RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.77 16.0496 0.479682
2 to 25 15.68 18.1699 0.621800
3 to 26 16.01 11.4572 0.168164
4 to 27 15.81 13.3779 0.289454
5 to 28 15.93 9.4574 0.075189
6 to 29 15.62 28.6993 0.962599
7 to 30 15.68 10.3549 0.111929
8 to 31 15.84 16.4984 0.511181
9 to 32 15.99 14.0721 0.338008
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.463580
Tough bday spacings test for dh-ranFile-2018-07-05_09:31: 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 14 37 79 79 107 85 54 29 10 4 2
(O-E)^2/E 2.6 0.0 0.4 3.6 0.9 0.6 0.1 0.0 1.6 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 11.853, p= 0.705
RESULTS OF GCD FOR dh-ranFile-2018-07-05_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.040248
p-value, dist. of gcd's: 0.255943
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.678 0.020 0.444 0.037 0.308 0.272 0.475 0.024
Bits 8 to 15---> 0.276 0.113 0.845 0.077 0.638 0.884 0.896 0.435
Bits 16 to 23---> 0.828 0.360 0.047 0.685 0.144 0.921 0.975 0.744
Bits 24 to 31---> 0.169 0.314 0.988 0.297 0.194 0.132 0.255 0.186
KS test for the above 32 p values: 0.863
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_09:31,
p-values for 5 runs: 0.7722, 0.7061, 0.7110, 0.8060, 0.3910
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 193 211.4 1.605 1.605
r= 29 5136 5134.0 0.001 1.605
r= 30 23094 23103.0 0.004 1.609
r= 31 11577 11551.5 0.056 1.665
chi-square = 1.665 with df = 3; p-value = 0.355
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5041 5134.0 1.685 1.713
r= 31 23195 23103.0 0.366 2.079
r= 32 11555 11551.5 0.001 2.080
chi-square = 2.080 with df = 3; p-value = 0.444
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_09:31
b-rank test for bits 1 to 8, p=0.54279
b-rank test for bits 2 to 9, p=0.58183
b-rank test for bits 3 to 10, p=0.63702
b-rank test for bits 4 to 11, p=0.43394
b-rank test for bits 5 to 12, p=0.76204
b-rank test for bits 6 to 13, p=0.00769
b-rank test for bits 7 to 14, p=0.35828
b-rank test for bits 8 to 15, p=0.78799
b-rank test for bits 9 to 16, p=0.07522
b-rank test for bits 10 to 17, p=0.69083
b-rank test for bits 11 to 18, p=0.50589
b-rank test for bits 12 to 19, p=0.86599
b-rank test for bits 13 to 20, p=0.69881
b-rank test for bits 14 to 21, p=0.56854
b-rank test for bits 15 to 22, p=0.60132
b-rank test for bits 16 to 23, p=0.09665
b-rank test for bits 17 to 24, p=0.02855
b-rank test for bits 18 to 25, p=0.37319
b-rank test for bits 19 to 26, p=0.50249
b-rank test for bits 20 to 27, p=0.14936
b-rank test for bits 21 to 28, p=0.57361
b-rank test for bits 22 to 29, p=0.37320
b-rank test for bits 23 to 30, p=0.42141
b-rank test for bits 24 to 31, p=0.38656
b-rank test for bits 25 to 32, p=0.39106
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 = 0.235625
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_09:31
(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 141355 -1.30 0.097632
2 142593 1.60 0.944907
3 142045 0.32 0.624373
4 141713 -0.46 0.323219
5 142042 0.31 0.621711
6 141789 -0.28 0.389300
7 142230 0.75 0.773140
8 141670 -0.56 0.288019
9 142128 0.51 0.695293
10 142063 0.36 0.640218
11 141161 -1.75 0.040194
12 141729 -0.42 0.336756
13 142205 0.69 0.755160
14 141887 -0.05 0.479196
15 142246 0.79 0.784246
16 142050 0.33 0.628797
17 142406 1.16 0.877066
