Adjusted power-divergence test statistics for simple goodness-of-fit under clustered sampling

Two-different types of adjustments to the power-divergence test statistics have been introduced for the problem of testing goodness-of-fit under clustered sampling. Penalization has also been introduced to handle the cells with zero frequencies. The asymptotic distribution of the proposed power-divergence test statistics has been investigated under clustered sampling and the performances of the proposed statistics for finite samples have been studied through a designed simulation study.