## Real Analysis Exchange

### Optimal Quantizers for some Absolutely Continuous Probability Measures

Mrinal Kanti Roychowdhury

#### Abstract

The representation of a given quantity with less information is often referred to as ‘quantization’ and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit discs, squares, and the real line. For these probability measures the optimal sets of $n$-means and the $n$th quantization errors are calculated for some positive integers $n$.

#### Article information

Source
Real Anal. Exchange, Volume 43, Number 1 (2018), 105-136.

Dates
First available in Project Euclid: 2 May 2018

https://projecteuclid.org/euclid.rae/1525226426

Digital Object Identifier
doi:10.14321/realanalexch.43.1.0105

Mathematical Reviews number (MathSciNet)
MR3816435

Zentralblatt MATH identifier
06924877

#### Citation

Roychowdhury, Mrinal Kanti. Optimal Quantizers for some Absolutely Continuous Probability Measures. Real Anal. Exchange 43 (2018), no. 1, 105--136. doi:10.14321/realanalexch.43.1.0105. https://projecteuclid.org/euclid.rae/1525226426