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Estimating the probability of rare events : addressing zero failure data

Quigley, John and Revie, Matthew John Thomas (2011) Estimating the probability of rare events : addressing zero failure data. Risk Analysis, 31 (7). pp. 1120-1132. ISSN 0272-4332

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Abstract

Traditional statistical procedures for estimating the probability of an event result in an estimate of zero when no events are realized. Alternative inferential procedures have been proposed for the situation where zero events have been realized but often these are ad hoc, relying on selecting methods dependent on the data that have been realized. Such data-dependent inference decisions violate fundamental statistical principles, resulting in estimation procedures whose benefits are difficult to assess. In this article, we propose estimating the probability of an event occurring through minimax inference on the probability that future samples of equal size realize no more events than that in the data on which the inference is based. Although motivated by inference on rare events, the method is not restricted to zero event data and closely approximates the maximum likelihood estimate (MLE) for nonzero data. The use of the minimax procedure provides a risk adverse inferential procedure where there are no events realized. A comparison is made with the MLE and regions of the underlying probability are identified where this approach is superior. Moreover, a comparison is made with three standard approaches to supporting inference where no event data are realized, which we argue are unduly pessimistic. We show that for situations of zero events the estimator can be simply approximated with 1/2.5n, where n is the number of trials.

Item type: Article
ID code: 29656
Keywords: zero event, binomial, minimax, Risk Management, Physiology (medical), Safety, Risk, Reliability and Quality
Subjects: Social Sciences > Industries. Land use. Labor > Risk Management
Department: Strathclyde Business School > Management Science
Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 31 Mar 2011 20:46
    Last modified: 02 May 2014 05:05
    URI: http://strathprints.strath.ac.uk/id/eprint/29656

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