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Likelihood as an index of fit

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Summary

In this paper likelihood is characterized as an index which measures how much a model fits a sample. Some properties required to an index of fit are introduced and discussed, while stressing how they describe aspects inner to idea of fit. Finally we prove that, if an index of fit is maximal when the model reaches the distribution of the sample, then such an index is an increasing continuous transform of\(\mathop \Pi \limits_{\iota - 1}^n (p_i )^{qi} \), where thep i's are the theoretical relative frequencies provided by the model and theq i's are the actual relative frequencies of the sample.

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Di Bacco, M., Regoli, G. Likelihood as an index of fit. J. It. Statist. Soc. 3, 243–253 (1994). https://doi.org/10.1007/BF02589229

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