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Properties of scalar quantization with $r$th power distortion and constrainedR\'enyi entropy of order $\alpha\in (0,1)$ are investigated. For anasymptotically (high-rate) optimal sequence of quantizers, the contribution tothe R\'enyi entropy due to source values in a fixed interval is identified interms of the "entropy density" of the quantizer sequence. This extends resultsrelated to the well-known point density concept in optimal fixed-ratequantization. A dual of the entropy density result quantifies the distortioncontribution of a given interval to the overall distortion. The distortion lossresulting from a mismatch of source densities in the design of anasymptotically optimal sequence of quantizers is also determined. This extendsBucklew's fixed-rate ($\alpha=0$) and Gray \emph{et al.}'s variable-rate($\alpha=1$) mismatch results to general values of the entropy order parameter$\alpha$.

Entropy Density and Mismatch in High-Rate Scalar Quantization with Renyi Entropy Constraint