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- W3210052215 abstract "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 $kgeq 2$, let ${S_j : 1leq jleq k}$ be a set of $k$ contractive similarity mappings such that $S_j(x)=frac 1 {2k-1} x +frac{2 (j-1)} {2k-1}$ for all $xin mathbb R$, and let $P= frac 1 k sum_{j=1}^kPcirc S_j^{-1}$. Then, $P$ is a unique Borel probability measure on $mathbb R$ such that $P$ has support the Cantor set generated by the similarity mappings $S_j$ for $1leq jleq k$. In this paper, for the probability measure $P$, when $k=3$, we investigate the optimal sets of $n$-means and the $n$th quantization errors for all $ngeq 2$. We further show that the quantization coefficient does not exist though the quantization dimension exists." @default.
- W3210052215 created "2021-11-08" @default.
- W3210052215 creator A5006255270 @default.
- W3210052215 date "2018-09-01" @default.
- W3210052215 modified "2023-09-25" @default.
- W3210052215 title "The quantization of the standard triadic Cantor distribution" @default.
- W3210052215 hasPublicationYear "2018" @default.
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