Relations between Renyi Distance and Fisher Information

In this paper, we first show that renyi distance betweenany member of a parametric family and its perturbations, is proportionalto its fisher information. we, then, prove some relationsbetween the renyi distance of two distributions and the fisher informationof their exponentially twisted family of densities. finally, weshow that the partial ordering of families induced by renyi distanceis the same as that induced by fisher information