Created
January 19, 2016 06:25
-
-
Save robertcampion/ed6287fc82adff9e8a1d to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| NOTE: Most of the tests in DIEHARD return a p-value, which | |
| should be uniform on [0,1) if the input file contains truly | |
| independent random bits. Those p-values are obtained by | |
| p=F(X), where F is the assumed distribution of the sample | |
| random variable X---often normal. But that assumed F is just | |
| an asymptotic approximation, for which the fit will be worst | |
| in the tails. Thus you should not be surprised with | |
| occasional p-values near 0 or 1, such as .0012 or .9983. | |
| When a bit stream really FAILS BIG, you will get p's of 0 or | |
| 1 to six or more places. By all means, do not, as a | |
| Statistician might, think that a p < .025 or p> .975 means | |
| that the RNG has "failed the test at the .05 level". Such | |
| p's happen among the hundreds that DIEHARD produces, even | |
| with good RNG's. So keep in mind that " p happens". | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: This is the BIRTHDAY SPACINGS TEST :: | |
| :: Choose m birthdays in a year of n days. List the spacings :: | |
| :: between the birthdays. If j is the number of values that :: | |
| :: occur more than once in that list, then j is asymptotically :: | |
| :: Poisson distributed with mean m^3/(4n). Experience shows n :: | |
| :: must be quite large, say n>=2^18, for comparing the results :: | |
| :: to the Poisson distribution with that mean. This test uses :: | |
| :: n=2^24 and m=2^9, so that the underlying distribution for j :: | |
| :: is taken to be Poisson with lambda=2^27/(2^26)=2. A sample :: | |
| :: of 500 j's is taken, and a chi-square goodness of fit test :: | |
| :: provides a p value. The first test uses bits 1-24 (counting :: | |
| :: from the left) from integers in the specified file. :: | |
| :: Then the file is closed and reopened. Next, bits 2-25 are :: | |
| :: used to provide birthdays, then 3-26 and so on to bits 9-32. :: | |
| :: Each set of bits provides a p-value, and the nine p-values :: | |
| :: provide a sample for a KSTEST. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| BIRTHDAY SPACINGS TEST, M= 512 N=2**24 LAMBDA= 2.0000 | |
| Results for random.bin | |
| For a sample of size 500: mean | |
| random.bin using bits 1 to 24 2.066 | |
| duplicate number number | |
| spacings observed expected | |
| 0 57. 67.668 | |
| 1 127. 135.335 | |
| 2 148. 135.335 | |
| 3 96. 90.224 | |
| 4 48. 45.112 | |
| 5 16. 18.045 | |
| 6 to INF 8. 8.282 | |
| Chisquare with 6 d.o.f. = 4.18 p-value= .347168 | |
| ::::::::::::::::::::::::::::::::::::::::: | |
| For a sample of size 500: mean | |
| random.bin using bits 2 to 25 2.032 | |
| duplicate number number | |
| spacings observed expected | |
| 0 64. 67.668 | |
| 1 140. 135.335 | |
| 2 127. 135.335 | |
| 3 95. 90.224 | |
| 4 41. 45.112 | |
| 5 28. 18.045 | |
| 6 to INF 5. 8.282 | |
| Chisquare with 6 d.o.f. = 8.29 p-value= .782614 | |
| ::::::::::::::::::::::::::::::::::::::::: | |
| For a sample of size 500: mean | |
| random.bin using bits 3 to 26 1.972 | |
| duplicate number number | |
| spacings observed expected | |
| 0 71. 67.668 | |
| 1 142. 135.335 | |
| 2 127. 135.335 | |
| 3 84. 90.224 | |
| 4 46. 45.112 | |
| 5 27. 18.045 | |
| 6 to INF 3. 8.282 | |
| Chisquare with 6 d.o.f. = 9.27 p-value= .840805 | |
| ::::::::::::::::::::::::::::::::::::::::: | |
| For a sample of size 500: mean | |
| random.bin using bits 4 to 27 2.066 | |
| duplicate number number | |
| spacings observed expected | |
| 0 66. 67.668 | |
| 1 122. 135.335 | |
| 2 144. 135.335 | |
| 3 90. 90.224 | |
| 4 46. 45.112 | |
| 5 24. 18.045 | |
| 6 to INF 8. 8.282 | |
| Chisquare with 6 d.o.f. = 3.90 p-value= .310185 | |
| ::::::::::::::::::::::::::::::::::::::::: | |
| For a sample of size 500: mean | |
| random.bin using bits 5 to 28 2.050 | |
| duplicate number number | |
| spacings observed expected | |
| 0 64. 67.668 | |
| 1 140. 135.335 | |
| 2 132. 135.335 | |
| 3 88. 90.224 | |
| 4 43. 45.112 | |
| 5 19. 18.045 | |
| 6 to INF 14. 8.282 | |
| Chisquare with 6 d.o.f. = 4.59 p-value= .403183 | |
| ::::::::::::::::::::::::::::::::::::::::: | |
| For a sample of size 500: mean | |
| random.bin using bits 6 to 29 1.918 | |
| duplicate number number | |
| spacings observed expected | |
| 0 77. 67.668 | |
| 1 136. 135.335 | |
| 2 131. 135.335 | |
| 3 90. 90.224 | |
| 4 46. 45.112 | |
| 5 14. 18.045 | |
| 6 to INF 6. 8.282 | |
| Chisquare with 6 d.o.f. = 2.98 p-value= .188967 | |
| ::::::::::::::::::::::::::::::::::::::::: | |
| For a sample of size 500: mean | |
| random.bin using bits 7 to 30 2.006 | |
| duplicate number number | |
| spacings observed expected | |
| 0 64. 67.668 | |
| 1 142. 135.335 | |
| 2 136. 135.335 | |
| 3 80. 90.224 | |
| 4 49. 45.112 | |
| 5 22. 18.045 | |
| 6 to INF 7. 8.282 | |
| Chisquare with 6 d.o.f. = 3.09 p-value= .202432 | |
| ::::::::::::::::::::::::::::::::::::::::: | |
| For a sample of size 500: mean | |
| random.bin using bits 8 to 31 1.972 | |
| duplicate number number | |
| spacings observed expected | |
| 0 71. 67.668 | |
| 1 132. 135.335 | |
| 2 145. 135.335 | |
| 3 80. 90.224 | |
| 4 46. 45.112 | |
| 5 19. 18.045 | |
| 6 to INF 7. 8.282 | |
| Chisquare with 6 d.o.f. = 2.36 p-value= .116355 | |
