RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_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 15.91 16.9274 0.540702
2 to 25 15.84 19.0790 0.675986
3 to 26 15.54 24.1602 0.884852
4 to 27 15.70 14.1160 0.341123
5 to 28 15.73 23.1363 0.855135
6 to 29 15.70 21.1078 0.778494
7 to 30 15.77 17.2005 0.559136
8 to 31 15.90 24.0278 0.881318
9 to 32 15.67 15.9750 0.474393
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.113126
Tough bday spacings test for dh-ranFile-2018-06-25_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 32 65 110 97 71 61 25 16 10 5
(O-E)^2/E 0.1 0.6 0.9 1.6 0.0 0.7 1.5 0.8 0.1 1.7 0.2
Birthday Spacings: Sum(O-E)^2/E= 8.190, p= 0.390
RESULTS OF GCD FOR dh-ranFile-2018-06-25_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.788393
p-value, dist. of gcd's: 0.971257
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.905 0.721 0.916 0.373 0.139 0.256 0.952 0.413
Bits 8 to 15---> 0.919 0.422 0.439 0.036 0.751 0.978 0.403 0.221
Bits 16 to 23---> 0.348 0.990 0.604 0.278 0.075 0.938 0.974 0.321
Bits 24 to 31---> 0.260 0.632 0.902 0.836 0.992 0.893 0.774 0.441
KS test for the above 32 p values: 0.975
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_19:31,
p-values for 5 runs: 0.6016, 0.5104, 0.3405, 0.3951, 0.6625
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 4968 5134.0 5.368 6.117
r= 30 23185 23103.0 0.291 6.408
r= 31 11623 11551.5 0.442 6.850
chi-square = 6.850 with df = 3; p-value = 0.923
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 204 211.4 0.260 0.260
r= 30 5169 5134.0 0.238 0.499
r= 31 23149 23103.0 0.091 0.590
r= 32 11478 11551.5 0.468 1.058
chi-square = 1.058 with df = 3; p-value = 0.213
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_19:31
b-rank test for bits 1 to 8, p=0.44587
b-rank test for bits 2 to 9, p=0.02317
b-rank test for bits 3 to 10, p=0.38187
b-rank test for bits 4 to 11, p=0.15388
b-rank test for bits 5 to 12, p=0.07196
b-rank test for bits 6 to 13, p=0.80881
b-rank test for bits 7 to 14, p=0.28790
b-rank test for bits 8 to 15, p=0.40673
b-rank test for bits 9 to 16, p=0.23260
b-rank test for bits 10 to 17, p=0.29776
b-rank test for bits 11 to 18, p=0.64946
b-rank test for bits 12 to 19, p=0.04466
b-rank test for bits 13 to 20, p=0.73762
b-rank test for bits 14 to 21, p=0.73792
b-rank test for bits 15 to 22, p=0.49010
b-rank test for bits 16 to 23, p=0.90346
b-rank test for bits 17 to 24, p=0.26502
b-rank test for bits 18 to 25, p=0.73947
b-rank test for bits 19 to 26, p=0.80551
b-rank test for bits 20 to 27, p=0.66705
b-rank test for bits 21 to 28, p=0.63360
b-rank test for bits 22 to 29, p=0.04122
b-rank test for bits 23 to 30, p=0.14672
b-rank test for bits 24 to 31, p=0.43177
b-rank test for bits 25 to 32, p=0.04709
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 = 0.215936
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_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 142218 0.72 0.764604
2 141356 -1.29 0.098035
3 142227 0.74 0.771023
4 141153 -1.77 0.038604
5 142547 1.49 0.931873
6 141428 -1.12 0.130379
7 142249 0.79 0.786292
8 141989 0.19 0.573834
9 141614 -0.69 0.245090
10 141553 -0.83 0.202550
11 141732 -0.41 0.339319
12 140782 -2.63 0.004220
13 141768 -0.33 0.370621
14 141939 0.07 0.527634
15 141633 -0.65 0.259259
16 141968 0.14 0.554516
