How to convert a gaussian distributed rnd sequence to uniform dist and viceversa

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SUMMARY

The discussion focuses on converting a uniformly distributed random number sequence generated by a microcontroller into a Gaussian distribution and vice versa. Devanand T suggests using the cumulative distribution function (CDF) of the Gaussian distribution, denoted as F, to achieve this transformation. Specifically, for a uniform random variable x in the range [0, 1], the transformation y = F^{-1}(x) yields a Gaussian distributed variable. The reverse process involves applying the uniform distribution transformation to Gaussian variables.

PREREQUISITES
  • Understanding of Gaussian distribution and its properties
  • Familiarity with cumulative distribution functions (CDF)
  • Basic knowledge of random number generation
  • Experience with MATLAB for statistical analysis
NEXT STEPS
  • Research the implementation of the inverse CDF method for Gaussian distribution
  • Explore MATLAB functions for generating Gaussian random numbers
  • Learn about the Box-Muller transform for generating Gaussian distributions from uniform distributions
  • Investigate statistical properties of uniform and Gaussian distributions
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Data scientists, statisticians, and engineers working with random number generation and statistical modeling will benefit from this discussion.

dexterdev
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Hi PF,
I have a device (with a microcontroller) which generates random numbers. when I analyzed those numbers using Matlab software I found that it is following a uniform distribution. How can I mathematically (any algorithm?) convert this random output to a gaussian one. Also I would like to know the reverse case ie gaussian to uniform one.

-Devanand T
 
Physics news on Phys.org
If F is the cdf of the Gaussian distribution, and x is a point from your uniform distribution 0<=x<=1, then y= F^{-1} (x) has a Gaussian distribution.
 

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