A POWER APPROXIMATION FOR THE MULTINOMIAL GOODNESS-OF-FIT TEST BASED ON A NORMALIZING TRANSFORMATION

Cressie and Read(1984)introduced the class of multinomial goodness-of-fit statistics, Ra, based on measures of the divergence between discrete distributions. All Ra have the same chi-squared limiting null distribution. The power of Ra is usually approximated by a noncentral chi-squared distribution that is also the same for all a. In this paper, we propose a new approximation of the power of Ra. The new power approximation, NT, is a normal approximation based on a normalizing transformation. The NT approximation is numerically compared with the other approximations. As a result of the comparison, we find that the NT approximation is superior to the other approximations when a=0(the loglikelihood ratio statistic)and is effective when a