Conditional Quantization for Some Discrete Distributions - Edgar A. Gonzalez; Mrinal Kanti Roychowdhury; David A. Salinas; Vishal Veeramachaneni (Mathematics)
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 <semantics>{<mstyle scriptlevel="0" displaystyle="true">12n</mstyle>:n∈N}</semantics>. We have also investigated the conditional quantization for an infinite discrete distribution with support <semantics>{<mstyle scriptlevel="0" displaystyle="true">1n</mstyle>:n∈N}</semantics>. At the end of the paper, we have given a conjecture and discussed about some open problems based on the conjecture.