Monotony of Lloyd´s method II for log-concave density and convex error weighting function (Corresp.)

Kieffer recently showed that for a log-concave probability density there is a unique -level quantizer which is a stationary point of the expected value of an increasing, convex, and continuously differentiable error weighting function, dependent on the absolute quantization error. It is shown that the requirement of continuous differentiability can be dropped, using the monotony of Lloyd\´s Method II, the proof of which is based on a generalization of previous work by the author.