arXiv subjects

Evans Nyanney

Publications and source records attributed to Evans Nyanney.

2 recordsLinked to original sources

arXiv2025

Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions

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.

math.PR↗

arXiv2025

Conditional constrained and unconstrained quantization for uniform distributions on regular polygons

In this paper, we have considered a uniform distribution on a regular polygon with $k$-sides for some $k\geq 3$ and the set of all its $k$ vertices as a conditional set. For the uniform distribution under the conditional set first, for all positive integers $n\geq k$, we obtain the conditional optimal sets of $n$-points and the $n$th conditional quantization errors, and then we calculate the conditional quantization dimension and the conditional quantization coefficient in the unconstrained scenario. Then, for the uniform distribution on the polygon taking the same conditional set, we investigate the conditional constrained optimal sets of $n$-points and the conditional constrained quantization errors for all $n \geq 6$, taking the constraint as the circumcircle, incircle, and then the different diagonals of the polygon.

math.PR↗