This project contains utility functions and scripts for working with the normal (Gaussian) distribution, including visualization and maximum likelihood estimation of parameters.
The normal distribution probability density function:
f(x) = (1 / (sqrt(2*pi) * sigma)) * exp(-(x - mu)^2 / (2*sigma^2))
Maximum likelihood estimation:
mu_est = mean(samples)sigma_est = std(samples)
The superimposed problem demonstrates two overlapping normal distributions with different parameters.
| File | Description |
|---|---|
Normal_dist.m |
Function: computes the normal distribution PDF |
plot_normal_dists.m |
Plots normal distributions for various sigma values |
superimposed_problem.m |
Demonstrates two overlapping distributions with samples |
test_max_likelihood_normal.m |
Tests maximum likelihood parameter estimation |
- Demonstrates how sigma controls the spread of the distribution
- Maximum likelihood estimation accurately recovers true parameters from samples
- Visualization of superimposed distributions shows the challenge of distinguishing overlapping populations
Left: Normal distributions with varying sigma values. Right: Maximum likelihood estimation showing true vs. estimated distributions from 20 samples.
Keivan Hassani Monfared, k1monfared@gmail.com