18 141546 -0.85 0.197968
19 141743 -0.39 0.348778
20 142189 0.65 0.743262
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_09:31
Bits used No. missing words z-score p-value
23 to 32 142131 0.7644 0.777679
22 to 31 142061 0.5230 0.699513
21 to 30 142157 0.8540 0.803457
20 to 29 141798 -0.3839 0.350528
19 to 28 141905 -0.0149 0.494044
18 to 27 142264 1.2230 0.889335
17 to 26 141821 -0.3046 0.380341
16 to 25 142117 0.7161 0.763036
15 to 24 141900 -0.0322 0.487167
14 to 23 142179 0.9299 0.823788
13 to 22 142146 0.8161 0.792780
12 to 21 141373 -1.8494 0.032199
11 to 20 142220 1.0713 0.857977
10 to 19 141692 -0.7494 0.226804
9 to 18 141613 -1.0218 0.153431
8 to 17 141641 -0.9253 0.177411
7 to 16 142062 0.5264 0.700712
6 to 15 141754 -0.5356 0.296110
5 to 14 141562 -1.1977 0.115519
4 to 13 141638 -0.9356 0.174734
3 to 12 141886 -0.0804 0.467940
2 to 11 142046 0.4713 0.681278
1 to 10 142117 0.7161 0.763036
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_09:31
Bits used No. missing words z-score p-value
28 to 32 142143 0.7921 0.785849
27 to 31 142098 0.6396 0.738770
26 to 30 141511 -1.3503 0.088465
25 to 29 142243 1.1311 0.870990
24 to 28 142003 0.3175 0.624578
23 to 27 142277 1.2463 0.893680
22 to 26 141825 -0.2859 0.387491
21 to 25 141659 -0.8486 0.198059
20 to 24 141741 -0.5706 0.284132
19 to 23 142089 0.6091 0.728755
18 to 22 141989 0.2701 0.606446
17 to 21 141989 0.2701 0.606446
16 to 20 142007 0.3311 0.629710
15 to 19 142121 0.7175 0.763475
14 to 18 141768 -0.4791 0.315939
13 to 17 142202 0.9921 0.839426
12 to 16 141754 -0.5265 0.299256
11 to 15 142231 1.0904 0.862233
10 to 14 142178 0.9107 0.818785
9 to 13 142073 0.5548 0.710489
8 to 12 142231 1.0904 0.862233
7 to 11 142397 1.6531 0.950847
6 to 10 141663 -0.8350 0.201854
5 to 9 141350 -1.8960 0.028978
4 to 8 141419 -1.6621 0.048243
3 to 7 142322 1.3989 0.919076
2 to 6 141935 0.0870 0.534671
1 to 5 142049 0.4735 0.682057
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_09:31
Bits used No. missing words z-score p-value
31 to 32 142358 1.3235 0.907167
30 to 31 141589 -0.9449 0.172348
29 to 30 141673 -0.6971 0.242858
28 to 29 141892 -0.0511 0.479615
27 to 28 142009 0.2940 0.615626
26 to 27 142034 0.3678 0.643473
25 to 26 142070 0.4740 0.682233
24 to 25 142548 1.8840 0.970216
23 to 24 141712 -0.5821 0.280252
22 to 23 141966 0.1672 0.566381
21 to 22 142197 0.8486 0.801944
20 to 21 141860 -0.1455 0.442152
19 to 20 142188 0.8220 0.794472
18 to 19 141936 0.0787 0.531354
17 to 18 141743 -0.4906 0.311837
16 to 17 141356 -1.6322 0.051314
15 to 16 141629 -0.8269 0.204138
14 to 15 141484 -1.2547 0.104801
13 to 14 141779 -0.3845 0.350321
12 to 13 142087 0.5241 0.699896
11 to 12 142130 0.6509 0.742459
10 to 11 141915 0.0167 0.506672
9 to 10 141414 -1.4612 0.071987
8 to 9 142013 0.3058 0.620126
7 to 8 141823 -0.2547 0.399493
6 to 7 142372 1.3648 0.913843
5 to 6 142466 1.6421 0.949715
4 to 5 141766 -0.4228 0.336220
3 to 4 141479 -1.2694 0.102147
2 to 3 141975 0.1937 0.576801
1 to 2 141477 -1.2753 0.101100
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2563.53 0.898 0.815526
Test results for specific bytes for dh-ranFile-2018-07-05_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2486.33 -0.193 0.423358
2 to 9 2486.72 -0.188 0.425538
3 to 10 2530.95 0.438 0.669199
