RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_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 15.61 30.7809 0.978767
2 to 25 15.80 16.1134 0.484192
3 to 26 15.73 15.1835 0.417736
4 to 27 15.57 17.6769 0.590505
5 to 28 15.76 15.4329 0.435667
6 to 29 15.96 15.2192 0.420301
7 to 30 15.86 23.0389 0.852011
8 to 31 15.74 9.7468 0.086108
9 to 32 15.91 14.4429 0.364458
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.672087
Tough bday spacings test for dh-ranFile-2018-06-30_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 8 37 83 108 87 72 49 33 15 6 2
(O-E)^2/E 0.1 0.0 1.3 1.1 1.2 0.5 0.2 0.4 0.0 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 5.828, p= 0.171
RESULTS OF GCD FOR dh-ranFile-2018-06-30_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.239205
p-value, dist. of gcd's: 0.253920
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.872 0.865 0.783 0.736 0.444 0.812 0.977 0.694
Bits 8 to 15---> 0.191 0.894 0.038 0.812 0.496 0.784 0.463 0.985
Bits 16 to 23---> 0.290 0.192 0.897 0.534 0.312 0.325 0.044 0.333
Bits 24 to 31---> 0.363 0.891 0.561 0.367 0.603 0.964 0.329 0.486
KS test for the above 32 p values: 0.777
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_19:31,
p-values for 5 runs: 0.1079, 0.8574, 0.0861, 0.6350, 0.9363
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 237 211.4 3.095 3.095
r= 29 5047 5134.0 1.475 4.570
r= 30 23030 23103.0 0.231 4.801
r= 31 11686 11551.5 1.565 6.367
chi-square = 6.367 with df = 3; p-value = 0.905
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 223 211.4 0.634 0.634
r= 30 5074 5134.0 0.701 1.336
r= 31 23128 23103.0 0.027 1.363
r= 32 11575 11551.5 0.048 1.411
chi-square = 1.411 with df = 3; p-value = 0.297
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_19:31
b-rank test for bits 1 to 8, p=0.57783
b-rank test for bits 2 to 9, p=0.17519
b-rank test for bits 3 to 10, p=0.86168
b-rank test for bits 4 to 11, p=0.83015
b-rank test for bits 5 to 12, p=0.08294
b-rank test for bits 6 to 13, p=0.41713
b-rank test for bits 7 to 14, p=0.86710
b-rank test for bits 8 to 15, p=0.12880
b-rank test for bits 9 to 16, p=0.13559
b-rank test for bits 10 to 17, p=0.69591
b-rank test for bits 11 to 18, p=0.85026
b-rank test for bits 12 to 19, p=0.39737
b-rank test for bits 13 to 20, p=0.50697
b-rank test for bits 14 to 21, p=0.84792
b-rank test for bits 15 to 22, p=0.09846
b-rank test for bits 16 to 23, p=0.85891
b-rank test for bits 17 to 24, p=0.42694
b-rank test for bits 18 to 25, p=0.52910
b-rank test for bits 19 to 26, p=0.41180
b-rank test for bits 20 to 27, p=0.07204
b-rank test for bits 21 to 28, p=0.76078
b-rank test for bits 22 to 29, p=0.58593
b-rank test for bits 23 to 30, p=0.43021
b-rank test for bits 24 to 31, p=0.93008
b-rank test for bits 25 to 32, p=0.01730
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 = 0.752335
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_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 141818 -0.21 0.415512
2 142366 1.07 0.857011
3 142134 0.52 0.700184
4 141798 -0.26 0.397387
5 142350 1.03 0.848402
6 141777 -0.31 0.378591
7 141774 -0.32 0.375929
8 140975 -2.18 0.014517
9 142192 0.66 0.745516
10 141019 -2.08 0.018753
11 141637 -0.64 0.262295
12 142099 0.44 0.671173
13 142132 0.52 0.698558
14 142511 1.41 0.920104
15 142931 2.39 0.991509