| ::::::::::::::::::::::::::::::::::::::::: | |
| For a sample of size 500: mean | |
| random.bin using bits 9 to 32 1.950 | |
| duplicate number number | |
| spacings observed expected | |
| 0 81. 67.668 | |
| 1 133. 135.335 | |
| 2 123. 135.335 | |
| 3 92. 90.224 | |
| 4 44. 45.112 | |
| 5 20. 18.045 | |
| 6 to INF 7. 8.282 | |
| Chisquare with 6 d.o.f. = 4.26 p-value= .359013 | |
| ::::::::::::::::::::::::::::::::::::::::: | |
| The 9 p-values were | |
| .347168 .782614 .840805 .310185 .403183 | |
| .188967 .202432 .116355 .359013 | |
| A KSTEST for the 9 p-values yields .684805 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: THE OVERLAPPING 5-PERMUTATION TEST :: | |
| :: This is the OPERM5 test. It looks at a sequence of one mill- :: | |
| :: ion 32-bit random integers. Each set of five consecutive :: | |
| :: integers can be in one of 120 states, for the 5! possible or- :: | |
| :: derings of five numbers. Thus the 5th, 6th, 7th,...numbers :: | |
| :: each provide a state. As many thousands of state transitions :: | |
| :: are observed, cumulative counts are made of the number of :: | |
| :: occurences of each state. Then the quadratic form in the :: | |
| :: weak inverse of the 120x120 covariance matrix yields a test :: | |
| :: equivalent to the likelihood ratio test that the 120 cell :: | |
| :: counts came from the specified (asymptotically) normal dis- :: | |
| :: tribution with the specified 120x120 covariance matrix (with :: | |
| :: rank 99). This version uses 1,000,000 integers, twice. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| OPERM5 test for file random.bin | |
| For a sample of 1,000,000 consecutive 5-tuples, | |
| chisquare for 99 degrees of freedom=108.450; p-value= .757608 | |
| OPERM5 test for file random.bin | |
| For a sample of 1,000,000 consecutive 5-tuples, | |
| chisquare for 99 degrees of freedom= 96.791; p-value= .455899 | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: This is the BINARY RANK TEST for 31x31 matrices. The leftmost :: | |
| :: 31 bits of 31 random integers from the test sequence are used :: | |
| :: to form a 31x31 binary matrix over the field {0,1}. The rank :: | |
| :: is determined. That rank can be from 0 to 31, but ranks< 28 :: | |
| :: are rare, and their counts are pooled with those for rank 28. :: | |
| :: Ranks are found for 40,000 such random matrices and a chisqua-:: | |
| :: re test is performed on counts for ranks 31,30,29 and <=28. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| Binary rank test for random.bin | |
| Rank test for 31x31 binary matrices: | |
| rows from leftmost 31 bits of each 32-bit integer | |
| rank observed expected (o-e)^2/e sum | |
| 28 211 211.4 .000826 .001 | |
| 29 5161 5134.0 .141886 .143 | |
| 30 23170 23103.0 .194032 .337 | |
| 31 11458 11551.5 .757200 1.094 | |
| chisquare= 1.094 for 3 d. of f.; p-value= .369264 | |
| -------------------------------------------------------------- | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: This is the BINARY RANK TEST for 32x32 matrices. A random 32x :: | |
| :: 32 binary matrix is formed, each row a 32-bit random integer. :: | |
| :: The rank is determined. That rank can be from 0 to 32, ranks :: | |
| :: less than 29 are rare, and their counts are pooled with those :: | |
| :: for rank 29. Ranks are found for 40,000 such random matrices :: | |
| :: and a chisquare test is performed on counts for ranks 32,31, :: | |
| :: 30 and <=29. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| Binary rank test for random.bin | |
| Rank test for 32x32 binary matrices: | |
| rows from leftmost 32 bits of each 32-bit integer | |
| rank observed expected (o-e)^2/e sum | |
| 29 201 211.4 .513367 .513 | |
| 30 5206 5134.0 1.009449 1.523 | |
| 31 23160 23103.0 .140400 1.663 | |
| 32 11433 11551.5 1.216120 2.879 | |
| chisquare= 2.879 for 3 d. of f.; p-value= .634256 | |
| -------------------------------------------------------------- | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: This is the BINARY RANK TEST for 6x8 matrices. From each of :: | |
| :: six random 32-bit integers from the generator under test, a :: | |
| :: specified byte is chosen, and the resulting six bytes form a :: | |
| :: 6x8 binary matrix whose rank is determined. That rank can be :: | |
| :: from 0 to 6, but ranks 0,1,2,3 are rare; their counts are :: | |
| :: pooled with those for rank 4. Ranks are found for 100,000 :: | |
| :: random matrices, and a chi-square test is performed on :: | |
| :: counts for ranks 6,5 and <=4. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| Binary Rank Test for random.bin | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 1 to 8 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 992 944.3 2.409 2.409 | |
| r =5 21985 21743.9 2.673 5.083 | |
| r =6 77023 77311.8 1.079 6.162 | |
| p=1-exp(-SUM/2)= .95408 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 2 to 9 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 939 944.3 .030 .030 | |
| r =5 21927 21743.9 1.542 1.572 | |
| r =6 77134 77311.8 .409 1.981 | |
| p=1-exp(-SUM/2)= .62852 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 3 to 10 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 953 944.3 .080 .080 | |
| r =5 21824 21743.9 .295 .375 | |
| r =6 77223 77311.8 .102 .477 | |
