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Testing for goodness rather than lack of fit of continuous probability distributions

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  • Stefan Wellek

Abstract

The vast majority of testing procedures presented in the literature as goodness-of-fit tests fail to accomplish what the term is promising. Actually, a significant result of such a test indicates that the true distribution underlying the data differs substantially from the assumed model, whereas the true objective is usually to establish that the model fits the data sufficiently well. Meeting that objective requires to carry out a testing procedure for a problem in which the statement that the deviations between model and true distribution are small, plays the role of the alternative hypothesis. Testing procedures of this kind, for which the term tests for equivalence has been coined in statistical usage, are available for establishing goodness-of-fit of discrete distributions. We show how this methodology can be extended to settings where interest is in establishing goodness-of-fit of distributions of the continuous type.

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  • Stefan Wellek, 2021. "Testing for goodness rather than lack of fit of continuous probability distributions," PLOS ONE, Public Library of Science, vol. 16(9), pages 1-12, September.
    • Handle: RePEc:plo:pone00:0256499
    DOI: 10.1371/journal.pone.0256499
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    References listed on IDEAS

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    1. Miller, Forrest R. & Neill, James W., 2016. "Lack of fit tests for linear regression models with many predictor variables using minimal weighted maximal matchings," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 14-26.
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