The normal distribution derived from qualitative conditions

Autor(en): Suck, R
Stichwörter: Mathematical Methods In Social Sciences; Mathematics; Mathematics, Interdisciplinary Applications; Psychology; Psychology, Mathematical; Social Sciences, Mathematical Methods
Erscheinungsdatum: 2001
Herausgeber: ACADEMIC PRESS INC
Journal: JOURNAL OF MATHEMATICAL PSYCHOLOGY
Volumen: 45
Ausgabe: 2
Startseite: 370
Seitenende: 388
Zusammenfassung: 
The normal distribution is characterized in a measurement theoretic framework. The qualitative conditions guarantee that representations can be regarded as random variables. Additional axioms, also qualitative in the measurement sense, yield the normal. One characterization draws on a limit theorem. The main result derives the normal distribution from conjoint measurement axioms. This approach consists of formulating properties of a linear model as a component structure with error as one component. The normal distribution of errors is shown to be a consequence of the measurement theoretic assumptions. The possible impact of these results on statistical models is discussed. (C) 2001 Academic Press.
ISSN: 00222496
DOI: 10.1006/jmps.2000.1328

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