Computational Efficiency of Polar and Box Muller Method: Using Monte Carlo Application

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CATEGORY: APPLIED MATHEMATICS Computational Efficiency of Box-Muller and Polar Method Using Monte-Carlo Application by : Joy V. Lorin-Picar Mathematics Department Davao del Norte State College, New Visayas, Panabo City ABSTRACT 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…show more content…
The derivation is based on the fact that, in a two-dimensional cartesian system where X and Y coordinates are described by two independent and normally distributed random variables, the random variables for R2 and Θ in the corresponding polar coordinates are also independent and can be expressed as and C. Marsaglia Polar Method The Marsaglia Polar Method is a method for generating a pair of independent standard normal random variables by choosing random points (x, y) in the square −1 < x < 1, −1 < y < 1 until which returns the required pair of normal random variables as If u is uniformly distributed in the interval 0 ≤ u < 1, then the point (cos(2πu), sin(2πu)) is uniformly distributed on the unit circumference x2 + y2 = 1, and multiplying that point by an independent random variable ρ whose distribution is will produce a point whose coordinates are jointly distributed as two independent standard normal random variables. The polar form takes two samples from a different interval, [−1, +1], and maps them to two normally distributed samples without the use of sine or cosine functions. Two uniformly distributed values, u and v are used to produce the value s = R2, which is likewise uniformly distributed. This polar form is attributed by Devroye[1] to Marsaglia. It is also mentioned without attribution in Carter.[2] Given u and v, independent and uniformly

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