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Rapport Année : 1997

On the Prequential Approach for Testing Exponentiality

Résumé

We present a prequential (predictive-sequential) approach for testing the goodness-of-fit of an exponential distribution when the parameter $\lambda$ is unknown. Instead of using all the available observations, $\lambda$ is estimated by a prequential approach where at each step $i$, only the $i\!-\!1$ first observations are used. We show that this approach provides a sequence of \ks type distances whose expressions do not depend on $\lambda$ and which converge in distribution (under the null hypothesis) to the \ks distribution. This leads to a simple technique for testing the goodness-of-fit of exponential distributions with unknown parameter using standard quantile tables of the \ks distribution. Even if Monte~Carlo simulations show that the prequential test is less powerful than the standard exponentiality test, the developed results represent a first step in the theoretical study of the {\it u-plot} which is a prequential empirical tool commonly used for the validation of reliability-growth models.
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Dates et versions

inria-00073609 , version 1 (24-05-2006)

Identifiants

  • HAL Id : inria-00073609 , version 1

Citer

Mhamed-Ali El Aroui. On the Prequential Approach for Testing Exponentiality. RR-3082, INRIA. 1997. ⟨inria-00073609⟩
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