Quantization for Uniform Distributions on Hexagonal, Semicircular, and Elliptical Curves

In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon and then investigate the optimal sets of n -means and the n th quantization errors for all positive integers n . We give an exact formula to determine them, if n is of the form $$n=6k$$ n = 6 k 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 the boundary of a semicircular disc and obtain a sequence and an algorithm, with the help of which we determine the optimal sets of n -means and the n th quantization errors for all positive integers n with respect to the mixed distribution. Finally, for a uniform distribution defined on an elliptical curve, we investigate the optimal sets of n -means and the n th quantization errors for all positive integers n .