Large deviations associated with Poisson--Dirichlet distribution and Ewens sampling formula

Several results of large deviations are obtained for distributions that are associated with the Poisson--Dirichlet distribution and the Ewens sampling formula when the parameter $\theta$ approaches infinity. The motivation for these results comes from a desire of understanding the exact meaning of $\theta$ going to infinity. In terms of the law of large numbers and the central limit theorem, the limiting procedure of $\theta$ going to infinity in a Poisson--Dirichlet distribution corresponds to a finite allele model where the mutation rate per individual is fixed and the number of alleles going to infinity. We call this the finite allele approximation. The first main result of this article is concerned with the relation between this finite allele approximation and the Poisson--Dirichlet distribution in terms of large deviations. Large $\theta$ can also be viewed as a limiting procedure of the effective population size going to infinity. In the second result a comparison is done between the sample size and the effective population size based on the Ewens sampling formula.Comment: Published in at http://dx.doi.org/10.1214/105051607000000230 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Development of diagnostic and prognostic algorithms for SF6 puffer circuit breakers from transient waveforms: a validation proposal

- This paper presents a validation proposal for development of diagnostic and prognostic algorithms for SF6 puffer circuit-breakers reproduced from actual site waveforms. The re-ignition/restriking rates are duplicated in given circuits and the cumulative energy dissipated in interrupters by the restriking currents. The targeted objective is to provide a simulated database for diagnosis of re-ignition/restrikes relating to the phase to earth voltage and the number of re-ignition/restrikes as well as estimating the remaining life of SF6 circuit-breakers. The model-based diagnosis of a tool will be useful in monitoring re-ignition/restrikes as well as predicting a nozzle’s lifetime. This will help ATP users with practical study cases and component data compilation for shunt reactor switching and capacitor switching. This method can be easily applied with different data for the different dielectric curves of circuit breakers and networks. This paper presents modelling details and some of the available cases, required project support, the validation proposal, the specific plan for implementation and the propsed main contributions