2.1 The Polar Method If X and Y are independent standard normal random variables, then the po- lar coordinates, R and are also random variables. From Equation (7), the probability density function for R is f(r) = re-r²; r≥ 0 (8) So observations of R can be generated using the Inverse Cumulative Method. The corresponding observations for are even easier to generate: is uniformly distributed on the interval [0, 27]. Then one can generate a pairs (X,Y) of independent standard normal random variables via: Rcos() Y = Rsin(0) X - (10)
2.1 The Polar Method If X and Y are independent standard normal random variables, then the po- lar coordinates, R and are also random variables. From Equation (7), the probability density function for R is f(r) = re-r²; r≥ 0 (8) So observations of R can be generated using the Inverse Cumulative Method. The corresponding observations for are even easier to generate: is uniformly distributed on the interval [0, 27]. Then one can generate a pairs (X,Y) of independent standard normal random variables via: Rcos() Y = Rsin(0) X - (10)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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