Suppose X1,…,Xn is a random sample from bounded and decreasing density f0 on [0,?). We are interested in estimating such f0, with special interest f0(0). This problem encountered various statistical applications has gained quite some attention the literature. It well known that maximum likelihood estimator inconsistent at zero. led several authors to propose alternative estimators which consist...

This paper presents a formalization of decreasing diagrams in the theorem prover Isabelle. It discusses mechanical proofs showing that any locally decreasing abstract rewrite system is confluent. The valley and the conversion version of decreasing diagrams are considered. 1998 ACM Subject Classification F.3.1, F.4.2

The decreasing diagrams technique is a complete method to reduce confluence of a rewrite relation to local confluence. Whereas previous presentations have focussed on the proof the technique is correct, here we focus on applicability. We present a simple but powerful generalisation of the technique, requiring peaks to be closed only by conversions instead of valleys, which is demonstrated to fu...