Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform distributions on curves and quantization   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
have defined 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 values of $n$ with respect to the uniform
distributions defined on the curves. In each case, we have further calculated
the quantization dimension and show that it is equal to the dimension of the
object, and the quantization coefficient exists as a finite positive number,
which supports the well-known result of Bucklew and Wise (1982), which says
that for a Borel probability measure $P$ with non-vanishing absolutely
continuous part the quantization coefficient exists as a finite positive
number.

10
The categories of this paper are: q-bio
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The categories of this paper are: stat
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc