Non-Parametric Estimators Related to Local Load-Sharing Models

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Rydén, Patrik (författare): Umeå universitet,Institutionen för matematik och matematisk statistik

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Abstract Ämnesord

Stäng

We consider the problem of estimating the cumulative distribution function of failure stresses of bundles (i.e. the tensile forces that destroy bundles), constructed of several statistically similar fibres, given a particu-lar kind of censored data. Each bundle consists of several fibres which have their own independent identically distributed failure stresses, and where the force applied on a bundle at any moment is distributed between the fibres in the bundle according to the local load-sharing model. The testing of several bundles generates a special kind of censored data, which is complexly structured. Consistent non-parametric estima-tors of the distribution laws of bundles are obtained by applying the theory of martingales, and by using the observed data. It is showed that ran-dom sampling, with replacement from the statistical data related to each tested bundle, can be used to estimate the accuracy of our non-parametric estimators. Numerical examples illustrate the behavior of the obtained es-timators.

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