Test di adattamento nel caso di stima dei parametri per distribuzioni di cui siano note frequenze e quantità

Abstract

We consider a new inferential procedure which can be used in goodness-of-fit problems when a parametric model has to be adapted to an observed distribution with class amounts known. Referring to a random sample of independent observations grouped in T fixed intervals, the method is based on an approximation to the joint likelihood which can be derived considering both the distributions of quantities.  We propose a new test statistics S² which is the sum of the classical X²  introduced by Pearson and of the statistic V²  considered by Dancelli (1993). We show that, when the s parameters are estimated maximizing the joint likelihood, S²  has an asymptotic Chi-Square distribution with (2T - s - 1) degrees of freedom. 
We have performed some numerical evaluation considering the normal model of order 'rho'.
Our results indicate that, in this case, the power function of the new test is always greater than that of the usual test based on X² .