Random Number Generator
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This document describes two random number generation algorithms: 1. The mid-square method, which squares a seed number and takes the middle digits as the next number. 2. The modified mod-square method, which squares the seed, sums the removed higher and lower order digits to the middle digits, and squares that number to generate the next random number. The document provides examples of both methods and compares their statistical test results to analyze the randomness of the generated numbers.
Random Number Generator
- 2. Starting with an n digit number, squaring it and taking the n digit in the middle as the next number, which is then squared to obtain the next number. E.g.: Seed= 5673, Square= 32182929. 1829² = 3345241…
- 3. Converge on a constant. • Seed= 2500, Square= 6250000, 2500, 2500… • Seed= 2504, Square= 6270016, 2700²= 7290000, 2900²= 8410000…
- 4. Starting with an n digit number, squaring it and taking the n digit in the middle as the random number. For the next seed, add the removing higher order and lower order digits to the middle n digit number (random number), which is then squared to obtain the next number.
- 5. Seed, X0= 5673. 5673²= 32182929. X1= 1829+3+2+2+9= 1845. 1845²= 3404025. X2= 4040+3+2+5= 4050. 4050²= 16402500. X3= 4025+ 1+6= 4032. Random Numbers= 1829, 4040, 4025, 2570…
- 6. Seed, X0= 5673 MID-SQUARE Modified MOD-SQUARE KS Test, D= 0.2536 KS Test, D= 0.3282 Chi-Square, X²0= 5.29 Chi-Square, X²0= 5.31 Runs Up & Down, Z= - Runs Up & Down, Z= 0.366 0.188 Runs above & Below Runs above & Below mean, Z=0.844 mean, Z= -0.161