Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Quantization For A Mixture Of Uniform Distributions Associated With Probability Vectors, Mrinal Kanti Roychowdhury, Wasiela Salinas
Quantization For A Mixture Of Uniform Distributions Associated With Probability Vectors, Mrinal Kanti Roychowdhury, Wasiela Salinas
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixtures of probability distributions, also known as mixed distributions, are an exciting new area for optimal quantization. In this paper, we investigate the optimal quantization for three different mixed distributions generated by uniform distributions associated with probability vectors
The Quantization Of The Standard Triadic Cantor Distribution, Mrinal Kanti Roychowdhury
The Quantization Of The Standard Triadic Cantor Distribution, Mrinal Kanti Roychowdhury
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. For a given k ≥ 2, let {Sj : 1 ≤ j ≤ k} be a set of k contractive similarity mappings such that Sj(x) = 1 2k−1x + 2(j−1) 2k−1 for all x ∈ R, and let P = 1 k Pk j=1 P ◦ S−1 j . Then, P is a unique Borel probability measure on R such that P has support the Cantor set generated by the similarity mappings …