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Full-Text Articles in Physical Sciences and Mathematics
Uniform Distributions On Curves And Quantization, Joseph Rosenblatt, Mrinal Kanti Roychowdhury
Uniform Distributions On Curves And Quantization, Joseph Rosenblatt, Mrinal Kanti Roychowdhury
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 to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n -means and the n th quantization errors for different …
Quantization Coefficients For Uniform Distributions On The Boundaries Of Regular Polygons, Joel Hansen, Itzamar Marquez, Mrinal Kanti Roychowdhury, Eduardo Torres
Quantization Coefficients For Uniform Distributions On The Boundaries Of Regular Polygons, Joel Hansen, Itzamar Marquez, Mrinal Kanti Roychowdhury, Eduardo Torres
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular m-sided polygons inscribed in a circle. The result shows that the quantization coefficient for the uniform distribution on the boundary of a regular m-sided polygon inscribed in a circle is an increasing function of m, and approaches to the quantization coefficient for the uniform distribution on the circle as m tends to infinity.
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