Generate Elliptical Distribution from Box-Muller Transform

In summary, the Box-Muller transform can be used to generate a distribution with two different standard deviations, and can also be used to transform a standard normal distribution into a distribution with a specified mean and standard deviation. This can be helpful for generating random variables with specific properties, such as generating an elliptical distribution on the x/y plane. Pseudo code can be used to illustrate this process.
  • #1
ireland01
17
0
Can i use box muller transform to generate a distribution with two different sigma (i.e. sigma_x and sigma_y)?

I want to generate a random gaussian angle (C) relative to z axis on circle plane, then set the angle relative to the x, A and y axis, B, wrt to the original angle.
However, I want the output to be elliptical on x/y plane...

Some pseudo code would help.
 
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  • #2
If X is normal with zero mean and std dev = 1, then you can transform it into a random variable Z with mean u and std dev sigma as follows:

Z = sigma*X + u

The Box-Muller transform gives you two random variables which are standard normally distributed iirc, so just apply the above transformation to each.
 

1. What is the Box-Muller Transform?

The Box-Muller Transform is a mathematical method used to convert a set of uniformly distributed random numbers into a set of normally distributed random numbers. It is commonly used in statistics and probability theory.

2. How does the Box-Muller Transform work?

The Box-Muller Transform works by taking a pair of uniformly distributed random numbers and using them to generate a pair of normally distributed random numbers. This is done using trigonometric functions and the properties of the normal distribution.

3. What is an elliptical distribution?

An elliptical distribution is a type of probability distribution that is characterized by its shape, which resembles an ellipse. It is a generalization of the normal distribution and can take on a variety of shapes depending on its parameters.

4. Why is the Box-Muller Transform used to generate an elliptical distribution?

The Box-Muller Transform is used to generate an elliptical distribution because it is a convenient and efficient method for converting uniformly distributed random numbers into normally distributed random numbers. Since the elliptical distribution is a generalization of the normal distribution, the Box-Muller Transform is well-suited for this task.

5. Can the Box-Muller Transform be used to generate other types of distributions?

Yes, the Box-Muller Transform can be used to generate other types of distributions besides elliptical distributions. It can be used to generate any type of distribution that can be expressed as a function of the normal distribution, such as log-normal, chi-squared, and exponential distributions.

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