Theses and Dissertations

Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Dr. Mrinal Kanti Roychowdhury

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Tamer Oraby


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. Let P be a Borel probability measure on R such that P := 1/4 P◦ S1−1 + 1\2 PS2−1 + 1/4 PS3−1, where S1, S2 and S3 are three contractive similarity mappings such that Sj(x) = 1/5x+2(j−1)/5, for all x ∈ R. For this probability measure, in this thesis, we determine the optimal sets of n-means and the nth quantization errors for all positive integers n. We also calculate the quantization dimension of the probability measure and show that it equals the Hausdorff dimension of the Cantor set which is the support of the measure P.


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