Su alcuni nuovi contributi alla teoria dei test secondo Neyman-Pearson

Abstract

Given two simple hypotheses H0:Teta=Teta0 and H1: Teta=Teta1 concerning the unknown parameter Teta which characterizes the probability distribution Fi(x;Teta) of a random variable X, it is well known that Neyman-Pearson lemma ensure the existence and the uniqueness of the most powerful test. In this paper, following Migliorati, it is demonstrated that the most powerful test is not unique whenever the probability distribution of X can be factored as Fi(x;Teta)= f(x)h(Teta). Besides, in this case there exists a perfect negative linear relationship between the probabilities of first and second type errors alfa e beta. Finally, it is shown that the theorem based on monotone likelihood ratio, which is considered a sort of generalization of Neyman-Pearson lemma, generates some "irregularities".