A Possibilistic View of Binomial Parameter Estimation

Abstract

This paper deals with the possibility roots of binomial parameter interval estimation. It shows that conventional probability methods consist to obtain confidence intervals representing de dicto parameter uncertainty from coverage intervals representing de re uncertainty of observed samples. We relate the different types of coverage intervals to equivalent de re possibility distributions whose lead after inversion to de dicto possibility distributions corresponding to the stacking up of all confidence intervals at all levels. The different choices for the centre of the intervals corresponds to the different existing methods, in the same vein a novel one centred on the mean is proposed. © Springer International Publishing Switzerland 2014.