RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.69 19.8561 0.718345
2 to 25 15.90 14.4863 0.367571
3 to 26 15.59 19.0156 0.672362
4 to 27 15.73 16.2715 0.495323
5 to 28 15.98 20.2905 0.740357
6 to 29 15.59 20.6357 0.756989
7 to 30 15.71 14.0055 0.333290
8 to 31 15.81 18.9611 0.669230
9 to 32 15.51 25.4277 0.914463
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.178433
Tough bday spacings test for dh-ranFile-2018-07-07_14:31: 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 13 40 73 91 94 79 51 39 11 6 3
(O-E)^2/E 1.6 0.3 0.0 0.5 0.1 0.0 0.0 2.9 1.0 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 6.764, p= 0.252
RESULTS OF GCD FOR dh-ranFile-2018-07-07_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.528955
p-value, dist. of gcd's: 0.435654
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.635 0.482 0.630 0.502 0.687 0.509 0.167 0.442
Bits 8 to 15---> 0.904 0.236 0.094 0.420 0.032 0.500 0.940 0.964
Bits 16 to 23---> 0.019 0.718 0.324 0.466 0.572 0.873 0.329 0.706
Bits 24 to 31---> 0.754 0.737 0.910 0.645 0.982 0.897 0.765 0.771
KS test for the above 32 p values: 0.826
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_14:31,
p-values for 5 runs: 0.2158, 0.8091, 0.2674, 0.1955, 0.7209
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 203 211.4 0.335 0.335
r= 29 4997 5134.0 3.656 3.992
r= 30 23226 23103.0 0.654 4.646
r= 31 11574 11551.5 0.044 4.690
chi-square = 4.690 with df = 3; p-value = 0.804
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 228 211.4 1.301 1.301
r= 30 5115 5134.0 0.070 1.371
r= 31 23246 23103.0 0.885 2.255
r= 32 11411 11551.5 1.709 3.965
chi-square = 3.965 with df = 3; p-value = 0.735
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_14:31
b-rank test for bits 1 to 8, p=0.88637
b-rank test for bits 2 to 9, p=0.95828
b-rank test for bits 3 to 10, p=0.55657
b-rank test for bits 4 to 11, p=0.15734
b-rank test for bits 5 to 12, p=0.20225
b-rank test for bits 6 to 13, p=0.80564
b-rank test for bits 7 to 14, p=0.61391
b-rank test for bits 8 to 15, p=0.78872
b-rank test for bits 9 to 16, p=0.95173
b-rank test for bits 10 to 17, p=0.25795
b-rank test for bits 11 to 18, p=0.21875
b-rank test for bits 12 to 19, p=0.61758
b-rank test for bits 13 to 20, p=0.87384
b-rank test for bits 14 to 21, p=0.92536
b-rank test for bits 15 to 22, p=0.70432
b-rank test for bits 16 to 23, p=0.57212
b-rank test for bits 17 to 24, p=0.36877
b-rank test for bits 18 to 25, p=0.90216
b-rank test for bits 19 to 26, p=0.49709
b-rank test for bits 20 to 27, p=0.04573
b-rank test for bits 21 to 28, p=0.34676
b-rank test for bits 22 to 29, p=0.96154
b-rank test for bits 23 to 30, p=0.23349
b-rank test for bits 24 to 31, p=0.68101
b-rank test for bits 25 to 32, p=0.22989
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 = 0.275972
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_14:31
(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 141808 -0.24 0.406425
2 141798 -0.26 0.397387
3 142198 0.67 0.749991
4 141367 -1.27 0.102555
5 141518 -0.91 0.180274
6 141043 -2.02 0.021478
7 142366 1.07 0.857011
8 141453 -1.07 0.143169
9 141057 -1.99 0.023217
10 141514 -0.92 0.177830
11 141456 -1.06 0.144758
12 142252 0.80 0.788327
13 142302 0.92 0.820547
14 142041 0.31 0.620822
15 141871 -0.09 0.464320