16 142381 1.10 0.864776
17 141173 -1.72 0.042680
18 141598 -0.73 0.233489
19 142041 0.31 0.620822
20 142351 1.03 0.848950
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-30_19:31
Bits used No. missing words z-score p-value
23 to 32 141933 0.0816 0.532526
22 to 31 141946 0.1264 0.550312
21 to 30 141955 0.1575 0.562568
20 to 29 142275 1.2609 0.896333
19 to 28 141336 -1.9770 0.024021
18 to 27 141729 -0.6218 0.267028
17 to 26 141845 -0.2218 0.412224
16 to 25 141704 -0.7080 0.239462
15 to 24 141441 -1.6149 0.053163
14 to 23 141776 -0.4598 0.322845
13 to 22 141708 -0.6942 0.243765
12 to 21 141740 -0.5839 0.279645
11 to 20 142062 0.5264 0.700712
10 to 19 142099 0.6540 0.743455
9 to 18 142625 2.4678 0.993203
8 to 17 142300 1.3471 0.911032
7 to 16 141786 -0.4253 0.335318
6 to 15 141566 -1.1839 0.118227
5 to 14 141579 -1.1391 0.127337
4 to 13 141177 -2.5253 0.005780
3 to 12 142145 0.8127 0.791792
2 to 11 141768 -0.4873 0.313007
1 to 10 141454 -1.5701 0.058196
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-30_19:31
Bits used No. missing words z-score p-value
28 to 32 141465 -1.5062 0.066008
27 to 31 141688 -0.7503 0.226546
26 to 30 141996 0.2938 0.615543
25 to 29 141107 -2.7198 0.003266
24 to 28 142253 1.1650 0.877987
23 to 27 141852 -0.1943 0.422955
22 to 26 141645 -0.8960 0.185117
21 to 25 141963 0.1819 0.572182
20 to 24 141841 -0.2316 0.408414
19 to 23 141780 -0.4384 0.330546
18 to 22 142032 0.4158 0.661233
17 to 21 141849 -0.2045 0.418978
16 to 20 142086 0.5989 0.725374
15 to 19 142216 1.0396 0.850728
14 to 18 141881 -0.0960 0.461747
13 to 17 142185 0.9345 0.824970
12 to 16 141987 0.2633 0.603836
11 to 15 142440 1.7989 0.963981
10 to 14 141930 0.0701 0.527930
9 to 13 142292 1.2972 0.902717
8 to 12 142001 0.3107 0.622003
7 to 11 141736 -0.5876 0.278414
6 to 10 141777 -0.4486 0.326869
5 to 9 141772 -0.4655 0.320778
4 to 8 142547 2.1616 0.984675
3 to 7 141865 -0.1503 0.440275
2 to 6 141887 -0.0757 0.469831
1 to 5 142133 0.7582 0.775835
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-30_19:31
Bits used No. missing words z-score p-value
31 to 32 141929 0.0580 0.523135
30 to 31 141836 -0.2163 0.414372
29 to 30 141996 0.2557 0.600895
28 to 29 142092 0.5388 0.705005
27 to 28 142395 1.4327 0.924022
26 to 27 141878 -0.0924 0.463183
25 to 26 141467 -1.3048 0.095979
24 to 25 141905 -0.0128 0.494905
23 to 24 142243 0.9843 0.837510
22 to 23 141573 -0.9921 0.160569
21 to 22 141867 -0.1249 0.450314
20 to 21 142051 0.4179 0.661992
19 to 20 142775 2.5536 0.994669
18 to 19 141820 -0.2635 0.396079
17 to 18 141787 -0.3609 0.359104
16 to 17 142144 0.6922 0.755607
15 to 16 141959 0.1465 0.558244
14 to 15 141932 0.0669 0.526659
13 to 14 142307 1.1731 0.879616
12 to 13 141732 -0.5231 0.300453
11 to 12 141853 -0.1662 0.434014
10 to 11 142247 0.9961 0.840394
9 to 10 141989 0.2350 0.592901
8 to 9 142428 1.5300 0.936992
7 to 8 141934 0.0728 0.529007
6 to 7 142296 1.1406 0.872986
5 to 6 141847 -0.1839 0.427060
4 to 5 141451 -1.3520 0.088187
3 to 4 142110 0.5919 0.723057
2 to 3 142025 0.3412 0.633527
1 to 2 142280 1.0934 0.862896
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2582.62 1.168 0.878687
Test results for specific bytes for dh-ranFile-2018-06-30_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2668.56 2.384 0.991432
2 to 9 2371.40 -1.819 0.034482
