0.1620,
0.1667,0.1686,0.1688,0.1694,0.1731,0.1738,0.1819,0.1823,0.1889,0.1902,
0.1924,0.1924,0.1927,0.2041,0.2056,0.2059,0.2088,0.2168,0.2188,0.2379,
0.2430,0.2433,0.2448,0.2544,0.2546,0.2577,0.2594,0.2605,0.2641,0.2645,
0.2728,0.2743,0.2763,0.2834,0.2849,0.2918,0.2928,0.2944,0.2951,0.2976,
0.3077,0.3077,0.3080,0.3147,0.3149,0.3150,0.3213,0.3260,0.3266,0.3293,
0.3392,0.3392,0.3404,0.3431,0.3462,0.3488,0.3504,0.3618,0.3626,0.3669,
0.3694,0.3804,0.3843,0.3871,0.3891,0.3901,0.4006,0.4006,0.4029,0.4041,
0.4110,0.4134,0.4190,0.4265,0.4280,0.4283,0.4319,0.4338,0.4343,0.4365,
0.4468,0.4485,0.4537,0.4607,0.4694,0.4694,0.4702,0.4789,0.4808,0.4829,
0.4840,0.4851,0.4858,0.4899,0.4948,0.4961,0.4982,0.5000,0.5009,0.5047,
0.5054,0.5064,0.5135,0.5173,0.5230,0.5236,0.5251,0.5287,0.5351,0.5397,
0.5477,0.5489,0.5565,0.5650,0.5687,0.5722,0.5760,0.5883,0.5968,0.6038,
0.6064,0.6095,0.6104,0.6233,0.6275,0.6501,0.6571,0.6588,0.6609,0.6636,
0.6693,0.6711,0.6762,0.6766,0.6767,0.6829,0.6923,0.6984,0.7030,0.7066,
0.7117,0.7126,0.7138,0.7145,0.7197,0.7256,0.7265,0.7272,0.7328,0.7333,
0.7416,0.7440,0.7440,0.7453,0.7470,0.7481,0.7540,0.7693,0.7709,0.7720,
0.7758,0.7855,0.7868,0.7878,0.7882,0.7885,0.7926,0.7956,0.8025,0.8044,
0.8051,0.8098,0.8138,0.8206,0.8266,0.8312,0.8317,0.8350,0.8378,0.8388,
0.8403,0.8415,0.8433,0.8467,0.8556,0.8623,0.8641,0.8650,0.8696,0.8719,
0.8737,0.8744,0.8760,0.8794,0.8834,0.8841,0.8856,0.8858,0.8877,0.8891,
0.8950,0.9024,0.9037,0.9049,0.9053,0.9057,0.9062,0.9088,0.9120,0.9132,
0.9132,0.9187,0.9215,0.9217,0.9258,0.9412,0.9472,0.9588,0.9630,0.9641,
0.9680,0.9750,0.9772,0.9792,0.9810,0.9837,0.9872,0.9893,0.9981,
Overall p-value after applying KStest on 269 p-values = 0.765662
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.