| p=1-exp(-SUM/2)= .21227 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 4 to 11 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 937 944.3 .056 .056 | |
| r =5 21832 21743.9 .357 .413 | |
| r =6 77231 77311.8 .084 .498 | |
| p=1-exp(-SUM/2)= .22037 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 5 to 12 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 915 944.3 .909 .909 | |
| r =5 21621 21743.9 .695 1.604 | |
| r =6 77464 77311.8 .300 1.903 | |
| p=1-exp(-SUM/2)= .61393 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 6 to 13 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 964 944.3 .411 .411 | |
| r =5 21851 21743.9 .528 .938 | |
| r =6 77185 77311.8 .208 1.146 | |
| p=1-exp(-SUM/2)= .43629 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 7 to 14 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 959 944.3 .229 .229 | |
| r =5 21806 21743.9 .177 .406 | |
| r =6 77235 77311.8 .076 .482 | |
| p=1-exp(-SUM/2)= .21434 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 8 to 15 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 935 944.3 .092 .092 | |
| r =5 21549 21743.9 1.747 1.839 | |
| r =6 77516 77311.8 .539 2.378 | |
| p=1-exp(-SUM/2)= .69546 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 9 to 16 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 932 944.3 .160 .160 | |
| r =5 21437 21743.9 4.332 4.492 | |
| r =6 77631 77311.8 1.318 5.810 | |
| p=1-exp(-SUM/2)= .94525 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 10 to 17 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 993 944.3 2.511 2.511 | |
| r =5 21427 21743.9 4.619 7.130 | |
| r =6 77580 77311.8 .930 8.060 | |
| p=1-exp(-SUM/2)= .98223 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 11 to 18 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 945 944.3 .001 .001 | |
| r =5 21702 21743.9 .081 .081 | |
| r =6 77353 77311.8 .022 .103 | |
| p=1-exp(-SUM/2)= .05030 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 12 to 19 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 950 944.3 .034 .034 | |
| r =5 21555 21743.9 1.641 1.675 | |
| r =6 77495 77311.8 .434 2.110 | |
| p=1-exp(-SUM/2)= .65173 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 13 to 20 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 963 944.3 .370 .370 | |
| r =5 21573 21743.9 1.343 1.713 | |
| r =6 77464 77311.8 .300 2.013 | |
| p=1-exp(-SUM/2)= .63452 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 14 to 21 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 959 944.3 .229 .229 | |
| r =5 21674 21743.9 .225 .454 | |
| r =6 77367 77311.8 .039 .493 | |
| p=1-exp(-SUM/2)= .21843 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 15 to 22 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 889 944.3 3.239 3.239 | |
| r =5 21563 21743.9 1.505 4.744 | |
| r =6 77548 77311.8 .722 5.465 | |
| p=1-exp(-SUM/2)= .93495 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 16 to 23 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 878 944.3 4.655 4.655 | |
| r =5 21991 21743.9 2.808 7.463 | |
| r =6 77131 77311.8 .423 7.886 | |
| p=1-exp(-SUM/2)= .98061 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 17 to 24 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 987 944.3 1.931 1.931 | |
| r =5 21967 21743.9 2.289 4.220 | |
| r =6 77046 77311.8 .914 5.134 | |
| p=1-exp(-SUM/2)= .92322 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 18 to 25 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 963 944.3 .370 .370 | |
| r =5 21960 21743.9 2.148 2.518 | |
| r =6 77077 77311.8 .713 3.231 | |
| p=1-exp(-SUM/2)= .80122 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 19 to 26 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 986 944.3 1.841 1.841 | |
| r =5 21861 21743.9 .631 2.472 | |
| r =6 77153 77311.8 .326 2.798 | |
| p=1-exp(-SUM/2)= .75318 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 20 to 27 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 922 944.3 .527 .527 | |
| r =5 21645 21743.9 .450 .977 | |
| r =6 77433 77311.8 .190 1.167 | |
| p=1-exp(-SUM/2)= .44192 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 21 to 28 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 896 944.3 2.471 2.471 | |
| r =5 21755 21743.9 .006 2.476 | |
| r =6 77349 77311.8 .018 2.494 | |
| p=1-exp(-SUM/2)= .71266 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 22 to 29 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 929 944.3 .248 .248 | |
| r =5 21755 21743.9 .006 .254 | |
| r =6 77316 77311.8 .000 .254 | |
| p=1-exp(-SUM/2)= .11919 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 23 to 30 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 898 944.3 2.270 2.270 | |
| r =5 21678 21743.9 .200 2.470 | |
| r =6 77424 77311.8 .163 2.633 | |
| p=1-exp(-SUM/2)= .73190 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 24 to 31 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 962 944.3 .332 .332 | |
| r =5 21686 21743.9 .154 .486 | |
| r =6 77352 77311.8 .021 .507 | |
| p=1-exp(-SUM/2)= .22384 | |
| Rank of a 6x8 binary matrix, | |
| rows formed from eight bits of the RNG random.bin | |
| b-rank test for bits 25 to 32 | |
| OBSERVED EXPECTED (O-E)^2/E SUM | |
| r<=4 928 944.3 .281 .281 | |
| r =5 21890 21743.9 .982 1.263 | |
| r =6 77182 77311.8 .218 1.481 | |
| p=1-exp(-SUM/2)= .52313 | |
| TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices | |
| These should be 25 uniform [0,1] random variables: | |
| .954077 .628519 .212272 .220366 .613930 | |
| .436290 .214336 .695462 .945246 .982229 | |
| .050296 .651731 .634522 .218434 .934951 | |
| .980610 .923221 .801217 .753177 .441921 | |
| .712661 .119193 .731902 .223842 .523125 | |
| brank test summary for random.bin | |
| The KS test for those 25 supposed UNI's yields | |
| KS p-value= .838396 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: THE BITSTREAM TEST :: | |
| :: The file under test is viewed as a stream of bits. Call them :: | |
| :: b1,b2,... . Consider an alphabet with two "letters", 0 and 1 :: | |
| :: and think of the stream of bits as a succession of 20-letter :: | |
| :: "words", overlapping. Thus the first word is b1b2...b20, the :: | |
| :: second is b2b3...b21, and so on. The bitstream test counts :: | |
| :: the number of missing 20-letter (20-bit) words in a string of :: | |
| :: 2^21 overlapping 20-letter words. There are 2^20 possible 20 :: | |
| :: letter words. For a truly random string of 2^21+19 bits, the :: | |
| :: number of missing words j should be (very close to) normally :: | |
| :: distributed with mean 141,909 and sigma 428. Thus :: | |
| :: (j-141909)/428 should be a standard normal variate (z score) :: | |
| :: that leads to a uniform [0,1) p value. The test is repeated :: | |
| :: twenty times. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| THE OVERLAPPING 20-tuples BITSTREAM TEST, 20 BITS PER WORD, N words | |
| This test uses N=2^21 and samples the bitstream 20 times. | |
| No. missing words should average 141909. with sigma=428. | |
| --------------------------------------------------------- | |
| tst no 1: 141995 missing words, .20 sigmas from mean, p-value= .57933 | |
| tst no 2: 141834 missing words, -.18 sigmas from mean, p-value= .43015 | |
| tst no 3: 142571 missing words, 1.55 sigmas from mean, p-value= .93894 | |
| tst no 4: 142079 missing words, .40 sigmas from mean, p-value= .65411 | |
| tst no 5: 142241 missing words, .77 sigmas from mean, p-value= .78081 | |
| tst no 6: 141772 missing words, -.32 sigmas from mean, p-value= .37416 | |
| tst no 7: 141768 missing words, -.33 sigmas from mean, p-value= .37062 | |
| tst no 8: 141415 missing words, -1.15 sigmas from mean, p-value= .12405 | |
| tst no 9: 142323 missing words, .97 sigmas from mean, p-value= .83311 | |
| tst no 10: 142288 missing words, .88 sigmas from mean, p-value= .81185 | |
| tst no 11: 142330 missing words, .98 sigmas from mean, p-value= .83717 | |
| tst no 12: 142406 missing words, 1.16 sigmas from mean, p-value= .87707 | |
| tst no 13: 141693 missing words, -.51 sigmas from mean, p-value= .30663 | |
| tst no 14: 142104 missing words, .45 sigmas from mean, p-value= .67539 | |
| tst no 15: 142240 missing words, .77 sigmas from mean, p-value= .78012 | |
| tst no 16: 142493 missing words, 1.36 sigmas from mean, p-value= .91367 | |
| tst no 17: 141980 missing words, .17 sigmas from mean, p-value= .56558 | |
| tst no 18: 142054 missing words, .34 sigmas from mean, p-value= .63233 | |
| tst no 19: 141953 missing words, .10 sigmas from mean, p-value= .54064 | |
| tst no 20: 142645 missing words, 1.72 sigmas from mean, p-value= .95718 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: The tests OPSO, OQSO and DNA :: | |
| :: OPSO means Overlapping-Pairs-Sparse-Occupancy :: | |
| :: The OPSO test considers 2-letter words from an alphabet of :: | |
| :: 1024 letters. Each letter is determined by a specified ten :: | |
| :: bits from a 32-bit integer in the sequence to be tested. OPSO :: | |
| :: generates 2^21 (overlapping) 2-letter words (from 2^21+1 :: | |
| :: "keystrokes") and counts the number of missing words---that :: | |
| :: is 2-letter words which do not appear in the entire sequence. :: | |
| :: That count should be very close to normally distributed with :: | |
| :: mean 141,909, sigma 290. Thus (missingwrds-141909)/290 should :: | |
| :: be a standard normal variable. The OPSO test takes 32 bits at :: | |
| :: a time from the test file and uses a designated set of ten :: | |
| :: consecutive bits. It then restarts the file for the next de- :: | |
| :: signated 10 bits, and so on. :: | |
| :: :: | |
| :: OQSO means Overlapping-Quadruples-Sparse-Occupancy :: | |
| :: The test OQSO is similar, except that it considers 4-letter :: | |
| :: words from an alphabet of 32 letters, each letter determined :: | |
| :: by a designated string of 5 consecutive bits from the test :: | |
| :: file, elements of which are assumed 32-bit random integers. :: | |
| :: The mean number of missing words in a sequence of 2^21 four- :: | |
| :: letter words, (2^21+3 "keystrokes"), is again 141909, with :: | |
| :: sigma = 295. The mean is based on theory; sigma comes from :: | |
| :: extensive simulation. :: | |
| :: :: | |
| :: The DNA test considers an alphabet of 4 letters:: C,G,A,T,:: | |
| :: determined by two designated bits in the sequence of random :: | |
| :: integers being tested. It considers 10-letter words, so that :: | |
| :: as in OPSO and OQSO, there are 2^20 possible words, and the :: | |
| :: mean number of missing words from a string of 2^21 (over- :: | |
| :: lapping) 10-letter words (2^21+9 "keystrokes") is 141909. :: | |
| :: The standard deviation sigma=339 was determined as for OQSO :: | |
