Year: 2025
Type: article
Abstract: Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the finite support are preselected, then the quantization is called a conditional quantization. In this paper, we have determined the conditional quantization, first for two different finite discrete distributions with a same conditional set, and for a finite discrete distribution with two different conditional sets. Next, we have determined the conditional and unconditional quantization for an infinite discrete distribution with support {12n:n∈N}. We have also investigated the conditional quantization for an infinite discrete distribution with support {1n:n∈N}. At the end of the paper, we have given a conjecture and discussed about some open problems based on the conjecture.
Source: Mathematics
DOI: 10.3390/math13111717
Authors: Edgar A. Gonzalez, Mrinal Kanti Roychowdhury, David A. Salinas, Vishal Veeramachaneni
Institution: The University of Texas Rio Grande Valley
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4410628718