Generate Elliptical Distribution from Box-Muller Transform

  • Context: Graduate 
  • Thread starter Thread starter ireland01
  • Start date Start date
  • Tags Tags
    Box Transform
Click For Summary
SUMMARY

The Box-Muller Transform can be effectively utilized to generate an elliptical distribution by applying different standard deviations (sigma_x and sigma_y) to the two output variables. By transforming standard normally distributed variables into a random variable Z with a specified mean (u) and standard deviation (sigma), one can achieve the desired elliptical shape on the x/y plane. The transformation can be expressed as Z = sigma*X + u, where X is the standard normal variable generated by the Box-Muller method.

PREREQUISITES
  • Understanding of the Box-Muller Transform
  • Familiarity with Gaussian distributions
  • Knowledge of statistical transformations
  • Basic programming skills for implementing pseudo code
NEXT STEPS
  • Implement the Box-Muller Transform in Python or R
  • Explore the concept of elliptical distributions in statistics
  • Learn about random variable transformations in probability theory
  • Study the application of Gaussian distributions in data modeling
USEFUL FOR

Data scientists, statisticians, and programmers interested in generating random variables with specific distributions for simulations or modeling purposes.

ireland01
Messages
17
Reaction score
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.
 
Physics news on Phys.org
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.
 

Similar threads

Graduate Derivation of Box-Muller Transform: Exponential Distrib.
  • · Replies 3 ·
Replies
3
Views
2K
High School Having trouble deriving the volume of an elliptical ring toroid
  • · Replies 4 ·
Replies
4
Views
4K
MCNP6.2 - Combination of transformations
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Sampling of a gaussian distribution
  • · Replies 1 ·
Replies
1
Views
3K
Identifying and understanding random number algorithms
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad "Map" point between coordinate systems
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Sampling with multidimensional transformations
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Variable transformation for a multivariate normal distribution
  • · Replies 1 ·
Replies
1
Views
2K
Elliptical paraboloid surface in matlab using F/D = 0.3
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Question about factoring the Klein-Gordon equation
  • · Replies 6 ·
Replies
6
Views
2K