# Learning Center

SAFE TOOLBOXES® comes with three high-quality random number generators (Mersenne Twister, RanLux and Generalized Feedback Shift Register Generator), two low discrepancy sequences (Fauré and Halton) and one procedure to generate alternate uniform random numbers (antithetic simulation).

The usage of uniform number generators is at the core of running Monte Carlo Simulations. By using the appropriate uniform random number generator you can do a variety of things, such as:

• create a replicated experiment
• increase the results precision
• draw random numbers for other distributions
• generate multivariate random numbers

Some usages of uniform random number generators can be seen in the following examples: A B C D 1 Sample from a normal distribution 0.49 =sRAND_Normal(0,1) 2 Sample from a normal distribution using RanLux uniform random generator with a seed number 123 -1.32 =sRAND_Normal(0,1, sRAND_Uniform_RanLuxHighQuality(123)) 3 Sample from a normal distribution using a Halton Sequence 1.25 =sRAND_Normal(0,1, sRAND_Uniform_HaltonSequence(1,1000)) 4 Sample from a normal distribution using an antithetic uniform number 0.49 =sRAND_Normal(0,1, sRAND_Uniform_Antithetic(1000)) 5 Sample from a bivariate normal distribution with a correlation of 0.5. -0.55 =sRAND_Normal (0,1,B8) 6 -0.30 =sRAND_Normal (0,1,C8) 7 8 Uniform correlated random numbers. 0.35 0.22 9 ={sRAND_Uniform_Correlated(B10:C11)} Note: After entering this formula, click on the MVF button. 10 Correlation matrix 1 0.5 11 0.5 1

Please note that sequentially generated uniform numbers - as numbers generated using a seed or low discrepancy sequences - can be restarted using the clear memory button .