抄録
In this paper we propose three approximations to the power of the power-divergence statistic Ra on the test of homogeneity for multinomial populations. These approximations are based on the approximation theories for the multinomial goodness-of-fit test as proposed by Broffitt and Randles (1977) and Drost et al. (1989). One approximation is constructed from a limiting normal distribution of Ra. The others are constructed from the linear and quadratic terms of a Taylor series expansion of Ra. These approximations are compared with the power directly calculated from the product multinomial model. As a result of this comparison, the latter approximations are found to perform well when a≥0. On the homogeneity of two populations, we investigate the power of representative power divergence statistics R0, R2/8 and R1 using the latter approximations. Then, corresponding to alternatives, relations to the power of the three statistics are discussed.
