Computational Efficiency of Box-Muller and Polar Method
Using Monte-Carlo Application
by : Joy V. Lorin-Picar
Davao del Norte State College, New Visayas, Panabo City
The efficiency of Mean Square Error (MSE) of the random normal variables generated from both the Marsaglia Polar Method and Box-Muller Method was examined for small and large n with Monte-Carlo application using MATHLAB. The empirical results showed that MSE of the random normal variables using the Marsaglia Polar Method approaches zero as n becomes larger.
Moreover, when run in MATHLAB, the Box-Muller method encountered some problems like: a) it runs slow in generating its MSE because of many calls to the math library; b) it has numerical stability problems when x1 is very close to zero; as a consequence of b, as n becomes large, there are serious problems if you are doing stochastic modeling and generating millions of numbers. Apparently, the Polar Method computes the MSE faster even when n is large, since it does the equivalent of the sine and cosine geometrically without a call to the trigonometric function library.
Keywords: Mean Square Error (MSE), Marsaglia Polar Method, Box-Muller Method, Monte-Carlo application
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