Microsoft Windows* 8

Saving and Restoring Random Streams

Typically, to get one more correct decimal digit in Monte Carlo, you need to increase the sample by the factor of 100. That makes Monte Carlo applications computationally expensive. Some of them take days or weeks while others may take several months of computations. For such applications, saving intermediate results to a file is essential to be able to continue computation using that result in case the application is terminated intentionally or abnormally.

Acceptance/Rejection

The cumulative distribution functions and their inverses may often be much more complex computationally than the probability density function (for continuous distributions) and the probability mass function (for discrete distributions).

Special Properties

To improve the efficiency of the algorithms based on the general methods described above, you may have to use special properties of distributions. For example, use of polar coordinates for a pair of independent normal variates enables you to develop an efficient method of random number generation based on 2D inverse transformation known as the Box-Muller method:

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