3 to 10 2508.32 0.118 0.546835
4 to 11 2520.34 0.288 0.613192
5 to 12 2533.46 0.473 0.681940
6 to 13 2559.04 0.835 0.798122
7 to 14 2482.03 -0.254 0.399680
8 to 15 2486.55 -0.190 0.424570
9 to 16 2409.63 -1.278 0.100624
10 to 17 2474.26 -0.364 0.357932
11 to 18 2534.76 0.492 0.688479
12 to 19 2464.80 -0.498 0.309300
13 to 20 2441.23 -0.831 0.202939
14 to 21 2474.50 -0.361 0.359206
15 to 22 2430.14 -0.988 0.161581
16 to 23 2547.63 0.674 0.749716
17 to 24 2529.59 0.418 0.662201
18 to 25 2565.46 0.926 0.822702
19 to 26 2513.83 0.196 0.577551
20 to 27 2462.05 -0.537 0.295744
21 to 28 2554.99 0.778 0.781612
22 to 29 2431.75 -0.965 0.167220
23 to 30 2436.22 -0.902 0.183545
24 to 31 2493.98 -0.085 0.466097
25 to 32 2493.18 -0.096 0.461579
CDPARK for dh-ranFile-2018-06-30_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
3535 0.5479 0.708135
3562 1.7808 0.962529
3483 -1.8265 0.033889
3518 -0.2283 0.409702
3527 0.1826 0.572463
3538 0.6849 0.753306
3493 -1.3699 0.085365
3538 0.6849 0.753306
3510 -0.5936 0.276387
3553 1.3699 0.914635
Square side=100, avg. no. parked=3525.70 sample std.=23.77
p-value of the KSTEST for those 10 p-values: 0.828320
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_19:31
0.9219,0.3732,0.9539,0.0907,0.9410,0.5640,0.6934,0.4931,0.3002,0.4052,
The KS test for those 10 p-values: 0.558041
The 3DSPHERES test for dh-ranFile-2018-06-30_19:31
sample no r^3 equiv. uni.
1 4.153 0.129265
2 13.371 0.359631
3 37.162 0.710245
4 43.751 0.767386
5 45.594 0.781247
6 2.085 0.067135
7 15.980 0.412965
8 12.882 0.349111
9 17.751 0.446623
10 82.243 0.935522
11 10.585 0.297314
12 19.823 0.483545
13 31.013 0.644333
14 10.192 0.288029
15 70.981 0.906149
16 52.666 0.827185
17 7.131 0.211556
18 2.334 0.074837
19 81.381 0.933642
20 10.449 0.294112
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.957369
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.2 0.1 0.0 -0.7 1.5
0.1 -2.2 -0.5 -0.8 0.2 -1.0
-0.3 -1.2 0.6 0.6 1.2 0.4
-0.3 0.3 1.4 -0.6 -1.9 0.5
-0.1 0.8 0.7 0.2 0.6 0.5
0.8 -0.5 -1.1 0.9 -1.5 -2.5
0.5 -0.7 -1.2 -0.1 2.4 -1.0
1.8
Chi-square with 42 degrees of freedom:48.051706
z-score=0.660295, p-value=0.758971
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-30_19:31
Test no p-value
1 0.190191
2 0.791331
3 0.878043
4 0.388721
5 0.083098
6 0.391420
7 0.377880
8 0.767037
9 0.550256
10 0.329579
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.866963
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_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 66754 0.11 66568 0.15
3 25000.00 24829 1.17 25093 0.35
4 6666.67 6726 0.53 6688 0.07
5 1388.89 1417 0.57 1379 0.07
6 238.10 232 0.16 242 0.06
7 34.72 33 0.09 25 2.72
8 4.96 8 1.86 4 0.19
p=0.38872 p=0.26960
Number of rngs required: 687707, p-value: 0.211
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_19:31
No. of wins: Observed Expected
98772 98585.9
z-score= 0.833, pvalue=0.79745
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66661 66666.7 0.000 0.000
2 37394 37654.3 1.800 1.800
3 27031 26954.7 0.216 2.016
4 19506 19313.5 1.919 3.935
5 13769 13851.4 0.490 4.426
6 10093 9943.5 2.246 6.672
7 6961 7145.0 4.740 11.412
8 5245 5139.1 2.183 13.595
9 3664 3699.9 0.348 13.943
10 2603 2666.3 1.503 15.446
11 1938 1923.3 0.112 15.558
12 1410 1388.7 0.325 15.883
13 1026 1003.7 0.495 16.378
