Statistical hypothesis

A specific assumption on the properties of a probability distribution that underlies observable random phenomena. The results of observations are usually represented as the realization of a number of random variables, whether finite or infinite. The joint distribution of these random variables is thus not completely known, and it is assumed in a statistical hypothesis that it belongs to a certain specific class of distributions. The problem of statistical hypotheses testing (cf. Statistical hypotheses, verification of) arises in this type of situation.