4 to 11 2485.31 -0.208 0.417711
5 to 12 2450.74 -0.697 0.243033
6 to 13 2444.61 -0.783 0.216707
7 to 14 2621.94 1.724 0.957685
8 to 15 2525.90 0.366 0.642943
9 to 16 2569.00 0.976 0.835408
10 to 17 2458.03 -0.593 0.276430
11 to 18 2535.86 0.507 0.693995
12 to 19 2557.29 0.810 0.791088
13 to 20 2465.99 -0.481 0.315245
14 to 21 2544.34 0.627 0.734709
15 to 22 2355.48 -2.044 0.020487
16 to 23 2475.73 -0.343 0.365709
17 to 24 2501.30 0.018 0.507359
18 to 25 2501.17 0.017 0.506626
19 to 26 2540.34 0.571 0.715852
20 to 27 2418.35 -1.155 0.124116
21 to 28 2466.98 -0.467 0.320263
22 to 29 2464.12 -0.507 0.305916
23 to 30 2524.29 0.344 0.634399
24 to 31 2431.39 -0.970 0.165937
25 to 32 2613.24 1.601 0.945360
CDPARK for dh-ranFile-2018-07-05_09:31: 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
3540 0.7763 0.781201
3529 0.2740 0.607947
3539 0.7306 0.767486
3504 -0.8676 0.192812
3512 -0.5023 0.307734
3534 0.5023 0.692266
3561 1.7352 0.958644
3559 1.6438 0.949895
3562 1.7808 0.962529
3567 2.0091 0.977738
Square side=100, avg. no. parked=3540.70 sample std.=20.61
p-value of the KSTEST for those 10 p-values: 0.011335
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_09:31
0.1971,0.1367,0.4667,0.1931,0.6714,0.1441,0.2374,0.8799,0.2409,0.6392,
The KS test for those 10 p-values: 0.209458
The 3DSPHERES test for dh-ranFile-2018-07-05_09:31
sample no r^3 equiv. uni.
1 12.638 0.343777
2 37.334 0.711905
3 58.071 0.855675
4 8.777 0.253662
5 6.721 0.200705
6 5.236 0.160146
7 7.374 0.217932
8 13.673 0.366033
9 38.928 0.726809
10 4.830 0.148698
11 1.301 0.042448
12 155.077 0.994311
13 7.796 0.228842
14 48.545 0.801741
15 26.313 0.584015
16 5.557 0.169103
17 6.255 0.188186
18 19.985 0.486318
19 34.716 0.685639
20 61.581 0.871610
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.508630
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 -0.6 0.0 -0.5 0.2
0.6 -1.4 3.4 -0.1 -0.5 0.4
-0.7 -0.5 0.5 -1.2 -0.3 0.9
-0.6 0.8 -0.8 -0.1 0.2 -0.0
0.2 1.1 -0.0 0.4 -0.6 0.3
1.5 -0.7 0.9 -2.1 0.9 -0.8
0.3 -0.4 0.5 0.4 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:36.790966
z-score=-0.568352, p-value=0.301493
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_09:31
Test no p-value
1 0.085046
2 0.077670
3 0.660280
4 0.311644
5 0.104356
6 0.766221
7 0.909493
8 0.184414
9 0.209800
10 0.966434
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.339774
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_09:31:
(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 66722 0.05 66695 0.01
3 25000.00 24917 0.28 24824 1.24
4 6666.67 6704 0.21 6768 1.54
5 1388.89 1384 0.02 1416 0.53
6 238.10 229 0.35 248 0.41
7 34.72 33 0.09 44 2.48
8 4.96 10 5.12 4 0.19
p=0.58810 p=0.61995
Number of rngs required: 687663, p-value: 0.196
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_09:31
No. of wins: Observed Expected
98287 98585.9
z-score=-1.337, pvalue=0.09067
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66419 66666.7 0.920 0.920
2 37860 37654.3 1.123 2.044
3 26977 26954.7 0.018 2.062
4 19475 19313.5 1.351 3.413
5 13848 13851.4 0.001 3.414
6 9956 9943.5 0.016 3.430
7 7053 7145.0 1.185 4.615
8 5115 5139.1 0.113 4.728
9 3697 3699.9 0.002 4.730
10 2737 2666.3 1.875 6.605
11 1969 1923.3 1.084 7.689
12 1365 1388.7 0.406 8.095
13 998 1003.7 0.033 8.127
14 703 726.1 0.737 8.865
