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Math Help - Monte Carlo's Simulation

  1. #1
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    Monte Carlo's Simulation

    How do I use Monte Carlo's simulation to approximate part of the ellipsoid X^2/2+y^2/4+z^2/8=16, that lies in the first octant x>0,y>0,z>0?
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  2. #2
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    Quote Originally Posted by herbalist View Post
    How do I use Monte Carlo's simulation to approximate part of the ellipsoid X^2/2+y^2/4+z^2/8=16, that lies in the first octant x>0,y>0,z>0?
    Rejection sampling:

    Generate a point (x,y,z) uniformly distributed over [0,\sqrt{32}]\times[0,8]\times[0,\sqrt{128}] accept this point if:

    \frac{x^2}{2}+\frac{y^2}{4}+\frac{z^2}{8}\le 16

    If not accepted repeat until an acceped point is found

    The resultant (x,y,z) is uniformly distributed over the required ellipsoid.

    The efficiency of this process is \approx 0.507 which means the volume of the ellipsoid in the first octant is \approx 0.507 of the volume of [0,\sqrt{32}]\times[0,8]\times[0,\sqrt{128}]

    CB
    Last edited by CaptainBlack; May 19th 2010 at 02:35 AM.
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