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Copulas, degenerate distributions and quantile tests

Bedford, T.J. (2006) Copulas, degenerate distributions and quantile tests. Journal of Statistical Computation and Simulation, 136. pp. 1572-1587. ISSN 0094-9655

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Abstract

It is well known that, given observable data for a competing risk problem, there is always an independent model consistent with the data. It has been pointed out, however, that this independent model does not necessarily have to be one with proper marginals. One purpose of this paper is to explore the extent to which one might try to use the non-parametric assumption that the marginals are proper in order to test whether or not independence holds. This will lead us naturally to a closely related estimation problem - how we estimate the marginals given that a certain quantile of one variable is reached at the same time as a given quantile of the other variable. The problem will be considered using the copula-based approach of Zheng and Klein. Two different methods are discussed. One is a non-parametric maximum likelihood method. The other is a consistent estimator, called the bilinear adjustment estimator, that can be computed quickly and which thus lends itself more readily to simulation methods such as bootstrapping. The ultimate objective of the work in this paper is to provide an additional analytical tool to understand the effectiveness of preventive maintenance. Preventive maintenance censors component failure data and thus provides an important example of competing risk within the reliability area.

Item type: Article
ID code: 4323
Keywords: risk management, copula, reliability management, preventive maintenance, Management. Industrial Management, Risk Management, Statistics, Modelling and Simulation, Applied Mathematics, Statistics and Probability, Statistics, Probability and Uncertainty
Subjects: Social Sciences > Industries. Land use. Labor > Management. Industrial Management
Social Sciences > Industries. Land use. Labor > Risk Management
Social Sciences > Statistics
Department: Strathclyde Business School > Management Science
Related URLs:
    Depositing user: Strathprints Administrator
    Date Deposited: 17 Oct 2007
    Last modified: 04 Sep 2014 16:55
    URI: http://strathprints.strath.ac.uk/id/eprint/4323

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