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Conditional Quantization for Some Discrete Distributions

Author

Listed:
  • 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)

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.

Suggested Citation

  • Edgar A. Gonzalez & Mrinal Kanti Roychowdhury & David A. Salinas & Vishal Veeramachaneni, 2025. "Conditional Quantization for Some Discrete Distributions," Mathematics, MDPI, vol. 13(11), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1717-:d:1662951
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