Kybernetika

The distribution of each member of the family of statistics based on the $R_{\phi}$-divergence for testing goodness-of-fit is a chi-squared to $o(1)$ (M.C. Pardo: On Burbea--Rao divergences based goodness--of--fit tests for multinomial models. J. Multivariate Anal. {\mi 69} (1999), 65--87.). In this paper a closer approximation to the exact distribution is obtained by extracting the $\phi $-dependent second order component from the $o(1)$ term.