| :: by simulation. (Sigma for OPSO, 290, is the true value (to :: | |
| :: three places), not determined by simulation. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| OPSO test for generator random.bin | |
| Output: No. missing words (mw), equiv normal variate (z), p-value (p) | |
| mw z p | |
| OPSO for random.bin using bits 23 to 32 142201 1.006 .8427 | |
| OPSO for random.bin using bits 22 to 31 142123 .737 .7694 | |
| OPSO for random.bin using bits 21 to 30 142244 1.154 .8758 | |
| OPSO for random.bin using bits 20 to 29 142086 .609 .7288 | |
| OPSO for random.bin using bits 19 to 28 141812 -.336 .3686 | |
| OPSO for random.bin using bits 18 to 27 141612 -1.025 .1526 | |
| OPSO for random.bin using bits 17 to 26 141383 -1.815 .0348 | |
| OPSO for random.bin using bits 16 to 25 141632 -.956 .1695 | |
| OPSO for random.bin using bits 15 to 24 142315 1.399 .9191 | |
| OPSO for random.bin using bits 14 to 23 142417 1.751 .9600 | |
| OPSO for random.bin using bits 13 to 22 141542 -1.267 .1026 | |
| OPSO for random.bin using bits 12 to 21 141941 .109 .5435 | |
| OPSO for random.bin using bits 11 to 20 142110 .692 .7555 | |
| OPSO for random.bin using bits 10 to 19 141738 -.591 .2773 | |
| OPSO for random.bin using bits 9 to 18 141905 -.015 .4940 | |
| OPSO for random.bin using bits 8 to 17 141667 -.836 .2017 | |
| OPSO for random.bin using bits 7 to 16 142092 .630 .7356 | |
| OPSO for random.bin using bits 6 to 15 141956 .161 .5639 | |
| OPSO for random.bin using bits 5 to 14 141855 -.187 .4257 | |
| OPSO for random.bin using bits 4 to 13 141735 -.601 .2739 | |
| OPSO for random.bin using bits 3 to 12 141840 -.239 .4055 | |
| OPSO for random.bin using bits 2 to 11 142051 .489 .6874 | |
| OPSO for random.bin using bits 1 to 10 141442 -1.611 .0535 | |
| OQSO test for generator random.bin | |
| Output: No. missing words (mw), equiv normal variate (z), p-value (p) | |
| mw z p | |
| OQSO for random.bin using bits 28 to 32 141832 -.262 .3966 | |
| OQSO for random.bin using bits 27 to 31 142033 .419 .6625 | |
| OQSO for random.bin using bits 26 to 30 141688 -.750 .2265 | |
| OQSO for random.bin using bits 25 to 29 141687 -.754 .2255 | |
| OQSO for random.bin using bits 24 to 28 141827 -.279 .3901 | |
| OQSO for random.bin using bits 23 to 27 141717 -.652 .2572 | |
| OQSO for random.bin using bits 22 to 26 141682 -.771 .2205 | |
| OQSO for random.bin using bits 21 to 25 141735 -.591 .2773 | |
| OQSO for random.bin using bits 20 to 24 142287 1.280 .8998 | |
| OQSO for random.bin using bits 19 to 23 142117 .704 .7593 | |
| OQSO for random.bin using bits 18 to 22 141880 -.099 .4604 | |
| OQSO for random.bin using bits 17 to 21 141470 -1.489 .0682 | |
| OQSO for random.bin using bits 16 to 20 141703 -.699 .2421 | |
| OQSO for random.bin using bits 15 to 19 141866 -.147 .4416 | |
| OQSO for random.bin using bits 14 to 18 141690 -.743 .2286 | |
| OQSO for random.bin using bits 13 to 17 141980 .240 .5947 | |
| OQSO for random.bin using bits 12 to 16 141862 -.160 .4363 | |
| OQSO for random.bin using bits 11 to 15 141769 -.476 .3171 | |
| OQSO for random.bin using bits 10 to 14 141295 -2.082 .0186 | |
| OQSO for random.bin using bits 9 to 13 142181 .921 .8215 | |
| OQSO for random.bin using bits 8 to 12 141771 -.469 .3196 | |
| OQSO for random.bin using bits 7 to 11 141703 -.699 .2421 | |
| OQSO for random.bin using bits 6 to 10 141898 -.038 .4847 | |
| OQSO for random.bin using bits 5 to 9 141493 -1.411 .0791 | |
| OQSO for random.bin using bits 4 to 8 142413 1.707 .9561 | |
| OQSO for random.bin using bits 3 to 7 141883 -.089 .4644 | |
| OQSO for random.bin using bits 2 to 6 142038 .436 .6686 | |
| OQSO for random.bin using bits 1 to 5 141559 -1.188 .1175 | |
| DNA test for generator random.bin | |
| Output: No. missing words (mw), equiv normal variate (z), p-value (p) | |
| mw z p | |
| DNA for random.bin using bits 31 to 32 142018 .321 .6257 | |
| DNA for random.bin using bits 30 to 31 141234 -1.992 .0232 | |
| DNA for random.bin using bits 29 to 30 141567 -1.010 .1563 | |
| DNA for random.bin using bits 28 to 29 141759 -.443 .3287 | |
| DNA for random.bin using bits 27 to 28 142071 .477 .6833 | |
| DNA for random.bin using bits 26 to 27 141978 .203 .5803 | |
| DNA for random.bin using bits 25 to 26 141910 .002 .5008 | |
| DNA for random.bin using bits 24 to 25 142161 .742 .7711 | |
| DNA for random.bin using bits 23 to 24 141999 .265 .6043 | |
| DNA for random.bin using bits 22 to 23 142021 .329 .6291 | |
| DNA for random.bin using bits 21 to 22 142059 .442 .6706 | |
| DNA for random.bin using bits 20 to 21 141822 -.258 .3984 | |
| DNA for random.bin using bits 19 to 20 141862 -.140 .4445 | |
| DNA for random.bin using bits 18 to 19 141934 .073 .5290 | |
| DNA for random.bin using bits 17 to 18 142627 2.117 .9829 | |
| DNA for random.bin using bits 16 to 17 141617 -.862 .1943 | |
| DNA for random.bin using bits 15 to 16 142001 .270 .6066 | |
| DNA for random.bin using bits 14 to 15 141527 -1.128 .1297 | |
| DNA for random.bin using bits 13 to 14 141582 -.966 .1671 | |
| DNA for random.bin using bits 12 to 13 142042 .391 .6522 | |
| DNA for random.bin using bits 11 to 12 141798 -.328 .3713 | |
| DNA for random.bin using bits 10 to 11 142672 2.250 .9878 | |
| DNA for random.bin using bits 9 to 10 141514 -1.166 .1218 | |
