Conditional Quantization for Some Discrete Distributions

Edgar A. Gonzalez, Mrinal Kanti Roychowdhury (), David A. Salinas and Vishal Veeramachaneni
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Edgar A. Gonzalez: School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA
Mrinal Kanti Roychowdhury: School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA
David A. Salinas: School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA
Vishal Veeramachaneni: School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA

Mathematics, 2025, vol. 13, issue 11, 1-16

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 { 1 2 n : n ∈ N } . We have also investigated the conditional quantization for an infinite discrete distribution with support { 1 n : n ∈ N } . At the end of the paper, we have given a conjecture and discussed about some open problems based on the conjecture.

Keywords: discrete distribution; conditional optimal sets of n-points; conditional quantization error (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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