Optimal quantizers for probability distributions on nonhomogeneous R-triangles.

Quantization of a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this paper, we have considered a Borel probability measure $P$ on $\mathbb R^2$ which has support the R-triangle generated by a set of three contractive similarity mappings on $\mathbb R^2$. For this probability measure, the optimal sets of $n$-means and the $n$th quantization error are determined for all $n\geq 2$.