16 142262 0.82 0.795029
17 141941 0.07 0.529493
18 141370 -1.26 0.103814
19 141982 0.17 0.567412
20 141747 -0.38 0.352242
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_14:31
Bits used No. missing words z-score p-value
23 to 32 141961 0.1782 0.570706
22 to 31 142265 1.2264 0.889985
21 to 30 141859 -0.1736 0.431109
20 to 29 141554 -1.2253 0.110236
19 to 28 141749 -0.5529 0.290179
18 to 27 141896 -0.0460 0.481669
17 to 26 142016 0.3678 0.643499
16 to 25 141782 -0.4391 0.330306
15 to 24 142102 0.6644 0.746776
14 to 23 141810 -0.3425 0.365981
13 to 22 141980 0.2437 0.596264
12 to 21 141974 0.2230 0.588232
11 to 20 141900 -0.0322 0.487167
10 to 19 141905 -0.0149 0.494044
9 to 18 142132 0.7678 0.778705
8 to 17 142166 0.8851 0.811940
7 to 16 141670 -0.8253 0.204608
6 to 15 141876 -0.1149 0.454250
5 to 14 142394 1.6713 0.952666
4 to 13 142257 1.1989 0.884709
3 to 12 141768 -0.4873 0.313007
2 to 11 141730 -0.6184 0.268163
1 to 10 141845 -0.2218 0.412224
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_14:31
Bits used No. missing words z-score p-value
28 to 32 141763 -0.4960 0.309935
27 to 31 141472 -1.4825 0.069107
26 to 30 141719 -0.6452 0.259403
25 to 29 141958 0.1650 0.565521
24 to 28 141983 0.2497 0.598602
23 to 27 142125 0.7311 0.767636
22 to 26 141877 -0.1096 0.456366
21 to 25 141552 -1.2113 0.112893
20 to 24 141987 0.2633 0.603836
19 to 23 142049 0.4735 0.682057
18 to 22 141934 0.0836 0.533324
17 to 21 142196 0.9718 0.834416
16 to 20 141955 0.1548 0.561516
15 to 19 142293 1.3006 0.903298
14 to 18 141552 -1.2113 0.112893
13 to 17 141869 -0.1367 0.445629
12 to 16 142048 0.4701 0.680847
11 to 15 142361 1.5311 0.937126
10 to 14 142010 0.3413 0.633544
9 to 13 142252 1.1616 0.877300
8 to 12 142220 1.0531 0.853857
7 to 11 141765 -0.4893 0.312331
6 to 10 142483 1.9446 0.974091
5 to 9 142302 1.3311 0.908419
4 to 8 141852 -0.1943 0.422955
3 to 7 141949 0.1345 0.553486
2 to 6 142355 1.5107 0.934573
1 to 5 142466 1.8870 0.970421
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_14:31
Bits used No. missing words z-score p-value
31 to 32 141737 -0.5083 0.305605
30 to 31 141945 0.1052 0.541900
29 to 30 142131 0.6539 0.743410
28 to 29 142220 0.9164 0.820280
27 to 28 141572 -0.9951 0.159850
26 to 27 141843 -0.1957 0.422437
25 to 26 142505 1.7571 0.960553
24 to 25 142020 0.3265 0.627962
23 to 24 141758 -0.4464 0.327654
22 to 23 141737 -0.5083 0.305605
21 to 22 141677 -0.6853 0.246565
20 to 21 141401 -1.4995 0.066872
19 to 20 142028 0.3501 0.636853
18 to 19 141900 -0.0275 0.489022
17 to 18 141605 -0.8977 0.184665
16 to 17 142033 0.3648 0.642373
15 to 16 141696 -0.6293 0.264579
14 to 15 141230 -2.0039 0.022539
13 to 14 142167 0.7601 0.776399
12 to 13 141593 -0.9331 0.175377
11 to 12 142394 1.4297 0.923599
10 to 11 142238 0.9695 0.833859
9 to 10 141524 -1.1367 0.127839
8 to 9 141557 -1.0393 0.149328
7 to 8 141850 -0.1750 0.430534
6 to 7 141973 0.1878 0.574490
5 to 6 141351 -1.6470 0.049780
4 to 5 142053 0.4238 0.664146
3 to 4 142336 1.2586 0.895915
2 to 3 141565 -1.0157 0.154881
1 to 2 142244 0.9872 0.838234
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2512.11 0.171 0.567997
Test results for specific bytes for dh-ranFile-2018-07-07_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2499.46 -0.008 0.496936
2 to 9 2569.03 0.976 0.835514