15 485 525.8 3.171 12.036
16 363 381.2 0.864 12.901
17 281 276.5 0.072 12.972
18 172 200.8 4.139 17.111
19 134 146.0 0.984 18.095
20 105 106.2 0.014 18.109
21 288 287.1 0.003 18.112
Chisq= 18.11 for 20 degrees of freedom, p= 0.41994
SUMMARY of craptest
p-value for no. of wins: 0.090665
p-value for throws/game: 0.419942
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_09:31
No. of wins: Observed Expected
98757 98585.9
z-score= 0.765, pvalue=0.77800
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66397 66666.7 1.091 1.091
2 37842 37654.3 0.935 2.026
3 26803 26954.7 0.854 2.880
4 19179 19313.5 0.936 3.817
5 14009 13851.4 1.793 5.609
6 10095 9943.5 2.307 7.916
7 7166 7145.0 0.062 7.978
8 5166 5139.1 0.141 8.119
9 3678 3699.9 0.129 8.248
10 2650 2666.3 0.100 8.348
11 1936 1923.3 0.083 8.431
12 1408 1388.7 0.267 8.698
13 1014 1003.7 0.105 8.804
14 697 726.1 1.169 9.973
15 547 525.8 0.852 10.825
16 374 381.2 0.134 10.959
17 296 276.5 1.369 12.328
18 197 200.8 0.073 12.402
19 155 146.0 0.557 12.958
20 118 106.2 1.308 14.266
21 273 287.1 0.694 14.960
Chisq= 14.96 for 20 degrees of freedom, p= 0.22129
SUMMARY of craptest
p-value for no. of wins: 0.777996
p-value for throws/game: 0.221290
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0077,0.0113,0.0201,0.0205,0.0238,0.0285,0.0290,0.0322,0.0372,0.0402,
0.0402,0.0424,0.0467,0.0482,0.0513,0.0720,0.0752,0.0752,0.0771,0.0777,
0.0850,0.0885,0.0907,0.0967,0.0976,0.1011,0.1021,0.1044,0.1048,0.1119,
0.1130,0.1155,0.1241,0.1317,0.1367,0.1436,0.1441,0.1487,0.1494,0.1534,
0.1601,0.1659,0.1682,0.1688,0.1691,0.1723,0.1747,0.1774,0.1844,0.1864,
0.1882,0.1928,0.1931,0.1943,0.1961,0.1971,0.1980,0.1981,0.2007,0.2019,
0.2041,0.2095,0.2098,0.2167,0.2179,0.2213,0.2268,0.2288,0.2356,0.2374,
0.2409,0.2429,0.2430,0.2537,0.2547,0.2559,0.2717,0.2759,0.2764,0.2803,
0.2841,0.2880,0.2895,0.2961,0.2972,0.2993,0.3015,0.3059,0.3077,0.3078,
0.3116,0.3118,0.3138,0.3152,0.3159,0.3203,0.3232,0.3362,0.3368,0.3380,
0.3398,0.3438,0.3488,0.3503,0.3505,0.3553,0.3583,0.3600,0.3657,0.3660,
0.3732,0.3732,0.3803,0.3866,0.3875,0.3893,0.3910,0.3911,0.3995,0.4177,
0.4199,0.4214,0.4234,0.4255,0.4339,0.4347,0.4422,0.4440,0.4444,0.4636,
0.4667,0.4679,0.4746,0.4792,0.4796,0.4797,0.4863,0.4872,0.4940,0.5025,
0.5059,0.5066,0.5067,0.5074,0.5086,0.5112,0.5314,0.5347,0.5428,0.5664,
0.5685,0.5736,0.5768,0.5818,0.5840,0.5881,0.6013,0.6064,0.6064,0.6079,
0.6156,0.6200,0.6201,0.6217,0.6218,0.6244,0.6246,0.6288,0.6297,0.6344,
0.6370,0.6376,0.6392,0.6402,0.6429,0.6435,0.6603,0.6692,0.6714,0.6779,
0.6813,0.6821,0.6822,0.6846,0.6856,0.6908,0.6923,0.6940,0.6953,0.6988,
0.6995,0.6999,0.7007,0.7050,0.7061,0.7105,0.7110,0.7119,0.7159,0.7268,
0.7288,0.7347,0.7388,0.7425,0.7433,0.7438,0.7552,0.7620,0.7630,0.7630,
0.7635,0.7662,0.7675,0.7722,0.7731,0.7777,0.7780,0.7812,0.7842,0.7858,
0.7880,0.7911,0.7928,0.7945,0.8017,0.8019,0.8035,0.8060,0.8155,0.8188,
0.8238,0.8283,0.8354,0.8394,0.8449,0.8557,0.8580,0.8622,0.8622,0.8632,
0.8660,0.8710,0.8716,0.8771,0.8799,0.8838,0.8893,0.8937,0.8964,0.9072,
0.9095,0.9138,0.9191,0.9206,0.9449,0.9454,0.9497,0.9499,0.9508,0.9577,
0.9586,0.9625,0.9626,0.9664,0.9702,0.9753,0.9777,0.9885,0.9943,
Overall p-value after applying KStest on 269 p-values = 0.533201
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.