The quantization of the standard triadic Cantor distribution

Authors

Mrinal Kanti Roychowdhury, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2020

Abstract

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. For a given k ≥ 2, let {Sj : 1 ≤ j ≤ k} be a set of k contractive similarity mappings such that Sj(x) = 1 2k−1x + 2(j−1) 2k−1 for all x ∈ R, and let P = 1 k Pk j=1 P ◦ S−1 j . Then, P is a unique Borel probability measure on R such that P has support the Cantor set generated by the similarity mappings Sj for 1 ≤ j ≤ k. In this paper, for the probability measure P, when k = 3, we investigate the optimal sets of n-means and the nth quantization errors for all n ≥ 2. We further show that the quantization coefficient does not exist though the quantization dimension exists

Recommended Citation

Roychowdhury, Mrinal K. 2020. “The Quantization of the Standard Triadic Cantor Distribution.” HOUSTON JOURNAL OF MATHEMATICS 46 (2): 389–407.

First Page

389

Last Page

407

Publication Title

HOUSTON JOURNAL OF MATHEMATICS