3 to 10 2470.95 -0.411 0.340586
4 to 11 2372.60 -1.802 0.035795
5 to 12 2490.68 -0.132 0.447596
6 to 13 2371.68 -1.815 0.034781
7 to 14 2605.94 1.498 0.932966
8 to 15 2584.37 1.193 0.883587
9 to 16 2534.79 0.492 0.688634
10 to 17 2546.39 0.656 0.744120
11 to 18 2636.94 1.937 0.973605
12 to 19 2562.28 0.881 0.810793
13 to 20 2497.64 -0.033 0.486681
14 to 21 2507.92 0.112 0.544585
15 to 22 2539.85 0.564 0.713481
16 to 23 2378.05 -1.725 0.042296
17 to 24 2399.28 -1.424 0.077163
18 to 25 2448.68 -0.726 0.233984
19 to 26 2432.58 -0.953 0.170175
20 to 27 2552.13 0.737 0.769522
21 to 28 2465.96 -0.481 0.315117
22 to 29 2599.83 1.412 0.920987
23 to 30 2506.27 0.089 0.535303
24 to 31 2484.45 -0.220 0.412948
25 to 32 2447.59 -0.741 0.229300
CDPARK for dh-ranFile-2018-07-07_14:31: 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
3554 1.4155 0.921543
3541 0.8219 0.794438
3537 0.6393 0.738676
3523 0.0000 0.500000
3535 0.5479 0.708135
3527 0.1826 0.572463
3524 0.0457 0.518210
3485 -1.7352 0.041356
3562 1.7808 0.962529
3533 0.4566 0.676028
Square side=100, avg. no. parked=3532.10 sample std.=19.69
p-value of the KSTEST for those 10 p-values: 0.163267
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_14:31
0.2316,0.8868,0.1885,0.8245,0.7380,0.7604,0.7429,0.1259,0.2874,0.4160,
The KS test for those 10 p-values: 0.810745
The 3DSPHERES test for dh-ranFile-2018-07-07_14:31
sample no r^3 equiv. uni.
1 0.959 0.031451
2 48.420 0.800908
3 55.453 0.842516
4 74.671 0.917010
5 66.795 0.892096
6 29.782 0.629440
7 147.158 0.992593
8 4.838 0.148932
9 7.161 0.212347
10 15.618 0.405841
11 23.261 0.539470
12 25.335 0.570222
13 50.323 0.813146
14 19.729 0.481929
15 49.966 0.810909
16 0.102 0.003407
17 3.804 0.119095
18 7.317 0.216429
19 2.664 0.084985
20 21.315 0.508609
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.735197
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 2.0 -1.3 0.3 -1.2
1.3 -2.0 0.2 0.2 -0.4 1.9
0.8 0.2 -0.2 2.4 -2.1 0.6
0.5 0.1 -1.1 -1.4 -0.3 0.0
0.5 -1.2 -0.6 -0.7 1.6 -0.2
-0.5 -0.6 -0.8 0.8 0.5 1.0
1.0 -0.4 0.1 1.0 0.9 1.0
-1.1
Chi-square with 42 degrees of freedom:44.773670
z-score=0.302632, p-value=0.643804
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_14:31
Test no p-value
1 0.680083
2 0.258740
3 0.007573
4 0.923719
5 0.457450
6 0.381623
7 0.091690
8 0.005907
9 0.392863
10 0.876047
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.201706
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_14:31:
(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 66774 0.17 66832 0.41
3 25000.00 24954 0.08 24770 2.12
4 6666.67 6600 0.67 6735 0.70
5 1388.89 1380 0.06 1399 0.07
6 238.10 249 0.50 233 0.11
7 34.72 39 0.53 27 1.72
8 4.96 3 0.77 3 0.77
p=0.16441 p=0.56552
Number of rngs required: 687649, p-value: 0.192
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_14:31
No. of wins: Observed Expected
98545 98585.9
z-score=-0.183, pvalue=0.42750
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66465 66666.7 0.610 0.610
2 37910 37654.3 1.736 2.346
3 26683 26954.7 2.739 5.085
4 19468 19313.5 1.237 6.322
5 14002 13851.4 1.637 7.959
6 9988 9943.5 0.199 8.158
7 7108 7145.0 0.192 8.350
8 5069 5139.1 0.955 9.305
9 3689 3699.9 0.032 9.337
10 2630 2666.3 0.494 9.831
11 1918 1923.3 0.015 9.846
