Predicting maximum and minimum eigenvalues of a random matrix : A study in simulation for Poisson distribution. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Princila, ; Chakraborty, Soubhik
• Is Part Of: Journal of statistics & management systems. Volume 25:Issue 1(2022)
• Page Start: 125
• Page End: 136
• Publication Date: 2022-01-02
• Subjects: 62P99; Simulation -- Poisson distribution -- Random matrix -- Trace -- Eigenvalue -- Chebyshev's inequality -- Curve fitting; Statistics -- Periodicals; Mathematical models -- Periodicals; Mathematical models; Statistics; Periodicals; 519.5
• DOI: 10.1080/09720510.2020.1862960
• Languages: English
• ISSNs: 0972-0510

Abstract

Abstract: As we know that, collection of data from large population is very difficult, so in this paper we choose the method of simulation to generate random matrices of order 10×10 whose elements are from Poisson distribution with parameter λ . In the first study, for different values of λ, we generate 100 matrices of order 10×10 and obtain the mean of maximum eigenvalue of each of the 100 matrices using MATLAB and plot a graph between mean of maximum eigenvalues and parameter λ . Finally, we obtain the best curve fit. The equation of best fit enables us to predict the maximum eigenvalue of a random matrix for a given λ . The same procedure is followed for minimum eigenvalue case. In the second study, we repeat the process for random matrices of order 5×5 and observe that the regression equation for predicting the maximum or minimum eigenvalue does not get affected by reducing the order of the matrix. The paper also includes a theoretical analysis of predicting the range of the sum of all the eigenvalues of a diagonalizable random matrix with the help of its trace and Chebyshev's inequality.