Picture of a sphere with binary code

Making Strathclyde research discoverable to the world...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. It exposes Strathclyde's world leading Open Access research to many of the world's leading resource discovery tools, and from there onto the screens of researchers around the world.

Explore Strathclyde Open Access research content

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

Full text not available in this repository. (Request a copy from the Strathclyde author)

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.