Abstract
In this paper we consider a model selection problem for the distribution function of lifetimes in the presence of covariates. We propose a new model selection method by defining the closeness between two distribution functions by the Cramer–von Mises distance. This distance is used mostly in the literature to conduct goodness of fit tests. Given a set of data and two competing classes of parametric distribution functions, we define a test statistic, to decide which class approximates the underlying distribution better. With increasing sample size the asymptotic normality property of our test statistic is shown under suitable conditions. As an example, we apply our method to a real data set of lifetimes of DC-motors, which depend on the covariate load.
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