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Full-Text Articles in Physical Sciences and Mathematics
Local Dimensions And Quantization Dimensions In Dynamical Systems, Mrinal Kanti Roychowdhury, Bilel Selmi
Local Dimensions And Quantization Dimensions In Dynamical Systems, Mrinal Kanti Roychowdhury, Bilel Selmi
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Let μ be a Borel probability measure generated by a hyperbolic recurrent iterated function system defined on a nonempty compact subset of Rk. We study the Hausdorff and the packing dimensions, and the quantization dimensions of μ with respect to the geometric mean error. The results establish the connections with various dimensions of the measure μ and generalize many known results about local dimensions and quantization dimensions of measures.
Quantization For Uniform Distributions On Hexagonal, Semicircular, And Elliptical Curves, Gabriela Pena, Hansapani Rodrigo, Mrinal Kanti Roychowdhury, Josef A. Sifuentes, Erwin Suazo
Quantization For Uniform Distributions On Hexagonal, Semicircular, And Elliptical Curves, Gabriela Pena, Hansapani Rodrigo, Mrinal Kanti Roychowdhury, Josef A. Sifuentes, Erwin Suazo
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon, and then investigated 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 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 …
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 …