Quantization for Uniform Distributions on Hexagonal, Semicircular, and Elliptical Curves

Gabriela Pena (), Hansapani Rodrigo (), Mrinal Kanti Roychowdhury (), Josef Sifuentes () and Erwin Suazo ()
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Gabriela Pena: University of Texas Rio Grande Valley
Hansapani Rodrigo: University of Texas Rio Grande Valley
Mrinal Kanti Roychowdhury: University of Texas Rio Grande Valley
Josef Sifuentes: University of Texas Rio Grande Valley
Erwin Suazo: University of Texas Rio Grande Valley

Journal of Optimization Theory and Applications, 2021, vol. 188, issue 1, No 6, 113-142

Abstract: Abstract In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon and then investigate the optimal sets of n-means and the nth quantization errors for all positive integers n. We give an exact formula to determine them, if n is of the form $$n=6k$$ n = 6 k for some positive integer k. We further calculate the quantization dimension, the quantization coefficient, and show that the quantization dimension is equal to the dimension of the object, and the quantization coefficient exists as a finite positive number. Then, we define a mixture of two uniform distributions on the boundary of a semicircular disc and obtain a sequence and an algorithm, with the help of which we determine the optimal sets of n-means and the nth quantization errors for all positive integers n with respect to the mixed distribution. Finally, for a uniform distribution defined on an elliptical curve, we investigate the optimal sets of n-means and the nth quantization errors for all positive integers n.

Keywords: Uniform distribution; Optimal quantizers; Quantization error; Quantization dimension; Quantization coefficient; 60Exx; 94A34 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01771-1

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