# Second order asymptotic distribution of the Rφ-divergence goodness-of-fit statistics

María Carmen Pardo

# Abstract:

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. 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.