The quantization of the standard triadic Cantor distribution

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 Sj for 1 ≤ j ≤ k. In this paper, for the probability measure P, when k = 3, we investigate the optimal sets of n-means and the nth quantization errors for all n ≥ 2. We further show that the quantization coefficient does not exist though the quantization dimension exist