| DNA for random.bin using bits 8 to 9 142654 2.197 .9860 | |
| DNA for random.bin using bits 7 to 8 142509 1.769 .9615 | |
| DNA for random.bin using bits 6 to 7 141610 -.883 .1886 | |
| DNA for random.bin using bits 5 to 6 141894 -.045 .4820 | |
| DNA for random.bin using bits 4 to 5 142311 1.185 .8820 | |
| DNA for random.bin using bits 3 to 4 141909 -.001 .4996 | |
| DNA for random.bin using bits 2 to 3 141822 -.258 .3984 | |
| DNA for random.bin using bits 1 to 2 142160 .739 .7702 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: This is the COUNT-THE-1's TEST on a stream of bytes. :: | |
| :: Consider the file under test as a stream of bytes (four per :: | |
| :: 32 bit integer). Each byte can contain from 0 to 8 1's, :: | |
| :: with probabilities 1,8,28,56,70,56,28,8,1 over 256. Now let :: | |
| :: the stream of bytes provide a string of overlapping 5-letter :: | |
| :: words, each "letter" taking values A,B,C,D,E. The letters are :: | |
| :: determined by the number of 1's in a byte:: 0,1,or 2 yield A,:: | |
| :: 3 yields B, 4 yields C, 5 yields D and 6,7 or 8 yield E. Thus :: | |
| :: we have a monkey at a typewriter hitting five keys with vari- :: | |
| :: ous probabilities (37,56,70,56,37 over 256). There are 5^5 :: | |
| :: possible 5-letter words, and from a string of 256,000 (over- :: | |
| :: lapping) 5-letter words, counts are made on the frequencies :: | |
| :: for each word. The quadratic form in the weak inverse of :: | |
| :: the covariance matrix of the cell counts provides a chisquare :: | |
| :: test:: Q5-Q4, the difference of the naive Pearson sums of :: | |
| :: (OBS-EXP)^2/EXP on counts for 5- and 4-letter cell counts. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| Test results for random.bin | |
| Chi-square with 5^5-5^4=2500 d.of f. for sample size:2560000 | |
| chisquare equiv normal p-value | |
| Results fo COUNT-THE-1's in successive bytes: | |
| byte stream for random.bin 2527.13 .384 .649382 | |
| byte stream for random.bin 2567.96 .961 .831761 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: This is the COUNT-THE-1's TEST for specific bytes. :: | |
| :: Consider the file under test as a stream of 32-bit integers. :: | |
| :: From each integer, a specific byte is chosen , say the left- :: | |
| :: most:: bits 1 to 8. Each byte can contain from 0 to 8 1's, :: | |
| :: with probabilitie 1,8,28,56,70,56,28,8,1 over 256. Now let :: | |
| :: the specified bytes from successive integers provide a string :: | |
| :: of (overlapping) 5-letter words, each "letter" taking values :: | |
| :: A,B,C,D,E. The letters are determined by the number of 1's, :: | |
| :: in that byte:: 0,1,or 2 ---> A, 3 ---> B, 4 ---> C, 5 ---> D,:: | |
| :: and 6,7 or 8 ---> E. Thus we have a monkey at a typewriter :: | |
| :: hitting five keys with with various probabilities:: 37,56,70,:: | |
| :: 56,37 over 256. There are 5^5 possible 5-letter words, and :: | |
| :: from a string of 256,000 (overlapping) 5-letter words, counts :: | |
| :: are made on the frequencies for each word. The quadratic form :: | |
| :: in the weak inverse of the covariance matrix of the cell :: | |
| :: counts provides a chisquare test:: Q5-Q4, the difference of :: | |
| :: the naive Pearson sums of (OBS-EXP)^2/EXP on counts for 5- :: | |
| :: and 4-letter cell counts. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| Chi-square with 5^5-5^4=2500 d.of f. for sample size: 256000 | |
| chisquare equiv normal p value | |
| Results for COUNT-THE-1's in specified bytes: | |
| bits 1 to 8 2482.01 -.254 .399574 | |
| bits 2 to 9 2342.85 -2.222 .013127 | |
| bits 3 to 10 2413.19 -1.228 .109785 | |
| bits 4 to 11 2505.58 .079 .531458 | |
| bits 5 to 12 2584.23 1.191 .883199 | |
| bits 6 to 13 2506.29 .089 .535469 | |
| bits 7 to 14 2502.65 .037 .514937 | |
| bits 8 to 15 2483.86 -.228 .409749 | |
| bits 9 to 16 2458.99 -.580 .280954 | |
| bits 10 to 17 2555.30 .782 .782930 | |
| bits 11 to 18 2549.75 .704 .759151 | |
| bits 12 to 19 2589.73 1.269 .897773 | |
| bits 13 to 20 2614.83 1.624 .947809 | |
| bits 14 to 21 2517.38 .246 .597064 | |
| bits 15 to 22 2513.09 .185 .573439 | |
| bits 16 to 23 2508.87 .125 .549933 | |
| bits 17 to 24 2381.56 -1.675 .046972 | |
| bits 18 to 25 2498.22 -.025 .489966 | |
| bits 19 to 26 2495.24 -.067 .473146 | |
| bits 20 to 27 2521.61 .306 .620075 | |
| bits 21 to 28 2618.16 1.671 .952638 | |
| bits 22 to 29 2557.98 .820 .793892 | |
| bits 23 to 30 2449.60 -.713 .237995 | |
| bits 24 to 31 2477.11 -.324 .373098 | |
| bits 25 to 32 2573.74 1.043 .851478 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: THIS IS A PARKING LOT TEST :: | |
| :: In a square of side 100, randomly "park" a car---a circle of :: | |
| :: radius 1. Then try to park a 2nd, a 3rd, and so on, each :: | |
| :: time parking "by ear". That is, if an attempt to park a car :: | |
| :: causes a crash with one already parked, try again at a new :: | |
| :: random location. (To avoid path problems, consider parking :: | |
| :: helicopters rather than cars.) Each attempt leads to either :: | |
| :: a crash or a success, the latter followed by an increment to :: | |
| :: the list of cars already parked. If we plot n: the number of :: | |
| :: attempts, versus k:: the number successfully parked, we get a:: | |
