This paper outlines with modern notations the proof of Karl Pearson on the distribution of the statistic on which the chi-squared goodness of fit test with simple null hypothesis is based. It is then shown in details a proof due Ronald Aylmer Fisher, which in the opinion of the authors has not received the proper attention for its elegance and its immediate generalization to the case of composite null hypothesis. Finally, a new proof based on the Principle of mathematical induction is provided by making use of widely known probabilistic results.
On the Pearson-Fisher chi-squared theorem / Buonocore, Aniello; Pirozzi, Enrica. - In: APPLIED MATHEMATICAL SCIENCES. - ISSN 1312-885X. - 8:134(2014), pp. 6733-6744. [10.12988/ams.2014.49688]
On the Pearson-Fisher chi-squared theorem
BUONOCORE, ANIELLO;PIROZZI, ENRICA
2014
Abstract
This paper outlines with modern notations the proof of Karl Pearson on the distribution of the statistic on which the chi-squared goodness of fit test with simple null hypothesis is based. It is then shown in details a proof due Ronald Aylmer Fisher, which in the opinion of the authors has not received the proper attention for its elegance and its immediate generalization to the case of composite null hypothesis. Finally, a new proof based on the Principle of mathematical induction is provided by making use of widely known probabilistic results.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
