6533b862fe1ef96bd12c623a
RESEARCH PRODUCT
Testing for goodness rather than lack of fit of continuous probability distributions.
Stefan WellekStefan Welleksubject
Computer scienceStatement (logic)Alternative hypothesisScienceTest StatisticsResearch and Analysis MethodsStatistical InferenceMathematical and Statistical TechniquesStatistical inferenceEconometricsHumansLack-of-fit sum of squaresStatistical MethodsEquivalence (measure theory)Statistical hypothesis testingStatistical DataProbabilityMultidisciplinaryModels StatisticalApplied MathematicsSimulation and ModelingStatisticsQRProbability TheoryProbability DistributionTerm (time)Monte Carlo methodStatistical TheoriesPhysical SciencesProbability distributionMedicineMathematicsAlgorithmsResearch ArticleStatistical Distributionsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-09-10 | PLoS ONE |