17 142136 0.53 0.701806
18 142819 2.13 0.983223
19 142245 0.78 0.783561
20 141701 -0.49 0.313217
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_19:31
Bits used No. missing words z-score p-value
23 to 32 141788 -0.4184 0.337835
22 to 31 142520 2.1058 0.982387
21 to 30 142122 0.7333 0.768326
20 to 29 141399 -1.7598 0.039224
19 to 28 141761 -0.5115 0.304507
18 to 27 141455 -1.5667 0.058598
17 to 26 141841 -0.2356 0.406864
16 to 25 142233 1.1161 0.867811
15 to 24 141442 -1.6115 0.053537
14 to 23 141702 -0.7149 0.237326
13 to 22 141912 0.0092 0.503673
12 to 21 142276 1.2644 0.896953
11 to 20 141785 -0.4287 0.334062
10 to 19 141607 -1.0425 0.148586
9 to 18 141690 -0.7563 0.224732
8 to 17 142186 0.9540 0.829967
7 to 16 141897 -0.0425 0.483043
6 to 15 142046 0.4713 0.681278
5 to 14 141599 -1.0701 0.142286
4 to 13 142042 0.4575 0.676338
3 to 12 141843 -0.2287 0.409542
2 to 11 142155 0.8471 0.801541
1 to 10 142263 1.2196 0.888683
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_19:31
Bits used No. missing words z-score p-value
28 to 32 141644 -0.8994 0.184214
27 to 31 141762 -0.4994 0.308741
26 to 30 142184 0.9311 0.824095
25 to 29 142334 1.4396 0.925004
24 to 28 142115 0.6972 0.757157
23 to 27 141887 -0.0757 0.469831
22 to 26 141981 0.2429 0.595978
21 to 25 141807 -0.3469 0.364340
20 to 24 141445 -1.5740 0.057744
19 to 23 141791 -0.4011 0.344166
18 to 22 141890 -0.0655 0.473878
17 to 21 141444 -1.5774 0.057353
16 to 20 142195 0.9684 0.833571
15 to 19 141706 -0.6893 0.245332
14 to 18 141736 -0.5876 0.278414
13 to 17 141736 -0.5876 0.278414
12 to 16 141854 -0.1876 0.425611
11 to 15 141860 -0.1672 0.433598
10 to 14 142304 1.3379 0.909530
9 to 13 142087 0.6023 0.726503
8 to 12 142230 1.0870 0.861485
7 to 11 142185 0.9345 0.824970
6 to 10 141507 -1.3638 0.086310
5 to 9 142319 1.3887 0.917540
4 to 8 142356 1.5141 0.935004
3 to 7 141743 -0.5638 0.286435
2 to 6 142189 0.9480 0.828444
1 to 5 142013 0.3514 0.637365
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_19:31
Bits used No. missing words z-score p-value
31 to 32 141542 -1.0836 0.139278
30 to 31 141489 -1.2399 0.107504
29 to 30 141653 -0.7561 0.224784
28 to 29 141824 -0.2517 0.400632
27 to 28 142679 2.2704 0.988409
26 to 27 142057 0.4356 0.668438
25 to 26 141506 -1.1898 0.117070
24 to 25 141738 -0.5054 0.306640
23 to 24 142041 0.3884 0.651143
22 to 23 142088 0.5271 0.700921
21 to 22 141891 -0.0541 0.478439
20 to 21 141707 -0.5968 0.275306
19 to 20 141678 -0.6824 0.247496
18 to 19 141725 -0.5437 0.293308
17 to 18 141932 0.0669 0.526659
16 to 17 141376 -1.5732 0.057831
15 to 16 142011 0.2999 0.617878
14 to 15 142915 2.9666 0.998494
13 to 14 142393 1.4268 0.923175
12 to 13 142252 1.0108 0.843950
11 to 12 142373 1.3678 0.914306
10 to 11 142369 1.3560 0.912444
9 to 10 142835 2.7306 0.996839
8 to 9 140978 -2.7473 0.003005
7 to 8 142625 2.1111 0.982619
6 to 7 142261 1.0374 0.850219
5 to 6 142341 1.2734 0.898555
4 to 5 141469 -1.2989 0.096988
3 to 4 141468 -1.3019 0.096482
2 to 3 141514 -1.1662 0.121774
1 to 2 142395 1.4327 0.924022
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2486.43 -0.192 0.423925
Test results for specific bytes for dh-ranFile-2018-06-25_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2386.70 -1.602 0.054550
2 to 9 2489.70 -0.146 0.442112
3 to 10 2560.48 0.855 0.803800