12 1325 1388.7 2.926 12.771
13 1032 1003.7 0.797 13.569
14 743 726.1 0.391 13.960
15 559 525.8 2.092 16.052
16 396 381.2 0.579 16.630
17 267 276.5 0.329 16.959
18 196 200.8 0.116 17.075
19 146 146.0 0.000 17.075
20 130 106.2 5.326 22.401
21 276 287.1 0.430 22.832
Chisq= 22.83 for 20 degrees of freedom, p= 0.70287
SUMMARY of craptest
p-value for no. of wins: 0.427500
p-value for throws/game: 0.702866
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_14:31
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 67028 66666.7 1.958 1.958
2 37300 37654.3 3.334 5.293
3 26810 26954.7 0.777 6.070
4 19300 19313.5 0.009 6.079
5 14079 13851.4 3.739 9.818
6 9981 9943.5 0.141 9.959
7 7083 7145.0 0.538 10.498
8 5153 5139.1 0.038 10.535
9 3642 3699.9 0.905 11.440
10 2686 2666.3 0.146 11.586
11 1987 1923.3 2.108 13.694
12 1360 1388.7 0.595 14.289
13 926 1003.7 6.017 20.306
14 706 726.1 0.559 20.865
15 522 525.8 0.028 20.893
16 377 381.2 0.045 20.938
17 275 276.5 0.009 20.946
18 202 200.8 0.007 20.953
19 160 146.0 1.346 22.299
20 110 106.2 0.135 22.434
21 313 287.1 2.334 24.767
Chisq= 24.77 for 20 degrees of freedom, p= 0.78953
SUMMARY of craptest
p-value for no. of wins: 0.747629
p-value for throws/game: 0.789528
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0034,0.0059,0.0076,0.0192,0.0215,0.0225,0.0232,0.0315,0.0317,0.0348,
0.0358,0.0414,0.0423,0.0457,0.0498,0.0669,0.0691,0.0772,0.0850,0.0917,
0.0941,0.1026,0.1038,0.1102,0.1129,0.1129,0.1191,0.1259,0.1278,0.1432,
0.1448,0.1489,0.1493,0.1549,0.1573,0.1599,0.1633,0.1644,0.1667,0.1702,
0.1754,0.1778,0.1784,0.1803,0.1847,0.1885,0.1916,0.1955,0.2017,0.2023,
0.2046,0.2123,0.2158,0.2164,0.2188,0.2293,0.2299,0.2316,0.2335,0.2340,
0.2355,0.2466,0.2525,0.2579,0.2587,0.2594,0.2646,0.2674,0.2682,0.2760,
0.2874,0.2902,0.3056,0.3056,0.3099,0.3123,0.3130,0.3151,0.3244,0.3277,
0.3294,0.3303,0.3333,0.3406,0.3468,0.3522,0.3660,0.3676,0.3688,0.3816,
0.3929,0.3974,0.4058,0.4064,0.4122,0.4129,0.4160,0.4198,0.4224,0.4230,
0.4275,0.4305,0.4311,0.4357,0.4417,0.4456,0.4476,0.4542,0.4564,0.4575,
0.4643,0.4661,0.4817,0.4819,0.4824,0.4867,0.4872,0.4890,0.4940,0.4953,
0.4969,0.4971,0.5000,0.5002,0.5017,0.5086,0.5089,0.5182,0.5290,0.5295,
0.5333,0.5353,0.5395,0.5419,0.5446,0.5535,0.5566,0.5615,0.5655,0.5655,
0.5674,0.5680,0.5702,0.5707,0.5717,0.5721,0.5725,0.5745,0.5882,0.5963,
0.5986,0.6038,0.6139,0.6176,0.6208,0.6280,0.6294,0.6299,0.6335,0.6352,
0.6369,0.6424,0.6435,0.6438,0.6449,0.6641,0.6692,0.6724,0.6760,0.6801,
0.6808,0.6810,0.6821,0.6868,0.6886,0.7029,0.7043,0.7060,0.7081,0.7135,
0.7177,0.7183,0.7209,0.7347,0.7352,0.7374,0.7380,0.7387,0.7404,0.7429,
0.7434,0.7441,0.7468,0.7476,0.7500,0.7543,0.7570,0.7604,0.7651,0.7676,
0.7695,0.7708,0.7764,0.7787,0.7883,0.7887,0.7895,0.7944,0.7950,0.8009,
0.8040,0.8056,0.8091,0.8107,0.8108,0.8109,0.8119,0.8131,0.8203,0.8205,
0.8245,0.8262,0.8339,0.8344,0.8355,0.8382,0.8425,0.8539,0.8570,0.8728,
0.8738,0.8760,0.8773,0.8836,0.8847,0.8864,0.8868,0.8900,0.8921,0.8959,
0.8970,0.9022,0.9033,0.9037,0.9084,0.9100,0.9145,0.9170,0.9210,0.9215,
0.9236,0.9237,0.9254,0.9330,0.9346,0.9371,0.9398,0.9517,0.9527,0.9583,
0.9606,0.9615,0.9625,0.9642,0.9704,0.9736,0.9741,0.9819,0.9926,
Overall p-value after applying KStest on 269 p-values = 0.184493
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.