This function estimates the median of the Marčenko-Pastur distribution given a ratio parameter beta.
The Marčenko-Pastur distribution describes the asymptotic behavior of eigenvalues of large random matrices
and is widely used in random matrix theory and statistics for noise estimation and signal processing.
Usage
MedianMarcenkoPastur(beta)
Arguments
- beta
A numeric value between 0 and 1 representing the aspect ratio of the matrix (n/d),
where n is the number of columns and d is the number of rows.
This ratio defines the shape of the Marčenko-Pastur distribution.
Value
A numeric value representing the estimated median of the Marčenko-Pastur distribution.
Details
The function iteratively narrows down the interval containing the median of the Marčenko-Pastur
distribution by evaluating the distribution function until the interval is sufficiently small.
The bounds of the distribution are defined by (1 - sqrt(beta))^2 and (1 + sqrt(beta))^2.
