Abstract
Let X be a nonnegative random variable with cumulative distribution function F. In this article, we introduce a concept of deviation from exponentiality for F, based on the Mean Residual Life function. Our aim is to estimate this deviation under the random censorship model. For this purpose, we propose two slightly different estimators. For each one, we determine the limit distribution of an appropriately normalized version. Then, this work leads to the construction of a test of H 0 : F is exponential vs. H 1 : F is not exponential. It is applied to the Koziol and Green data set (Koziol, S. A., Green, S. B. (1976). A cramer-von mises statistic for randomly censored data. Biometrika 23:465–474).
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