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Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons

Author

Listed:
  • Pigar Biteng

    (School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA)

  • Mathieu Caguiat

    (School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA)

  • Tsianna Dominguez

    (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)

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 support are preselected, then the quantization is called a conditional quantization. In this paper, we investigate the conditional quantization for the uniform distributions defined on the unit line segments and m -sided regular polygons, where m ≥ 3 , inscribed in a unit circle.

Suggested Citation

  • Pigar Biteng & Mathieu Caguiat & Tsianna Dominguez & Mrinal Kanti Roychowdhury, 2025. "Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons," Mathematics, MDPI, vol. 13(7), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1024-:d:1617426
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    References listed on IDEAS

    as
    1. Abaya, Efren F. & Wise, Gary L., 1984. "Some remarks on the existence of optimal quantizers," Statistics & Probability Letters, Elsevier, vol. 2(6), pages 349-351, December.
    2. Hansen, Joel & Marquez, Itzamar & Roychowdhury, Mrinal K. & Torres, Eduardo, 2021. "Quantization coefficients for uniform distributions on the boundaries of regular polygons," Statistics & Probability Letters, Elsevier, vol. 173(C).
    Full references (including those not matched with items on IDEAS)

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