Statistical Evaluation of Learning Factor in Reliability Studies
A mathematical formulation is developed which allows the statistical evaluation of certain features of the probability distribution of the ratio between two random variables as in the determination of learning factors. This evaluation is of the mode, an s-confidence band for the ratio, and the effect of sample size.
Confidence Intervals for the Ratio of Two Poisson Means and Poisson Predictor Intervals
Easy-to-use charts are presented for confidence intervals for the ratio of two Poisson mean occurrence rates and for predictor intervals for the future value of a Poisson random variable, given a previously observed value. The use of the charts is illustrated and their theoretical basis is given.
The Globalization problem for inner automorphisms and Skolem-Noether theorems
We investigate the circumstances under which an inner automorphism of a ring with local units can be built from “local” information. Specifically, we consider three natural “inner” type properties for an automorphism of a ring with local units. We show that every inner automorphism is locally inner but the converse is false, even if the automorphism is “piecewise” inner. On the other hand, we construct a large class of rings for which every locally inner automorphism is actually inner. Finally we obtain some Skolem-Noether type Theorems for infinite matrix and triangular matrix rings.