The quantization of the Cantor distribution

TitleThe quantization of the Cantor distribution
Publication TypeJournal Article
Year of Publication1997
AuthorsHarald Luschgy, and Siegfried Graf
JournalMath. Nachrichten
KeywordsCantor distribution, quantization

For a real-valued random variable whose distribution is the classical Cantor probability, the $ n $-quantization error and the $ n $-optimal quantization rules are calculated for every natural number $ n $. Moreover, the connection between the rate of convergence of the logarithms of the quantization errors for $ n $ going to infinity and the Hausdorff dimension of the Cantor set is indicated.