| :: curve that should be similar to those provided by a perfect :: | |
| :: random number generator. Theory for the behavior of such a :: | |
| :: random curve seems beyond reach, and as graphics displays are :: | |
| :: not available for this battery of tests, a simple characteriz :: | |
| :: ation of the random experiment is used: k, the number of cars :: | |
| :: successfully parked after n=12,000 attempts. Simulation shows :: | |
| :: that k should average 3523 with sigma 21.9 and is very close :: | |
| :: to normally distributed. Thus (k-3523)/21.9 should be a st- :: | |
| :: andard normal variable, which, converted to a uniform varia- :: | |
| :: ble, provides input to a KSTEST based on a sample of 10. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| CDPARK: result of ten tests on file random.bin | |
| Of 12,000 tries, the average no. of successes | |
| should be 3523 with sigma=21.9 | |
| Successes: 3530 z-score: .320 p-value: .625377 | |
| Successes: 3509 z-score: -.639 p-value: .261324 | |
| Successes: 3521 z-score: -.091 p-value: .463618 | |
| Successes: 3466 z-score: -2.603 p-value: .004624 | |
| Successes: 3522 z-score: -.046 p-value: .481790 | |
| Successes: 3517 z-score: -.274 p-value: .392053 | |
| Successes: 3548 z-score: 1.142 p-value: .873180 | |
| Successes: 3526 z-score: .137 p-value: .554479 | |
| Successes: 3551 z-score: 1.279 p-value: .899470 | |
| Successes: 3533 z-score: .457 p-value: .676028 | |
| square size avg. no. parked sample sigma | |
| 100. 3522.300 22.457 | |
| KSTEST for the above 10: p= .266079 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: THE MINIMUM DISTANCE TEST :: | |
| :: It does this 100 times:: choose n=8000 random points in a :: | |
| :: square of side 10000. Find d, the minimum distance between :: | |
| :: the (n^2-n)/2 pairs of points. If the points are truly inde- :: | |
| :: pendent uniform, then d^2, the square of the minimum distance :: | |
| :: should be (very close to) exponentially distributed with mean :: | |
| :: .995 . Thus 1-exp(-d^2/.995) should be uniform on [0,1) and :: | |
| :: a KSTEST on the resulting 100 values serves as a test of uni- :: | |
| :: formity for random points in the square. Test numbers=0 mod 5 :: | |
| :: are printed but the KSTEST is based on the full set of 100 :: | |
| :: random choices of 8000 points in the 10000x10000 square. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| This is the MINIMUM DISTANCE test | |
| for random integers in the file random.bin | |
| Sample no. d^2 avg equiv uni | |
| 5 1.9790 2.1369 .863166 | |
| 10 .5505 1.4008 .424959 | |
| 15 .3998 1.2303 .330862 | |
| 20 1.5178 1.2251 .782471 | |
| 25 2.7155 1.3062 .934722 | |
| 30 2.0228 1.1854 .869057 | |
| 35 .4750 1.1153 .379576 | |
| 40 1.3005 1.1325 .729392 | |
| 45 .4269 1.0846 .348848 | |
| 50 1.5156 1.1285 .781986 | |
| 55 .6288 1.1075 .468451 | |
| 60 2.0025 1.1368 .866357 | |
| 65 1.4711 1.1256 .772020 | |
| 70 .7313 1.0652 .520493 | |
| 75 .3194 1.0348 .274557 | |
| 80 2.3196 1.0481 .902824 | |
| 85 3.7112 1.0580 .976004 | |
| 90 .2516 1.0562 .223399 | |
| 95 .6092 1.0361 .457874 | |
| 100 1.4253 1.0534 .761275 | |
| MINIMUM DISTANCE TEST for random.bin | |
| Result of KS test on 20 transformed mindist^2's: | |
| p-value= .493300 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: THE 3DSPHERES TEST :: | |
| :: Choose 4000 random points in a cube of edge 1000. At each :: | |
| :: point, center a sphere large enough to reach the next closest :: | |
| :: point. Then the volume of the smallest such sphere is (very :: | |
| :: close to) exponentially distributed with mean 120pi/3. Thus :: | |
| :: the radius cubed is exponential with mean 30. (The mean is :: | |
| :: obtained by extensive simulation). The 3DSPHERES test gener- :: | |
| :: ates 4000 such spheres 20 times. Each min radius cubed leads :: | |
| :: to a uniform variable by means of 1-exp(-r^3/30.), then a :: | |
| :: KSTEST is done on the 20 p-values. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| The 3DSPHERES test for file random.bin | |
| sample no: 1 r^3= 2.839 p-value= .09029 | |
| sample no: 2 r^3= 49.939 p-value= .81074 | |
| sample no: 3 r^3= 1.968 p-value= .06348 | |
| sample no: 4 r^3= 7.360 p-value= .21756 | |
| sample no: 5 r^3= 22.772 p-value= .53189 | |
| sample no: 6 r^3= 24.316 p-value= .55537 | |
| sample no: 7 r^3= 45.656 p-value= .78170 | |
| sample no: 8 r^3= 30.042 p-value= .63263 | |
| sample no: 9 r^3= 5.317 p-value= .16243 | |
| sample no: 10 r^3= 6.664 p-value= .19918 | |
| sample no: 11 r^3= 41.088 p-value= .74579 | |
| sample no: 12 r^3= 5.903 p-value= .17863 | |
| sample no: 13 r^3= 48.696 p-value= .80273 | |
| sample no: 14 r^3= 22.822 p-value= .53268 | |
| sample no: 15 r^3= 6.985 p-value= .20771 | |
| sample no: 16 r^3= 29.169 p-value= .62179 | |
| sample no: 17 r^3= 19.812 p-value= .48336 | |
| sample no: 18 r^3= 9.162 p-value= .26317 | |
| sample no: 19 r^3= 26.759 p-value= .59015 | |
| sample no: 20 r^3= 47.072 p-value= .79176 | |
| A KS test is applied to those 20 p-values. | |
| --------------------------------------------------------- | |
| 3DSPHERES test for file random.bin p-value= .492809 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: This is the SQEEZE test :: | |
| :: Random integers are floated to get uniforms on [0,1). Start- :: | |
| :: ing with k=2^31=2147483647, the test finds j, the number of :: | |
