Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions

Evans Nyanney, Megha Pandey and Mrinal Kanti Roychowdhury ()
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Evans Nyanney: School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA
Megha Pandey: School of Mathematics, Northwest University, Xi’an 710069, China
Mrinal Kanti Roychowdhury: School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA

Mathematics, 2025, vol. 13, issue 15, 1-15

Abstract: Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists as a finite positive number. By giving different examples, in this paper, we have shown that the quantization coefficients for absolutely continuous probability measures defined on the same Euclidean space can be different. We have taken uniform distribution as a prototype of an absolutely continuous probability measure. In addition, we have also calculated the conditional optimal sets of n -points and the n th conditional quantization errors for the uniform distributions in constrained and unconstrained scenarios.

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