4 to 11 2470.95 -0.411 0.340587
5 to 12 2503.35 0.047 0.518906
6 to 13 2656.97 2.220 0.986789
7 to 14 2501.73 0.024 0.509746
8 to 15 2505.15 0.073 0.529053
9 to 16 2505.44 0.077 0.530655
10 to 17 2400.33 -1.409 0.079347
11 to 18 2482.92 -0.242 0.404569
12 to 19 2419.54 -1.138 0.127589
13 to 20 2589.67 1.268 0.897614
14 to 21 2430.95 -0.977 0.164394
15 to 22 2559.13 0.836 0.798467
16 to 23 2476.82 -0.328 0.371511
17 to 24 2441.67 -0.825 0.204698
18 to 25 2403.85 -1.360 0.086948
19 to 26 2458.49 -0.587 0.278611
20 to 27 2562.82 0.888 0.812830
21 to 28 2494.53 -0.077 0.469180
22 to 29 2588.59 1.253 0.894865
23 to 30 2478.03 -0.311 0.377994
24 to 31 2324.79 -2.478 0.006609
25 to 32 2340.75 -2.252 0.012156
CDPARK for dh-ranFile-2018-06-25_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
3524 0.0457 0.518210
3528 0.2283 0.590298
3541 0.8219 0.794438
3518 -0.2283 0.409702
3538 0.6849 0.753306
3523 0.0000 0.500000
3552 1.3242 0.907282
3526 0.1370 0.554479
3489 -1.5525 0.060270
3564 1.8721 0.969407
Square side=100, avg. no. parked=3530.30 sample std.=19.38
p-value of the KSTEST for those 10 p-values: 0.394670
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_19:31
0.8267,0.7395,0.3757,0.1347,0.4316,0.3059,0.2249,0.8947,0.9679,0.9161,
The KS test for those 10 p-values: 0.496144
The 3DSPHERES test for dh-ranFile-2018-06-25_19:31
sample no r^3 equiv. uni.
1 64.303 0.882747
2 29.609 0.627296
3 36.228 0.701088
4 19.579 0.479332
5 21.185 0.506463
6 11.824 0.325736
7 89.113 0.948720
8 14.327 0.379712
9 15.354 0.400585
10 7.571 0.223049
11 34.069 0.678782
12 9.443 0.270048
13 6.420 0.192656
14 31.516 0.650248
15 11.029 0.307639
16 25.839 0.577382
17 23.715 0.546384
18 11.696 0.322843
19 32.693 0.663701
20 33.330 0.670771
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.280591
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.8 -0.6 -0.7 1.4 1.2
-1.4 -1.7 1.3 1.8 -0.3 0.7
-1.8 1.0 0.4 -0.5 0.6 0.4
-0.5 -0.1 -1.4 0.8 0.2 0.5
-0.5 -1.5 0.1 0.2 0.3 -0.8
-0.5 1.3 0.6 0.4 0.3 0.2
-0.7 -0.7 -0.8 0.4 -1.3 0.0
-0.1
Chi-square with 42 degrees of freedom:36.498474
z-score=-0.600266, p-value=0.289435
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_19:31
Test no p-value
1 0.871690
2 0.805620
3 0.796934
4 0.115666
5 0.006371
6 0.270167
7 0.021457
8 0.429072
9 0.142166
10 0.664063
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.248177
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_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 66728 0.06 66510 0.37
3 25000.00 24948 0.11 25023 0.02
4 6666.67 6659 0.01 6708 0.26
5 1388.89 1393 0.01 1473 5.09
6 238.10 242 0.06 239 0.00
7 34.72 26 2.19 37 0.15
8 4.96 3 0.77 9 3.29
p=0.21847 p=0.83646
Number of rngs required: 688204, p-value: 0.409
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_19:31
No. of wins: Observed Expected
98337 98585.9
z-score=-1.113, pvalue=0.13285
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66198 66666.7 3.295 3.295
2 37985 37654.3 2.904 6.199
3 27049 26954.7 0.330 6.528
4 19093 19313.5 2.517 9.045
5 13780 13851.4 0.368 9.413
6 9929 9943.5 0.021 9.435
7 7208 7145.0 0.555 9.990
8 5247 5139.1 2.267 12.256
9 3803 3699.9 2.875 15.131
10 2677 2666.3 0.043 15.174
11 1851 1923.3 2.720 17.894
12 1447 1388.7 2.444 20.338
13 1059 1003.7 3.045 23.383
14 796 726.1 6.721 30.104