| :: iterations necessary to reduce k to 1, using the reduction :: | |
| :: k=ceiling(k*U), with U provided by floating integers from :: | |
| :: the file being tested. Such j's are found 100,000 times, :: | |
| :: then counts for the number of times j was <=6,7,...,47,>=48 :: | |
| :: are used to provide a chi-square test for cell frequencies. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| RESULTS OF SQUEEZE TEST FOR random.bin | |
| Table of standardized frequency counts | |
| ( (obs-exp)/sqrt(exp) )^2 | |
| for j taking values <=6,7,8,...,47,>=48: | |
| -.8 .1 -.8 -.8 .5 .6 | |
| 1.1 -1.0 .4 .1 -.4 -1.4 | |
| 1.1 .6 1.2 .3 -1.6 .8 | |
| .8 .9 -1.0 -.9 -.3 -2.1 | |
| 1.8 -1.6 .8 .7 -1.0 1.4 | |
| -2.1 2.3 -.3 -1.2 -.2 -.5 | |
| .0 .5 .1 -.1 1.6 -1.0 | |
| -.1 | |
| Chi-square with 42 degrees of freedom: 46.312 | |
| z-score= .470 p-value= .701241 | |
| ______________________________________________________________ | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: The OVERLAPPING SUMS test :: | |
| :: Integers are floated to get a sequence U(1),U(2),... of uni- :: | |
| :: form [0,1) variables. Then overlapping sums, :: | |
| :: S(1)=U(1)+...+U(100), S2=U(2)+...+U(101),... are formed. :: | |
| :: The S's are virtually normal with a certain covariance mat- :: | |
| :: rix. A linear transformation of the S's converts them to a :: | |
| :: sequence of independent standard normals, which are converted :: | |
| :: to uniform variables for a KSTEST. The p-values from ten :: | |
| :: KSTESTs are given still another KSTEST. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| Test no. 1 p-value .652326 | |
| Test no. 2 p-value .783967 | |
| Test no. 3 p-value .067778 | |
| Test no. 4 p-value .649611 | |
| Test no. 5 p-value .692736 | |
| Test no. 6 p-value .598217 | |
| Test no. 7 p-value .268917 | |
| Test no. 8 p-value .863340 | |
| Test no. 9 p-value .084200 | |
| Test no. 10 p-value .532075 | |
| Results of the OSUM test for random.bin | |
| KSTEST on the above 10 p-values: .274531 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: This is the RUNS test. It counts runs up, and runs down, :: | |
| :: in a sequence of uniform [0,1) variables, obtained by float- :: | |
| :: ing the 32-bit integers in the specified file. This example :: | |
| :: shows how runs are counted: .123,.357,.789,.425,.224,.416,.95:: | |
| :: contains an up-run of length 3, a down-run of length 2 and an :: | |
| :: up-run of (at least) 2, depending on the next values. The :: | |
| :: covariance matrices for the runs-up and runs-down are well :: | |
| :: known, leading to chisquare tests for quadratic forms in the :: | |
| :: weak inverses of the covariance matrices. Runs are counted :: | |
| :: for sequences of length 10,000. This is done ten times. Then :: | |
| :: repeated. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| The RUNS test for file random.bin | |
| Up and down runs in a sample of 10000 | |
| _________________________________________________ | |
| Run test for random.bin : | |
| runs up; ks test for 10 p's: .074944 | |
| runs down; ks test for 10 p's: .396186 | |
| Run test for random.bin : | |
| runs up; ks test for 10 p's: .825835 | |
| runs down; ks test for 10 p's: .742302 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| :: This is the CRAPS TEST. It plays 200,000 games of craps, finds:: | |
| :: the number of wins and the number of throws necessary to end :: | |
| :: each game. The number of wins should be (very close to) a :: | |
| :: normal with mean 200000p and variance 200000p(1-p), with :: | |
| :: p=244/495. Throws necessary to complete the game can vary :: | |
| :: from 1 to infinity, but counts for all>21 are lumped with 21. :: | |
| :: A chi-square test is made on the no.-of-throws cell counts. :: | |
| :: Each 32-bit integer from the test file provides the value for :: | |
| :: the throw of a die, by floating to [0,1), multiplying by 6 :: | |
| :: and taking 1 plus the integer part of the result. :: | |
| ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | |
| Results of craps test for random.bin | |
| No. of wins: Observed Expected | |
| 98531 98585.86 | |
| 98531= No. of wins, z-score= -.245 pvalue= .40309 | |
| Analysis of Throws-per-Game: | |
| Chisq= 15.90 for 20 degrees of freedom, p= .27739 | |
| Throws Observed Expected Chisq Sum | |
| 1 66488 66666.7 .479 .479 | |
| 2 37588 37654.3 .117 .596 | |
| 3 27256 26954.7 3.367 3.963 | |
| 4 19320 19313.5 .002 3.965 | |
| 5 13675 13851.4 2.247 6.212 | |
| 6 9966 9943.5 .051 6.263 | |
| 7 7095 7145.0 .350 6.613 | |
| 8 5224 5139.1 1.404 8.017 | |
| 9 3726 3699.9 .185 8.201 | |
| 10 2666 2666.3 .000 8.201 | |
| 11 1869 1923.3 1.535 9.736 | |
| 12 1377 1388.7 .099 9.835 | |
| 13 1026 1003.7 .495 10.330 | |
| 14 767 726.1 2.299 12.629 | |
| 15 550 525.8 1.110 13.740 | |
| 16 382 381.2 .002 13.741 | |
| 17 276 276.5 .001 13.742 | |
| 18 210 200.8 .419 14.161 | |
| 19 149 146.0 .062 14.223 | |
| 20 94 106.2 1.405 15.628 | |
| 21 296 287.1 .275 15.903 | |
| SUMMARY FOR random.bin | |
| p-value for no. of wins: .403088 | |
| p-value for throws/game: .277389 | |
| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ | |
| Results of DIEHARD battery of tests sent to file random.log |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment