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 | %DIFDELCMD < {\rm %%% rd (x)-x | \leq \epsilon |x| or |%DIFDELCMD < {\rm %%% rd (x)-x| \leq \delta which depend linearly on \epsilon and \delta. We then show that if the perturbation corresponds to\operatorname{rd} }\to rounding to the nearest point in some fixed discrete set , the bounds on the difference of moments can be improved to quadratic in many cases.
<meaning-changed> 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 | %DIFDELCMD < {\rm %%% rd (x)-x | \leq \epsilon |x| or |%DIFDELCMD < {\rm %%% rd (x)-x| \leq \delta which depend linearly on \epsilon and \delta. We then show that if the perturbation corresponds to\operatorname{rd} }\to rounding to the nearest point in some fixed discrete set , the bounds on the difference of moments can be improved to quadratic in many cases.
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 | %DIFDELCMD < {\rm %%% rd (x)-x | \leq \epsilon |x| or |%DIFDELCMD < {\rm %%% rd for non-negative integer k. We consider the case that the rounding function\operatorname{rd} }\to rounding to the nearest point in some fixed discrete set , the bounds on the difference of moments can be improved to quadratic in many cases.