Probability distribution of the classical implication intensity seen as a random variable in Statistical Implicative Analysis

Abstract

Starting from mathematical didactic situations, the method of Statistical Implicative Analysis is developed in correspondence with the problems encountered and the issues raised. Its main objective is to structure data, interrelating subjects and variables, extracting inductive rules between variables and, from the contingency of these rules, the explanation and consequently a certain forecast in different areas: psychology, sociology, biology, etc. This is why the concepts of intensity of implication, class cohesion, implication-inclusion, meaning of hierarchical levels, contribution of supplementary variables, etc. were created. In this work, most of the fundamental concepts of Statistical Implicative Analysis (SIA) are offered. We also study the behavior of the classical Gras implication index as a random variable, when applied to a couple of Bernoulli variables (X, Y ), independent or not.