14 744 726.1 0.439 16.817
15 566 525.8 3.068 19.885
16 397 381.2 0.659 20.544
17 264 276.5 0.569 21.113
18 196 200.8 0.116 21.229
19 136 146.0 0.683 21.912
20 104 106.2 0.046 21.958
21 292 287.1 0.083 22.041
Chisq= 22.04 for 20 degrees of freedom, p= 0.66171
SUMMARY of craptest
p-value for no. of wins: 0.797446
p-value for throws/game: 0.661707
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_19:31
No. of wins: Observed Expected
98735 98585.9
z-score= 0.667, pvalue=0.74763
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66430 66666.7 0.840 0.840
2 37743 37654.3 0.209 1.049
3 26933 26954.7 0.018 1.067
4 19225 19313.5 0.405 1.472
5 14063 13851.4 3.232 4.704
6 9938 9943.5 0.003 4.707
7 7096 7145.0 0.336 5.043
8 5098 5139.1 0.328 5.371
9 3704 3699.9 0.005 5.376
10 2701 2666.3 0.452 5.828
11 1894 1923.3 0.447 6.275
12 1404 1388.7 0.168 6.443
13 1070 1003.7 4.377 10.820
14 712 726.1 0.275 11.095
15 548 525.8 0.934 12.030
16 403 381.2 1.253 13.282
17 273 276.5 0.045 13.327
18 211 200.8 0.515 13.842
19 167 146.0 3.025 16.868
20 104 106.2 0.046 16.914
21 283 287.1 0.059 16.973
Chisq= 16.97 for 20 degrees of freedom, p= 0.34527
SUMMARY of craptest
p-value for no. of wins: 0.747629
p-value for throws/game: 0.345268
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0033,0.0058,0.0145,0.0173,0.0188,0.0240,0.0339,0.0345,0.0375,0.0427,
0.0443,0.0532,0.0582,0.0660,0.0671,0.0720,0.0748,0.0829,0.0831,0.0854,
0.0861,0.0861,0.0882,0.0907,0.0960,0.0985,0.1006,0.1079,0.1182,0.1273,
0.1288,0.1293,0.1356,0.1606,0.1616,0.1672,0.1705,0.1752,0.1835,0.1851,
0.1902,0.1908,0.1923,0.2029,0.2106,0.2116,0.2265,0.2335,0.2392,0.2395,
0.2438,0.2539,0.2623,0.2670,0.2696,0.2764,0.2784,0.2796,0.2880,0.2897,
0.2941,0.2957,0.2969,0.2973,0.3002,0.3005,0.3093,0.3119,0.3130,0.3208,
0.3228,0.3249,0.3269,0.3287,0.3296,0.3305,0.3329,0.3353,0.3453,0.3491,
0.3579,0.3591,0.3592,0.3596,0.3627,0.3645,0.3675,0.3732,0.3759,0.3779,
0.3786,0.3887,0.3887,0.3914,0.3961,0.3974,0.3974,0.3997,0.4052,0.4084,
0.4097,0.4118,0.4122,0.4130,0.4144,0.4155,0.4171,0.4177,0.4190,0.4203,
0.4230,0.4246,0.4269,0.4271,0.4302,0.4340,0.4357,0.4403,0.4441,0.4466,
0.4503,0.4616,0.4617,0.4632,0.4632,0.4661,0.4698,0.4835,0.4842,0.4862,
0.4931,0.4949,0.4958,0.5070,0.5231,0.5267,0.5279,0.5290,0.5291,0.5325,
0.5340,0.5468,0.5503,0.5503,0.5580,0.5582,0.5606,0.5626,0.5640,0.5722,
0.5725,0.5776,0.5778,0.5859,0.5905,0.5929,0.6009,0.6032,0.6038,0.6132,
0.6155,0.6208,0.6220,0.6335,0.6350,0.6443,0.6612,0.6617,0.6620,0.6622,
0.6712,0.6721,0.6819,0.6885,0.6934,0.6936,0.6959,0.6986,0.7002,0.7007,
0.7050,0.7081,0.7102,0.7231,0.7254,0.7357,0.7435,0.7455,0.7476,0.7497,
0.7523,0.7533,0.7533,0.7556,0.7590,0.7608,0.7670,0.7674,0.7758,0.7768,
0.7812,0.7816,0.7825,0.7837,0.7913,0.7918,0.7974,0.7981,0.8121,0.8122,
0.8227,0.8250,0.8272,0.8283,0.8302,0.8375,0.8404,0.8479,0.8484,0.8489,
0.8503,0.8507,0.8520,0.8570,0.8574,0.8589,0.8617,0.8629,0.8648,0.8653,
0.8670,0.8671,0.8721,0.8730,0.8780,0.8780,0.8787,0.8796,0.8907,0.8938,
0.8963,0.8966,0.9027,0.9049,0.9061,0.9110,0.9146,0.9201,0.9219,0.9240,
0.9301,0.9336,0.9355,0.9363,0.9370,0.9410,0.9539,0.9574,0.9625,0.9635,
0.9640,0.9765,0.9788,0.9847,0.9855,0.9914,0.9915,0.9932,0.9947,
Overall p-value after applying KStest on 269 p-values = 0.163682
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.