Before revision: In this paper, we provide general bounds on the mean absolute difference and difference of moments of a random variable X and a perturbation rd (X), when |  rd (x)-x | \leq \epsilon |x| or | rd (x)-x| \leq \delta which depend linearly on \epsilon and \delta.
After revision: In this paper, we provide general bounds on the mean absolute difference and difference of moments of a random variable X and a perturbation rd (X), when |  rd \mathbf{E | \leq \epsilon |x| or | rd (x)-x| \leq \delta which depend linearly on \epsilon and \delta.