High Precision Numerical Computation of Principal Points for Univariate Distributions

Authors

Santanu Chakraborty, The University of Texas Rio Grande ValleyFollow
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande ValleyFollow
Josef A. Sifuentes, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

11-2021

Abstract

Principal points were first introduced in 1990: for a positive integer n, n principal points of a random variable are the n points that minimize the mean squared distance between the random variable and the nearest of the n points. In this paper, we give a high precision numerical method for calculating the n principal points and the n th quantization errors for all positive integers n. For some absolutely continuous univariate distributions, we calculate the n principal points for different n using Newton’s method. Additionally, we also provide the corresponding values of mean squared distances.

Comments

Original published version available at https://doi.org/10.1007/s13571-020-00239-6

Recommended Citation

Chakraborty, Santanu, Mrinal Kanti Roychowdhury, and Josef Sifuentes. "High precision numerical computation of principal points for univariate distributions." Sankhya B 83, no. Suppl 2 (2021): 558-584. https://doi.org/10.1007/s13571-020-00239-6

Publication Title

Sankhya B

DOI

10.1007/s13571-020-00239-6