La distanza delle alternative nelle verifiche di ipotesi riguardanti le distribuzioni multinomiali

Some meausures of distance between hypothesis and alternatives in the case of multinomial distribution are proposed. For a multinomial distribution with k classes one can meausure in several ways the distance between the probabilities specified by the null hypothesis and those specified by the alternative hypothesis. In this paper the author makes some comparisons between the distance functions H and ∆, and shows that if one meausures the distance with ∆ the test based on the K. Pearson X² statistic is not adeguate and that in this case it seems more reasonable to use a test statistic with a structure like ∆.