Statistical Inference deals with the drawing of conclusions about a random experiment on the basis of the information contained in a sample from it. A random experiment can be defined by means of the set of its possible outcomes (sample space) and the ability of observation of the experimenter. It is usually assumed that this ability allows the experimenter to describe the observable events as subsets of the sample space. In this paper, we will consider that the experimenter can only express the observable events as fuzzy subsets of the sample space and we will adopt an operative model (involving the concepts of fuzzy information system and the probability of a fuzzy event) characterizing the new situation.
The presence of fuzziness in the experimental observations entails a loss of information. Nevertheless, this loss can be removed by adequately increasing the sample size. We are going to formalize this last comment by verifying that the extension of the additive measures of directed divergence of order α (Rényi) permits us to determine the appropriate sample size. This procedure can also be applied to look for the suitable sample size from an experiment providing fuzzy observations in order to achieve a desired level of information.
@article{urn:eudml:doc:40510,
title = {Sobre el tama\~no de muestra para experimentos aleatorios con imprecisi\'on difusa.},
journal = {Trabajos de Estad\'\i stica},
volume = {3},
year = {1988},
pages = {33-53},
zbl = {0731.62018},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40510}
}
Gil Alvarez, M.ª Angeles; Gil Alvarez, Pedro. Sobre el tamaño de muestra para experimentos aleatorios con imprecisión difusa.. Trabajos de Estadística, Tome 3 (1988) pp. 33-53. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40510/