15 528 525.8 0.009 30.113
16 362 381.2 0.962 31.075
17 274 276.5 0.023 31.099
18 174 200.8 3.584 34.683
19 136 146.0 0.683 35.366
20 97 106.2 0.800 36.165
21 307 287.1 1.377 37.543
Chisq= 37.54 for 20 degrees of freedom, p= 0.98993
SUMMARY of craptest
p-value for no. of wins: 0.132845
p-value for throws/game: 0.989934
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_19:31
No. of wins: Observed Expected
98663 98585.9
z-score= 0.345, pvalue=0.63496
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66450 66666.7 0.704 0.704
2 37354 37654.3 2.395 3.099
3 27333 26954.7 5.308 8.408
4 19515 19313.5 2.103 10.511
5 13754 13851.4 0.685 11.196
6 9836 9943.5 1.163 12.359
7 7204 7145.0 0.487 12.846
8 5137 5139.1 0.001 12.847
9 3646 3699.9 0.784 13.631
10 2667 2666.3 0.000 13.631
11 1904 1923.3 0.194 13.825
12 1393 1388.7 0.013 13.839
13 1035 1003.7 0.975 14.814
14 765 726.1 2.080 16.893
15 575 525.8 4.597 21.490
16 383 381.2 0.009 21.499
17 272 276.5 0.075 21.573
18 215 200.8 1.000 22.573
19 144 146.0 0.027 22.600
20 115 106.2 0.727 23.327
21 303 287.1 0.879 24.206
Chisq= 24.21 for 20 degrees of freedom, p= 0.76648
SUMMARY of craptest
p-value for no. of wins: 0.634961
p-value for throws/game: 0.766478
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0030,0.0042,0.0064,0.0066,0.0122,0.0215,0.0232,0.0365,0.0386,0.0392,
0.0412,0.0447,0.0471,0.0535,0.0545,0.0574,0.0577,0.0578,0.0586,0.0603,
0.0720,0.0754,0.0793,0.0863,0.0869,0.0965,0.0970,0.0980,0.1075,0.1131,
0.1157,0.1171,0.1218,0.1276,0.1304,0.1328,0.1347,0.1392,0.1393,0.1422,
0.1423,0.1467,0.1486,0.1539,0.1644,0.1842,0.1927,0.2026,0.2047,0.2128,
0.2159,0.2185,0.2214,0.2230,0.2247,0.2248,0.2249,0.2326,0.2373,0.2451,
0.2453,0.2475,0.2482,0.2560,0.2593,0.2602,0.2650,0.2700,0.2702,0.2753,
0.2780,0.2784,0.2784,0.2786,0.2806,0.2864,0.2879,0.2894,0.2933,0.2978,
0.3045,0.3059,0.3066,0.3076,0.3087,0.3132,0.3214,0.3228,0.3257,0.3341,
0.3378,0.3393,0.3405,0.3406,0.3411,0.3442,0.3483,0.3643,0.3706,0.3715,
0.3732,0.3757,0.3780,0.3797,0.3819,0.3897,0.3947,0.3951,0.4006,0.4006,
0.4028,0.4046,0.4067,0.4069,0.4094,0.4095,0.4097,0.4131,0.4217,0.4239,
0.4256,0.4291,0.4316,0.4318,0.4336,0.4388,0.4409,0.4421,0.4459,0.4692,
0.4698,0.4739,0.4744,0.4784,0.4793,0.4830,0.4901,0.4961,0.5000,0.5037,
0.5065,0.5097,0.5104,0.5182,0.5189,0.5267,0.5276,0.5291,0.5307,0.5407,
0.5464,0.5545,0.5545,0.5591,0.5738,0.5774,0.5903,0.5960,0.6016,0.6038,
0.6179,0.6273,0.6322,0.6336,0.6350,0.6374,0.6495,0.6502,0.6511,0.6625,
0.6637,0.6641,0.6670,0.6684,0.6708,0.6760,0.6763,0.6788,0.6813,0.7009,
0.7011,0.7018,0.7208,0.7265,0.7376,0.7379,0.7395,0.7395,0.7506,0.7533,
0.7572,0.7646,0.7665,0.7683,0.7710,0.7737,0.7785,0.7836,0.7863,0.7884,
0.7944,0.7969,0.7985,0.8015,0.8038,0.8055,0.8056,0.8088,0.8128,0.8241,
0.8250,0.8267,0.8284,0.8300,0.8336,0.8358,0.8365,0.8440,0.8502,0.8551,
0.8615,0.8678,0.8717,0.8813,0.8827,0.8849,0.8887,0.8929,0.8947,0.8949,
0.8970,0.8976,0.8986,0.9022,0.9035,0.9055,0.9073,0.9095,0.9124,0.9143,
0.9161,0.9164,0.9175,0.9186,0.9232,0.9232,0.9240,0.9250,0.9319,0.9350,
0.9382,0.9487,0.9523,0.9679,0.9694,0.9713,0.9737,0.9746,0.9782,0.9824,
0.9826,0.9832,0.9868,0.9884,0.9899,0.9903,0.9925,0.9968,0.9985,
Overall p-value after applying KStest on 269 p-values = 0.304175
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.